Time-frequency analysis by a real-time differential spectral method for an application on sonar signal

The purpose of this paper is to present an algorithm (differential spectral analysis) for real‐time analysis of nonstationary or slightly nonstationary signals. The differential spectral analysis (DSA) gives the time derivative of Fourier complex coefficients, calculated by using a rectangular sliding window whose duration T is decided. The time evolution of these complex terms allows one to get a time‐frequency representation of the signal, i.e., the instantaneous amplitude, the phase, and the frequency. This method does not need an FFT calculation for each time window T. The small number of required operations makes this method useful for a real‐time analysis. The method is applied in oceanography for the acoustic exploration of particles. The DSA is a very fast and simple method for signal analysis, which can be very easily set to work, before using more complicated methods such as Hilbert and wavelet transforms.