ABSTRACT
This chapter discusses the applications of time–frequency signal representations (TFR) to signal analysis and detection problems in bioengineering. It reviews some of the TFRs commonly used in biomedical analysis and summarize their relative advantages and disadvantages. Further, each TFR within a given class is completely characterized by a unique set of kernels that provide valuable insight into whether or not a given TFR, satisfies other ideal TFR properties, is easy to compute, and reduces nonlinear cross-terms. One of the most commonly used TFRs for slowly time-varying or quasi-stationary signals is the spectrogram. Cohen’s class consists of all quadratic TFRs that satisfy the frequency-shift and time-shift covariance properties. The Hyperbolic class of TFRs consists of all TFRs that are covariant to scale changes and hyperbolic time shifts. Mixed TFRs map a one-dimensional signal into a two-dimensional function of time and frequency in order to analyze the time-varying spectral content of the signal.
