tailieunhanh - Digital Signal Processing Handbook P37

Time-frequency representations (TFR) combine the time-domain and frequency-domain representations into a single framework to obtain the notion of time-frequency. TFR offer the time localization vs. frequency localization tradeoff between two extreme cases of time-domain and frequency-domain representations. The short-time Fourier transform (STFT) [1, 2, 3, 4, 5] and the Gabor transform [6] are the classical examples of linear time-frequency transforms which use time-shifted and | Iraj Sodagar. Time-Varying Analysis-Synthesis Filter Banks 2000 CRC Press LLC. http . Time-Varying Analysis-Synthesis Filter Banks Iraj Sodagar Davi cSarnoffResearclCenter Introduction Analysis of Time-Varying Filter Banks Direct Switching of Filter Banks Time-Varying Filter Bank Design Techniques Approach I Intermediate Analysis-Synthesis IAS Approach II Instantaneous Transform Switching ITS Conclusion References Introduction Time-frequency representations TFR combine the time-domain and frequency-domain representations into a single framework to obtain the notion of time-frequency. TFR offer the time localization vs. frequency localization tradeoff between two extreme cases of time-domain and frequency-domain representations. The short-time Fourier transform STFT 1 2 3 4 5 and the Gabor transform 6 are the classical examples of linear time-frequency transforms which use time-shifted and frequency-shifted basis functions. In conventional time-frequency transforms the underlying basis functions are fixed in time and define a specific tiling of the time-frequency plane. The term time-frequency tile of a particular basis function is meant to designate the region in the plane that contains most of that function s energy. The short-time Fourier transform and the wavelet transform are just two of many possible tilings of the time-frequency plane. These two are illustrated in Fig. a and b respectively. In these figures the rectangular representation for a tile is purely symbolic since no function can have compact support in both time and frequency. Other arbitrary tilings of the time-frequency plane are possible such as the example shown in Fig. c . In the discrete domain linear time-frequency transforms can be implemented in the form of filter bank structures. It is well known that the time-frequency energy distribution of signals often changes with time. Thus in this sense the conventional linear time-frequency