{"id":16676,"date":"2026-09-18T03:45:28","date_gmt":"2026-09-18T03:45:28","guid":{"rendered":"https:\/\/sistc.com\/?p=16676"},"modified":"2026-09-18T04:40:11","modified_gmt":"2026-09-18T04:40:11","slug":"fft-stft-audio-signal-processing","status":"publish","type":"post","link":"https:\/\/sistc.com\/zh\/fft-stft-audio-signal-processing\/","title":{"rendered":"\u97f3\u9891\u4fe1\u53f7\u5904\u7406\u4e2d\u7684FFT\u4e0eSTFT\uff1a\u5b9e\u7528\u5de5\u7a0b\u6307\u5357"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Audio signals contain information in both <strong>time and frequency<\/strong>. Understanding how this information is represented is fundamental to modern audio engineering, from <a href=\"https:\/\/sistc.com\/product-category\/sensor-module\/\">MEMS microphone systems <\/a>and speech enhancement to noise reduction, beamforming, and AI-based audio processing.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Two of the most important tools for analyzing audio signals are the <a href=\"https:\/\/sistc.com\/product-category\/sensor-module\/arrays-microphone-module\/smart-conferencing\/\"><strong>Fast Fourier Transform (FFT)<\/strong> and the <strong>Short-Time Fourier Transform (STFT)<\/strong>.<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">FFT provides an efficient way to analyze the frequency content of a digital signal, while STFT extends this concept to show how the frequency content changes over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This guide explains the difference between DFT, FFT, and STFT, how they work, and why they are widely used in practical audio signal processing systems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What Is the Fourier Transform in Audio Processing?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">An audio waveform in the time domain shows how sound pressure or microphone output changes over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, a microphone recording can be represented as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>x(t)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where <em>t<\/em> represents time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, a time-domain waveform does not directly tell us which frequencies are present.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Fourier Transform provides another representation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>time domain \u2192 frequency domain<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Instead of asking:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">How does the signal change over time?<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">we can ask:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">What frequency components are contained in the signal?<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">This is particularly useful because many characteristics of speech, music, mechanical noise, and environmental noise are easier to identify in the frequency domain.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>low-frequency noise may appear as strong energy below a certain frequency;<\/li>\n\n\n\n<li>fan noise may contain relatively stable spectral components;<\/li>\n\n\n\n<li>speech contains characteristic harmonic and formant structures;<\/li>\n\n\n\n<li>tonal interference can appear as narrow peaks in the spectrum.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This frequency-domain information forms the foundation for many audio processing algorithms.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">DFT: The Foundation of Frequency Analysis<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>Discrete Fourier Transform (DFT)<\/strong> converts a finite sequence of discrete samples into a representation of its frequency components.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For a sequence of N samples, the DFT is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>X[k] = \u03a3 x[n]e^(-j2\u03c0kn\/N)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>x[n]<\/strong> is the input signal<\/li>\n\n\n\n<li><strong>X[k]<\/strong> is the complex frequency-domain representation<\/li>\n\n\n\n<li><strong>N<\/strong> is the number of samples<\/li>\n\n\n\n<li><strong>n<\/strong> is the time-domain sample index<\/li>\n\n\n\n<li><strong>k<\/strong> is the frequency-bin index<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The output contains both magnitude and phase information.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The magnitude can be calculated as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>|X[k]|<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and the phase as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u2220X[k]<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In practical audio systems, engineers frequently analyze the magnitude spectrum because it provides an intuitive view of where signal energy is concentrated.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">What Is FFT?<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>Fast Fourier Transform (FFT)<\/strong> is not a different mathematical transform from the DFT.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Instead, FFT refers to a family of algorithms that calculate the DFT much more efficiently.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A direct DFT implementation has computational complexity approximately proportional to:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>O(N\u00b2)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An FFT algorithm can reduce this to approximately:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>O(N log N)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">for common FFT structures.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This difference becomes significant when processing large numbers of audio samples or when FFT calculations must be repeated continuously in real time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, an audio DSP may calculate an FFT for every incoming frame.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using an efficient FFT implementation makes it practical to perform operations such as:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>spectral analysis<\/li>\n\n\n\n<li>noise estimation<\/li>\n\n\n\n<li>equalization<\/li>\n\n\n\n<li>filtering<\/li>\n\n\n\n<li>speech enhancement<\/li>\n\n\n\n<li>acoustic measurement<\/li>\n\n\n\n<li>feature extraction<\/li>\n\n\n\n<li>beamforming-related processing<\/li>\n\n\n\n<li>AI preprocessing<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Why Is FFT Important in Audio Processing?<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The FFT is widely used because many audio-processing problems are easier to solve or understand in the frequency domain.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A simplified processing chain can be:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Microphone \u2192 ADC \u2192 Audio Frame \u2192 FFT \u2192 Frequency Analysis \u2192 Processing \u2192 IFFT \u2192 Output<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Depending on the application, the frequency-domain processing stage may perform:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>noise suppression<\/li>\n\n\n\n<li>spectral filtering<\/li>\n\n\n\n<li>gain adjustment<\/li>\n\n\n\n<li>frequency-domain masking<\/li>\n\n\n\n<li>signal measurement<\/li>\n\n\n\n<li>feature extraction<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For example, a simple noise reduction system can estimate the background-noise spectrum and reduce the gain of frequency components dominated by noise.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This concept is used in classical algorithms such as spectral subtraction and Wiener filtering.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">FFT Frequency Resolution<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">One of the most important concepts when using an FFT is <strong>frequency resolution<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For a sampling rate of <strong>Fs<\/strong> and an FFT size of <strong>N<\/strong>, the frequency-bin spacing is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0394f = Fs \/ N<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, suppose:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>sampling rate = 16 kHz<\/li>\n\n\n\n<li>FFT size = 512<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0394f = 16000 \/ 512 = 31.25 Hz<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each FFT bin therefore represents approximately 31.25 Hz of frequency spacing.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Increasing the FFT size improves frequency resolution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Sampling Rate<\/th><th>FFT Size<\/th><th>Frequency Resolution<\/th><\/tr><\/thead><tbody><tr><td>16 kHz<\/td><td>256<\/td><td>62.5 Hz<\/td><\/tr><tr><td>16 kHz<\/td><td>512<\/td><td>31.25 Hz<\/td><\/tr><tr><td>16 kHz<\/td><td>1024<\/td><td>15.625 Hz<\/td><\/tr><tr><td>48 kHz<\/td><td>1024<\/td><td>46.875 Hz<\/td><\/tr><tr><td>48 kHz<\/td><td>2048<\/td><td>23.4375 Hz<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">However, a larger FFT is not automatically better.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A larger FFT also means a longer analysis window, which affects temporal resolution and processing latency.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This creates an important engineering trade-off:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Frequency resolution vs. time resolution vs. latency<\/strong><\/p>\n<\/blockquote>\n\n\n\n<h1 class=\"wp-block-heading\">FFT Size and Audio Processing Latency<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">In real-time audio systems, the choice of FFT size affects more than frequency resolution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For a sampling rate <strong>Fs<\/strong> and frame length <strong>N<\/strong>, the duration represented by one frame is approximately:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>T = N \/ Fs<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, with a 16 kHz sampling rate:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>256 samples = 16 ms<\/li>\n\n\n\n<li>512 samples = 32 ms<\/li>\n\n\n\n<li>1024 samples = 64 ms<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">A larger frame provides more frequency information but also increases the time span being analyzed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This can increase algorithmic latency depending on the complete processing architecture.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For voice communication, conferencing, interactive audio, and embedded systems, latency can be as important as spectral resolution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, FFT size should be selected according to the actual application rather than simply maximizing N.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">What Is STFT?<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>Short-Time Fourier Transform (STFT)<\/strong> applies Fourier analysis to short segments of an audio signal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is important because real-world audio signals are usually <strong>non-stationary<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Speech, for example, changes continuously.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A single FFT over an entire recording could tell us which frequencies occur somewhere in the recording, but it would not tell us precisely <strong>when<\/strong> those frequencies occur.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">STFT addresses this by dividing the signal into short, usually overlapping frames.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The basic process is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Audio signal<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Frame segmentation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Windowing<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>FFT for each frame<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Time-frequency representation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A simplified STFT equation is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>STFT{x}(m, k) = \u03a3 x[n]w[n \u2212 mH]e^(-j2\u03c0kn\/N)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>x[n]<\/strong> is the audio signal<\/li>\n\n\n\n<li><strong>w[n]<\/strong> is the analysis window<\/li>\n\n\n\n<li><strong>m<\/strong> represents the frame position<\/li>\n\n\n\n<li><strong>H<\/strong> is the hop size<\/li>\n\n\n\n<li><strong>k<\/strong> represents the frequency bin<\/li>\n\n\n\n<li><strong>N<\/strong> is the FFT size<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The result contains information about both <strong>time and frequency<\/strong>.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Why STFT Is Better Suited to Speech and Environmental Audio<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Consider a short voice recording.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At one moment, the speaker may produce a vowel with strong harmonic energy.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A few milliseconds later, the speaker may produce a consonant containing much broader high-frequency energy.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At the same time, a background fan or air-conditioning system may produce relatively stable low-frequency or tonal components.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A single FFT cannot clearly show this evolution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">STFT produces a time-frequency representation, often visualized as a <strong>spectrogram<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A spectrogram can show:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>horizontal axis \u2192 time<\/li>\n\n\n\n<li>vertical axis \u2192 frequency<\/li>\n\n\n\n<li>intensity \u2192 signal magnitude or power<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This makes STFT particularly useful for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>speech analysis<\/li>\n\n\n\n<li>speech enhancement<\/li>\n\n\n\n<li>noise analysis<\/li>\n\n\n\n<li>voice activity detection<\/li>\n\n\n\n<li>audio classification<\/li>\n\n\n\n<li>acoustic event detection<\/li>\n\n\n\n<li>music analysis<\/li>\n\n\n\n<li>machine listening<\/li>\n\n\n\n<li>AI audio processing<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Windowing: Why It Is Necessary<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Before applying an FFT to each STFT frame, engineers normally apply a window function.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common windows include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Hann window<\/li>\n\n\n\n<li>Hamming window<\/li>\n\n\n\n<li>Blackman window<\/li>\n\n\n\n<li>Rectangular window<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The purpose of windowing is to reduce <strong>spectral leakage<\/strong> caused by analyzing a finite segment of a signal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Without windowing, a frequency component that does not align perfectly with an FFT bin can spread its energy across neighboring bins.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The choice of window affects:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>main-lobe width<\/li>\n\n\n\n<li>side-lobe level<\/li>\n\n\n\n<li>amplitude accuracy<\/li>\n\n\n\n<li>frequency discrimination<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The Hann window is commonly used in practical audio applications because it provides a useful balance between spectral leakage and frequency resolution.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Spectral Leakage Explained<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose a sinusoidal signal has a frequency that does not correspond exactly to an FFT bin.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An ideal expectation might be:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">one frequency \u2192 one FFT peak<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">In practice, the energy spreads into neighboring frequency bins.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is called <strong>spectral leakage<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Windowing can reduce this leakage, although no window eliminates all trade-offs.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is why FFT results should not be interpreted without considering:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>sampling rate<\/li>\n\n\n\n<li>FFT size<\/li>\n\n\n\n<li>window type<\/li>\n\n\n\n<li>window length<\/li>\n\n\n\n<li>signal frequency<\/li>\n\n\n\n<li>overlap<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">These parameters all influence the resulting spectrum.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Overlap and Hop Size in STFT<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">STFT frames are commonly overlapped.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, a system might use:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>20\u201332 ms frame length<\/li>\n\n\n\n<li>50% overlap<\/li>\n\n\n\n<li>75% overlap<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>hop size<\/strong> determines how far the analysis window moves between successive frames.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>N = frame length<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>H = hop size<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">then the overlap ratio is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Overlap = 1 \u2212 H\/N<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, if:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>N = 512<\/li>\n\n\n\n<li>H = 128<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">then:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Overlap = 75%<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Higher overlap provides more frequent updates and smoother time-frequency tracking, but it also increases the number of FFT operations and therefore computational requirements.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">STFT and Noise Reduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">STFT is particularly important in <a href=\"https:\/\/sistc.com\/audio-noise-reduction-guide\/\">audio noise reduction<\/a> because it converts the problem into a series of time-frequency processing operations.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A typical STFT-based noise reduction system looks like this:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Noisy audio<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Framing<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Windowing<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>FFT<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Noise estimation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Gain calculation \/ spectral mask<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Frequency-domain processing<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Inverse FFT<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Overlap-add<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Enhanced audio<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This architecture is used in many traditional speech-enhancement systems.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, spectral subtraction can estimate the noise spectrum and attenuate frequency components associated with background noise.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wiener filtering can calculate a frequency-dependent gain based on estimated signal and noise power.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">STFT and <a href=\"https:\/\/sistc.com\/spectral-subtraction-audio-noise-reduction\/\" target=\"_blank\" rel=\"noreferrer noopener\">Spectral Subtraction<\/a><\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Spectral subtraction is a good example of why STFT is useful.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Y(f) = X(f) + N(f)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>X(f) = desired signal<\/li>\n\n\n\n<li>N(f) = noise<\/li>\n\n\n\n<li>Y(f) = observed signal<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">If the system can estimate the noise spectrum, it can attempt to recover the desired signal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In a simplified power-spectrum implementation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>P\u0302x(f) = max[Py(f) \u2212 \u03b1Pn(f), Pmin(f)]<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Py(f)<\/strong> = noisy-signal power spectrum<\/li>\n\n\n\n<li><strong>Pn(f)<\/strong> = estimated noise power spectrum<\/li>\n\n\n\n<li><strong>\u03b1<\/strong> = oversubtraction factor<\/li>\n\n\n\n<li><strong>Pmin(f)<\/strong> = spectral floor<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Because the speech and noise characteristics change over time, this operation is normally performed frame by frame.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That is where STFT becomes extremely useful.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">STFT and AI-Based Speech Enhancement<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">STFT is also widely used as a feature representation for AI-based audio processing.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A neural network can receive:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Noisy waveform<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 <strong>STFT<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 <strong>Magnitude \/ complex spectrum<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 <strong>Neural network<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 <strong>Enhanced spectrum<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 <strong>ISTFT<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 <strong>Enhanced waveform<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Depending on the model, the network may estimate:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>clean magnitude spectrum<\/li>\n\n\n\n<li>ideal ratio mask<\/li>\n\n\n\n<li>complex spectrum<\/li>\n\n\n\n<li>noise spectrum<\/li>\n\n\n\n<li>time-frequency mask<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This approach is common in speech enhancement and audio denoising research and engineering.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, modern neural networks can also operate directly on waveforms, so STFT is not mandatory for every AI audio system.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The choice depends on the model architecture, computational requirements, latency, and target application.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">FFT vs STFT: What Is the Difference?<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The simplest distinction is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>FFT analyzes frequency content efficiently. STFT analyzes how frequency content changes over time.<\/strong><\/p>\n<\/blockquote>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Feature<\/th><th>FFT<\/th><th>STFT<\/th><\/tr><\/thead><tbody><tr><td>Main purpose<\/td><td>Frequency analysis<\/td><td>Time-frequency analysis<\/td><\/tr><tr><td>Time information<\/td><td>Limited for one FFT<\/td><td>Preserved across frames<\/td><\/tr><tr><td>Processing<\/td><td>One signal segment<\/td><td>Multiple overlapping segments<\/td><\/tr><tr><td>Typical output<\/td><td>Spectrum<\/td><td>Spectrogram \/ time-frequency matrix<\/td><\/tr><tr><td>Computational load<\/td><td>Lower for one transform<\/td><td>Higher because many FFTs are performed<\/td><\/tr><tr><td>Common applications<\/td><td>Spectrum analysis, filtering<\/td><td>Speech, noise reduction, transient analysis<\/td><\/tr><tr><td>Key parameters<\/td><td>FFT size, sampling rate<\/td><td>FFT size, window, hop size, overlap<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">It is therefore more accurate to think of STFT as a <strong>framework that repeatedly applies Fourier analysis to short sections of a signal<\/strong>, rather than as a completely unrelated transform.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">FFT vs STFT: Which One Should You Use?<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The answer depends on the application.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Use FFT when you need:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>frequency spectrum measurement<\/li>\n\n\n\n<li>harmonic analysis<\/li>\n\n\n\n<li>frequency response analysis<\/li>\n\n\n\n<li>stationary signal analysis<\/li>\n\n\n\n<li>spectral monitoring<\/li>\n\n\n\n<li>simple frequency-domain processing<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Use STFT when you need:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>speech analysis<\/li>\n\n\n\n<li>changing noise analysis<\/li>\n\n\n\n<li>transient detection<\/li>\n\n\n\n<li>time-frequency visualization<\/li>\n\n\n\n<li>speech enhancement<\/li>\n\n\n\n<li>spectral noise reduction<\/li>\n\n\n\n<li>continuously changing audio analysis<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For most practical speech and environmental audio systems, STFT is often more informative because the acoustic signal changes over time.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Practical Example: Analyzing a Microphone Signal<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Consider a MEMS microphone recording a person speaking in a room with an air-conditioning system running in the background.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The microphone captures:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Speech + HVAC noise + room noise + microphone\/electronic noise<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A raw waveform may not make it immediately obvious which components belong to speech and which belong to the background.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An FFT can reveal the overall frequency distribution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An STFT can go further by showing:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>when the person is speaking<\/li>\n\n\n\n<li>which frequency bands contain speech energy<\/li>\n\n\n\n<li>whether the HVAC noise is relatively stable<\/li>\n\n\n\n<li>where transient noises occur<\/li>\n\n\n\n<li>how the spectrum changes between speech and silence<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This information can then be used by downstream processing such as:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>noise estimation<\/li>\n\n\n\n<li>voice activity detection<\/li>\n\n\n\n<li>spectral filtering<\/li>\n\n\n\n<li>beamforming<\/li>\n\n\n\n<li>speech enhancement<\/li>\n\n\n\n<li>AI-based noise suppression<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\"><a href=\"https:\/\/sistc.com\/product-category\/sensor-module\/arrays-microphone-module\/\">FFT and STFT in Microphone Array Systems<\/a><\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">FFT and STFT become even more useful when multiple microphones are involved.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A microphone array may contain several synchronized MEMS microphones.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each channel produces an audio stream:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mic 1 \u2192 x\u2081(t)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mic 2 \u2192 x\u2082(t)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mic 3 \u2192 x\u2083(t)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mic 4 \u2192 x\u2084(t)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and so on.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The signals can be transformed into the frequency domain and processed jointly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This enables techniques such as:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>frequency-domain beamforming<\/li>\n\n\n\n<li>spatial filtering<\/li>\n\n\n\n<li>direction-of-arrival estimation<\/li>\n\n\n\n<li>multi-channel noise reduction<\/li>\n\n\n\n<li>post-filtering<\/li>\n\n\n\n<li>acoustic source separation<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The relative phase and amplitude information between microphone channels becomes important.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is one reason why <strong>accurate synchronization and consistent microphone characteristics<\/strong> are important in microphone array design.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">FFT, STFT and Beamforming<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">In a frequency-domain beamforming system, the processing chain can be simplified as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Multiple MEMS microphones<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Synchronized audio channels<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>STFT<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Spatial filtering \/ beamforming<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Post-filtering<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Inverse STFT<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Enhanced audio<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The system can use differences in the arrival time and phase of sound between microphones to emphasize a target direction and reduce unwanted spatial components.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This connects FFT\/STFT directly to practical microphone array technologies.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Choosing FFT Parameters for Real-Time Audio<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">There is no universal FFT configuration.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Engineers normally consider several parameters together.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Sampling Rate<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Higher sampling rates provide a wider usable frequency range but increase data and processing requirements.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common speech\/audio processing rates include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>16 kHz<\/li>\n\n\n\n<li>24 kHz<\/li>\n\n\n\n<li>32 kHz<\/li>\n\n\n\n<li>44.1 kHz<\/li>\n\n\n\n<li>48 kHz<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The appropriate rate depends on the application and target frequency range.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">FFT Size<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Larger FFT sizes provide finer frequency spacing:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0394f = Fs\/N<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">but increase the analysis window length and computational workload.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Frame Length<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Frame length determines how much audio is analyzed at one time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Short frames provide better temporal resolution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Longer frames provide better frequency resolution.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Hop Size<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A smaller hop size means more frequent processing updates.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This can improve temporal tracking but increases computational load.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Window Function<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The window affects spectral leakage and frequency discrimination.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Hann window is a common starting point, but the optimal choice depends on the measurement or processing objective.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">A Practical STFT Configuration for Speech<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">As an engineering starting point, a speech-processing system might use:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sampling rate: <strong>16 kHz<\/strong><\/li>\n\n\n\n<li>Frame length: <strong>20\u201332 ms<\/strong><\/li>\n\n\n\n<li>FFT size: <strong>512<\/strong><\/li>\n\n\n\n<li>Window: <strong>Hann<\/strong><\/li>\n\n\n\n<li>Overlap: <strong>50\u201375%<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">These are examples rather than universal specifications.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The optimum parameters should be validated against:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>target latency<\/li>\n\n\n\n<li>speech quality<\/li>\n\n\n\n<li>noise characteristics<\/li>\n\n\n\n<li>processor capability<\/li>\n\n\n\n<li>memory requirements<\/li>\n\n\n\n<li>algorithm design<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For embedded systems, parameter selection should always be evaluated together with the complete processing chain.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Common FFT and STFT Mistakes<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Mistake 1: Assuming a Larger FFT Is Always Better<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A larger FFT improves frequency-bin spacing but can reduce temporal resolution and increase latency.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Mistake 2: Ignoring Windowing<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Applying FFT directly to a finite signal segment can produce significant spectral leakage.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Mistake 3: Confusing FFT Size With Frequency Resolution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Frequency resolution depends on both sampling rate and FFT size:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0394f = Fs\/N<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Increasing the sampling rate while keeping N unchanged actually increases the frequency-bin spacing.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Mistake 4: Ignoring Phase<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Magnitude spectra are useful, but phase information can also be important, particularly for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>multi-microphone processing<\/li>\n\n\n\n<li>beamforming<\/li>\n\n\n\n<li>signal reconstruction<\/li>\n\n\n\n<li>complex spectral enhancement<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Mistake 5: Treating STFT as a Zero-Latency Operation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Real-time STFT processing introduces frame-based buffering and processing delay.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The complete system latency depends on:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>frame length<\/li>\n\n\n\n<li>hop size<\/li>\n\n\n\n<li>buffering<\/li>\n\n\n\n<li>FFT\/IFFT processing<\/li>\n\n\n\n<li>algorithmic look-ahead<\/li>\n\n\n\n<li>hardware\/software implementation<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">Python Example: FFT of an Audio Signal<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A simple FFT workflow can be implemented with Python libraries such as NumPy and SciPy.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import numpy as np\nfrom scipy.io import wavfile\n\nfs, audio = wavfile.read(\"audio.wav\")\n\n# Use one channel if the recording is stereo\nif audio.ndim &gt; 1:\n    audio = audio&#91;:, 0]\n\nN = len(audio)\n\nspectrum = np.fft.rfft(audio)\nfrequencies = np.fft.rfftfreq(N, d=1\/fs)\n\nmagnitude = np.abs(spectrum)\n\nprint(\"Sampling rate:\", fs)\nprint(\"Number of samples:\", N)\nprint(\"Frequency resolution:\", fs \/ N)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">This example calculates the one-sided FFT spectrum of an audio recording.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For real-time audio processing, engineers normally process shorter frames rather than calculating one FFT over the entire recording.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Python Example: STFT<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">SciPy provides an STFT implementation that can be used for time-frequency analysis.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import numpy as np\nfrom scipy.io import wavfile\nfrom scipy.signal import stft\n\nfs, audio = wavfile.read(\"audio.wav\")\n\nif audio.ndim &gt; 1:\n    audio = audio&#91;:, 0]\n\nfrequencies, times, Zxx = stft(\n    audio,\n    fs=fs,\n    window=\"hann\",\n    nperseg=512,\n    noverlap=256\n)\n\nmagnitude = np.abs(Zxx)\n\nprint(\"Frequency bins:\", len(frequencies))\nprint(\"Time frames:\", len(times))<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">The resulting matrix contains the complex STFT representation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Its magnitude can be visualized as a spectrogram to observe how the audio spectrum changes over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">SciPy&#8217;s signal-processing documentation provides further implementation details for STFT and related signal-processing functions.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">From FFT and STFT to Modern Audio Intelligence<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">FFT and STFT are not simply academic signal-processing concepts.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">They remain important building blocks in practical audio systems.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A modern audio-processing pipeline may look like:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/sistc.com\/product-category\/mems-sensors\/mems-microphone\/\">MEMS Microphone<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analog \/ Digital Front End<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Audio Sampling<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Framing<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>FFT \/ STFT<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Noise Estimation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Beamforming<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>DSP Noise Reduction<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>AI Speech Enhancement<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2193<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Voice Recognition \/ Communication \/ Audio Output<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This architecture illustrates an important point:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Good audio intelligence begins with good signal representation.<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">The microphone provides the acoustic information, while DSP and AI algorithms determine how that information is analyzed and enhanced.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Conclusion<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">FFT and STFT are fundamental tools in digital audio signal processing.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The FFT provides an efficient way to calculate the frequency-domain representation of a sampled signal. It is widely used for spectrum analysis, filtering, feature extraction, and real-time DSP.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">STFT extends this approach by analyzing short, overlapping sections of the signal, making it possible to observe how frequency content changes over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For speech, environmental sound, and noise reduction, this time-frequency representation is particularly valuable.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In practical microphone systems, FFT and STFT can form part of a larger processing architecture involving <strong>noise estimation, spectral filtering, beamforming, microphone arrays, and AI-based speech enhancement<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The key engineering challenge is not simply choosing the largest FFT or the most sophisticated algorithm. It is selecting the appropriate combination of <strong>sampling rate, frame length, FFT size, window, overlap, latency, and processing architecture<\/strong> for the target application.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For developers working with MEMS microphones and multi-microphone systems, understanding FFT and STFT provides an essential foundation for designing more effective audio acquisition and noise reduction systems.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Frequently Asked Questions<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">What is FFT in audio processing?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">FFT is an efficient algorithm for calculating the Discrete Fourier Transform. It converts sampled audio from the time domain into a frequency-domain representation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What is STFT in audio processing?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">STFT applies Fourier analysis to short, usually overlapping sections of an audio signal. It provides information about how the frequency content changes over time.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What is the difference between FFT and STFT?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">FFT provides frequency information for a signal segment, while STFT repeatedly performs Fourier analysis on short segments to create a time-frequency representation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Why is STFT used for speech processing?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Speech is non-stationary and its frequency content changes continuously. STFT captures these changes and is therefore useful for speech enhancement, noise reduction, and speech analysis.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Does a larger FFT size improve audio quality?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Not necessarily. A larger FFT improves frequency-bin spacing but can increase processing time, computational requirements, and latency. The appropriate FFT size depends on the application.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What is FFT frequency resolution?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">FFT frequency-bin spacing is approximately:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0394f = Fs\/N<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where Fs is the sampling rate and N is the FFT size.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What window should be used for STFT?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The Hann window is a common choice for general audio analysis and processing, but the best window depends on the specific application and measurement requirements.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Is STFT necessary for AI noise reduction?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">No. Many AI models use STFT features or time-frequency representations, but some modern models process raw audio waveforms directly. The appropriate architecture depends on the model and application.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Can FFT and STFT be used with microphone arrays?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. FFT and STFT are widely used in multi-microphone processing, including frequency-domain beamforming, spatial filtering, noise reduction, and acoustic source analysis.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><\/p>\n<\/blockquote>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Audio signals contain information in both time and frequency. Understanding how this information is represented is fundamental to modern audio engineering, from MEMS microphone systems and speech enhancement to noise [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_joinchat":[],"footnotes":""},"categories":[103],"tags":[],"class_list":["post-16676","post","type-post","status-publish","format-standard","hentry","category-technical-blog"],"_links":{"self":[{"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/posts\/16676","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/comments?post=16676"}],"version-history":[{"count":5,"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/posts\/16676\/revisions"}],"predecessor-version":[{"id":16687,"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/posts\/16676\/revisions\/16687"}],"wp:attachment":[{"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/media?parent=16676"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/categories?post=16676"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sistc.com\/zh\/wp-json\/wp\/v2\/tags?post=16676"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}