Time-frequency synthesis and filtering

Abstract

This chapter presents methods and techniques to design time-varying linear systems such as filters with precise time-frequency (t,f) specifications; this capability can then allow one to model and predict accurately the effects of linear systems on nonstationary signals in applications such as signal cleansing and enhancement. This topic is covered in six sections. The design of time-varying filters is required in applications where it is desired to separate, suppress, or reduce undesirable nonstationary signal components. This can be performed with piece-wise harmonic decomposition methods such as the short-time Fourier transform (STFT) and the Gabor transform (Section 11.1). In particular, the use of the Gabor expansion for time-varying filtering is illustrated on an application that involves monitoring machine vibrations; in addition, an alternative method, the inverse STFT is applied to (t,f) filtering with an illustration on a speech signal (Section 11.2). Another illustration of the procedure for designing a time-varying filter is provided in the context of an application involving handsfree telephone speech signals (Section 11.3). Another important application of time-varying filtering procedure, namely signal enhancement, is described using an iterative algorithm based on time-frequency peak filtering (Section 11.4). Then, a method for subspace noise filtering using a time-frequency distribution is described (Section 11.5); and finally a comparison of denoising algorithms for speech enhancement completes the chapter (Section 11.6).