Efficient STFT approximation using a quantization and differencing method

A class of algorithms for efficiently computing approximations to the short-time Fourier transform (STFT) of any given signal is introduced. These algorithms may be classified in accordance with the number of quantization levels they use to represent the values in each short-time frame of the input signal. The structure and properties of these algorithms are illustrated through a specific case which uses a three-level quantization in each frame. Results obtained by applying an implementation of the three-level algorithm to musical and speech signals are also presented. The resulting approximations conform to the theoretical expectations of a 9-dB SNR in the STFT approximations. However, these approximations are found to require an order-of-magnitude-less computation than fast Fourier transform (FFT)-based algorithms for the exact STFT.<>