Time-frequency signal representations for biomedical signals

The first purpose of this chapter is to review several TFRs defined in Table 4.1 and to describe many of the desirable properties listed in Table 4.2 that an ideal TFR should satisfy. TFRs will be grouped into classes satisfying similar properties to provide a more intuitive understanding of their similarities, 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 (1) satisfies other ideal TFR properties, (2) is easy to compute, and (3) reduces nonlinear cross-terms. The second goal of this chapter is to discuss applications of TFRs to signal analysis and detection problems in bioengineering. Unfortunately, none of the current TFRs is ideal; some give erroneous information when the signal’s spectra are rapidly time-varying. Researchers often analyze several TFRs side by side, keeping in mind the relative strengths and weaknesses of each TFR before drawing any conclusions