The STFT slides a Fourier analysis window along a signal to create a time-frequency spectrogram

The DFT of a whole signal gives a single spectrum for the entire duration, losing time information. The Short-Time Fourier Transform (STFT) instead takes successive Fourier transforms of windowed segments, producing a sequence of spectra: the spectrogram. The choice of window function shapes the trade-off between time resolution and frequency resolution. Windows are overlapped and combined using overlap-add reconstruction. The fundamental frequency resolution of a frame equals the sample rate divided by the FFT size. Spectrograms underlie most analysis, effects, and feature extraction in computer music. The STFT is the engine behind the phase vocoder, which is used for time-stretching and pitch-shifting.

Examples

An FFT size of 1024 at 44,100 Hz gives a frequency resolution of approximately 43 Hz per bin and 23 ms per frame. Spectral stretching and vocoder effects exploit the STFT analysis-synthesis cycle.

Assessment

Given a 44,100 Hz sample rate and a 2048-point FFT with 50% overlap, what is the frequency resolution per bin and approximately how many frames per second are produced?