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... noise is reduced. This, in effect, corresponds to time smoothing of the short-time spectral magnitude. The neighborhood smoothing can be carried out using either linear smoothing or median smoothing =-=[26]-=- techniques. Multi-Window Smoothing This technique capitalizes on the flexibility in the choice of the analysis window. In its most general form, the idea is to obtain signal estimates using different...

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...ne dimensional signals, the entire discussion in this section is also applicable to multidimensional signals [24]. A number of classical techniques exist for filtering stationary stochastic processes =-=[23]-=-. In particular, a problem that has been widely considered is that of filtering additive stationary noise from stationary stochastic processes. This has resulted in the well-known non-causal Wiener fi...

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...h a transformation in the quantization noise associated with PCM signal coding. In the problem of noise filtering of speech or image data, it is often preferable to use short-time spectral processing =-=[6,22]-=-. This is primarily because long-time filtering tends to smooth out local variations that are often important attributes of the signal. In contrast, shorttime spectral processing attempts to preserve ...

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...ue based on such vocoders would suffer the same kind of pitch detection artifacts as those found in pitch-synchronous refinements of the Fairbanks approach. One exception to this is the Phase Vocoder =-=[14,2,19,20]-=-. This vocoder uses the short-time spectrum (both magnitude and phase) for representing the speech signal. Furthermore, it does not require voiced/unvoiced decisions or any pitch extraction procedures...

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...rum The short-time spectrum has been developed for continuous as well as discrete-time signals. Excellent references on the subject include the work of C. Weinstein [3], J. Allen [4], and M. Portnoff =-=[5]-=-. In this thesis, we are interested in discrete-time signal processing with the shorttime spectrum. For a discrete-time signal x(n), the short-time spectrum is a function of time as well as frequency ...

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...ue based on such vocoders would suffer the same kind of pitch detection artifacts as those found in pitch-synchronous refinements of the Fairbanks approach. One exception to this is the Phase Vocoder =-=[14,2,19,20]-=-. This vocoder uses the short-time spectrum (both magnitude and phase) for representing the speech signal. Furthermore, it does not require voiced/unvoiced decisions or any pitch extraction procedures...

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...proach first used in a technique known as Fairbank's method 13]. This approach and the various techniques based on it are described in section 6.2. An alternative approach, based on the Phase Vocoder =-=[14]-=-, was used by Portnoff [7] to develop a very successful time-scale modification technique. This approach, outlined in section 6.3, processes both the magnitude and the phase of the short-time spectrum...

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...s such as speech. The first formal definition of the short-time spectral magnitude was introduced by R. Fano [8] in his studies on speech analysis. Investigations by R. Fano, M. Schroeder and B. Atal =-=[9]-=-, and A. Kharkevich [10] were responsible for developing many aspects of short-time spectral analysis. - 10 - C. Weinstein [3] formally showed that continuous as well as discrete-time signals can be u...

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...tion [12]. Various strategies based on pitch detection have been designed to overcome the smooth transition problem in Fairbanks approach. These include the pitch-synchronous technique __ ____ - 65 - =-=[16,18]-=- and the pseudo-pitch-synchronous technique [17]. The pitch-synchronous technique chooses the short-time sections so that they correspond to multiples of the pitch period in voiced sections. This ensu...

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...y dividing out the analysis window from the various short-time sections. More recently, an alternative approach to unique signal representation with short-time spectral magnitude was used by R. Altes =-=[11]-=-. This approach places no restriction on the signal to be represented. However, the analysis window is required to satisfy a condition which in practice means that the analysis window has to be longer...

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...y the short-time spectral magnitude because it was physically easier to estimate for signals such as speech. The first formal definition of the short-time spectral magnitude was introduced by R. Fano =-=[8]-=- in his studies on speech analysis. Investigations by R. Fano, M. Schroeder and B. Atal [9], and A. Kharkevich [10] were responsible for developing many aspects of short-time spectral analysis. - 10 -...

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...ion have been designed to overcome the smooth transition problem in Fairbanks approach. These include the pitch-synchronous technique __ ____ - 65 - [16,18] and the pseudo-pitch-synchronous technique =-=[17]-=-. The pitch-synchronous technique chooses the short-time sections so that they correspond to multiples of the pitch period in voiced sections. This ensures a smoother transition between adjacent short...

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...tion [12]. Various strategies based on pitch detection have been designed to overcome the smooth transition problem in Fairbanks approach. These include the pitch-synchronous technique __ ____ - 65 - =-=[16,18]-=- and the pseudo-pitch-synchronous technique [17]. The pitch-synchronous technique chooses the short-time sections so that they correspond to multiples of the pitch period in voiced sections. This ensu...

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...rocessing of signals such as speech, spectral processing is often applied independently to various short-time sections of a signal. This type of processing is usually based on the short-time spectrum =-=[3]-=-. In section 1.1 of this chapter, we present the definition of the short-time spectrum for discrete-time signals. The magnitude and phase of the short-time spectrum of a signal are usually both requir...

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...his approach, outlined in section 6.3, processes both the magnitude and the phase of the short-time spectrum. The resulting time-scale modification is generally considered to be of acceptable quality =-=[7,15]-=- for many applications. However, from a practical point of view this technique has the major disadvantage of a complicated computational structure. The time-scale modification procedure developed in s...

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...h a transformation in the quantization noise associated with PCM signal coding. In the problem of noise filtering of speech or image data, it is often preferable to use short-time spectral processing =-=[6,22]-=-. This is primarily because long-time filtering tends to smooth out local variations that are often important attributes of the signal. In contrast, shorttime spectral processing attempts to preserve ...

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...astic process with known spectrum P, (w). Although for convenience we use the notation of one dimensional signals, the entire discussion in this section is also applicable to multidimensional signals =-=[24]-=-. A number of classical techniques exist for filtering stationary stochastic processes [23]. In particular, a problem that has been widely considered is that of filtering additive stationary noise fro...