Advanced implementation and realization of TFDs

Abstract

The design of efficient algorithms is the key to effective utilization of the properties of time-frequency distributions (TFDs) for real-life applications. This chapter presents the needed procedures, techniques, and methodologies for the effective implementation of such time-frequency (t,f) methods. This is an important chapter for those interested in practical implementations and it is the basis foundation of the (t,f) toolbox described in Chapter 17. The topic is covered in six sections with appropriate cross-referencing to the most relevant chapters. The discrete-time equivalent formulation of quadratic TFDs is first defined for the purpose of digital computation (Section 6.1). An alternative method for realization of quadratic TFDs uses the short-time Fourier transform as a basis (Section 6.2). The Gabor time-frequency representation may be expanded on a rectangular lattice, using the Fourier and Zak transforms for direct implementations (Section 6.3). The computation of other quadratic TFDs can also be done by using a spectrogram decomposition (Section 6.4). Finally, the computational procedure for implementing quadratic time-frequency methods directly is outlined, along with the required algorithms and MATLABtm code fragments (Section 6.5). The last section focuses on the design of memory-efficient algorithms to implement discrete-time TFDs to deal with the issues of memory limitations when processing large amount of data in applications such as biomedicine, telecommunications, or geophysics (Section 6.6).