Time-Frequency Analysis

The Fourier transform of a signal can provide only global frequency information. While a time-frequency distribution of a signal can provide information about how the frequency content of the signal evolves with time. This is performed by mapping a one-dimensional time domain signal into a two-dimensional time-frequency representation of the signal. A lot of techniques have been developed to extract local time-frequency information. In this chapter, we introduce basic concepts and theory in time-frequency analysis, including windowed Fourier transform, wavelet transform, multiresolution analysis, wavelet basis, Hilbert transform, instantaneous frequency, Wigner-Ville distribution, and empirical mode decomposition.