Скачать или смотреть [demo] 256 bin size FFT algo visualizer ( cooley tukey & bit reversal )

real-time audio spectrogram visualization implementing Cooley-Tukey FFT algorithm with synchronized playback using mp3 files. the system processes audio through overlapping 256-sample windows with 25% overlap, applying bit-reversal indexing and pre-computed twiddle factors for optimal frequency domain transformation. each frame extracts magnitude spectra from complex FFT outputs, creating a scrolling waterfall display that reveals the harmonic structure and temporal evolution of musical content as it plays.

the FFT implementation uses radix-2 decimation-in-time with N=256 samples, constraining frequency resolution to Δf = fs/N = 44100/256 ≈ 172.3 Hz per bin. this creates 128 usable frequency bins, where each bin represents the magnitude |X(k)| = √(Re²(k) + Im²(k)) of complex spectral components. the algorithm employs butterfly operations with twiddle factors W_N^k = e^(-j2πk/N), enabling O(N log N) computational complexity rather than the O(N²) of naive DFT approaches.

spectral magnitude processing involves logarithmic scaling to compress the dynamic range of audio signals, where raw magnitudes are transformed via log(magnitude + 1) × 20 to approximate human auditory perception. this prevents quiet spectral components from disappearing while avoiding saturation of dominant frequencies. the visualization maps these scaled values to a 16-color CGA palette, creating intensity gradients that highlight both fundamental frequencies and harmonic overtones across the entire audible spectrum.

windowing functions apply Hanning (raised cosine) weighting to each 256-sample frame, reducing spectral leakage artifacts that occur when analyzing non-periodic signals. mathematically, this involves multiplying samples by w(n) = 0.5 - 0.5cos(2πn/(N-1)), which tapers the signal smoothly to zero at frame boundaries. without windowing, sharp discontinuities at frame edges would create spurious high-frequency components that obscure the true spectral content of musical signals.

the scrolling spectrogram maintains a 1280×128 pixel history buffer, storing magnitude values for each frequency bin across time. new spectral data shifts the display leftward, creating a time-frequency representation where horizontal position indicates time, vertical position represents frequency, and color intensity shows spectral magnitude. this creates a visual analogue to traditional sonogram analysis used in acoustics and speech processing, revealing patterns like vibrato, formant transitions, and percussive attacks.

frequency bin mapping employs linear scaling across the vertical display axis, though this doesn't match human pitch perception which follows logarithmic (mel or bark) scales. lower frequencies appear compressed while higher frequencies are stretched, meaning bass notes occupy fewer pixels than treble content. this limitation could be addressed through non-linear bin remapping, but the current implementation prioritizes computational efficiency over perceptual accuracy.

the visualization demonstrates aliasing and quantization artifacts. sharp percussion hits create broadband spectral splashes, while sustained tones produce narrow vertical lines corresponding to their fundamental and harmonic frequencies. the system effectively transforms temporal audio waveforms into frequency-domain representations, revealing the underlying physics of sound waves through real-time mathematical analysis of their spectral characteristics.

मात्रात्मक रूप से - 多次元 - 라디오콘트라스트

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