Filter-bank analysis

We will now turn to the important problem of source-filter separation. In general, we wish to do this because the two components of the speech signal have quite different and independent linguistic ftmctions. The source controls the pitch, which is the acoustic correlate of intonation, while the filter controls the spectral envelope and formant positions, which determine which phones are being produced. There are three popular techniques for performing source-filter separation. First we will examine filter-bank analysis in this section, before turning to cepstral analysis and linear prediction in the next sections. 

Filter-bank analysis is a simple and robust technique for finding the spectral envelope, but it is only a partial solution to soince-filter separation. First, the amoimt of blinring required to eliminate the harmonics may be too severe and may eliminate some of the 

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Figure 9.2 Phase vocoder based on filter bank analysis/synthesis.

Figure 12.10 Filter bank analysis on magnitude spectra...

A very popular representation in speech recognition is the mel-frequency cepstral coefficient or MFCC. This is one of the few popular represenations lhat does not use linear prediction. This is formed by first performing a DFT on a frame of speech, then performing a filter bank analysis (see Section 12.2) in which the frequency bin locations are defined to lie on the mel-scale. This is set up to give say 20-30 coefficients. These are then transformed to the cepstral domain by the discrete cosine transform (we use this rather than the DFT as we only require the real part to be calculated) ... 

Figure 12.10 Filter-bank analysis on magnitude spectra (a) with evenly spaced bins and (b) with bins spaced according to the mel-scale.

A filter bank is used to decompose the input signal into subsampled spectral components (time/frequency domain). Together with the corresponding filter bank in the decoder it forms an analysis/synthesis system. 

Using either the time domain input signal or the output of the analysis filter bank, an estimate of the actual (time dependent) masked threshold is computed using rules known from psychoacoustics. This is called the perceptual model of the perceptual encoding system. 

In practice, the calculation of the PE requires an analysis filter bank and a perceptual model. The PE is defined as... 

The filter bank is the deciding factor for the basic structure of a perceptual coding system. Figure 2.6 shows the basic block diagram of an static n-channel analysis/synthesis filter bank with downsampling by k. If k = n, it is called a filter bank with critical sampling. A number of basic parameters can be used to describe filter banks used for audio coding ... 

In an analysis/synthesis filter bank, all quantization errors on the spectral components show up on the time domain output signal as the modulated signal multiplied by the synthesis window. Consequently, the error is smeared in time over the length of the synthesis window / prototype filter. As described above, this may lead to audible errors if premasking is not ensured. This pre-echo effect (a somewhat misleading name, a better word would be pre-noise) can be avoided if the filter bank is not static, but switched between different frequency/time resolutions for different blocks of the overlap/add. An example of this technique called adaptive window switching is described below. 

QMF filter banks. Quadrature mirror filters (QMF, see [Esteban and Galand, 1977]) have often been proposed for audio coding. The most common configuration is the tree of filters with a two-way split. In one of the early examples [Theile et al., 1987] the 64d filter design from [Johnston, 1980] has been used. The decomposition tree is set up so that the filter bands resemble critical bands. The QMF halfband filters are non-perfect reconstruction, but with perfect alias cancellation by design. The reconstruction error of the analysis/synthesis pair can be held at small amplitudes by increasing the filter length. 

Early approaches to music analysis relied on a running Fourier transform to measure sine-wave amplitude and frequency trajectories. This technique evolved into a filter-bank-based processor and ultimately to signal analysis/synthesis referred to as the phase vocoder [Flanagan and Golden, 1966], This section describes the history of the phase vocoder, its principles, and limitations that motivate sinusoidal analysis/synthesis. Other formulations and refinements of the phase vocoder are given in chapter 7. 

Figure 2.6 Basic block diagram of an n-channel analysis/synthesis filter bank with downsampling by k (Reprinted from [Herre, 1995] 1995, courtesy of the author)...

Perfect reconstmction filter banks allow the lossless reconstmction of the input signal in an analysis-synthesis system without quantization. While not a necessary feature, the use of a perfect reconstruction filter bank simplifies the design of a coding system, While at some point other filter banks have been proposed for use in perceptual coders (e.g. wave digital filters, see [Sauvagerd, 1988]), all currently used filter banks are either perfect reconstmction or near perfect... 

In most STSA techniques the short-time analysis of the signal is performed by use of the Short-Time Fourier Transform (STFT) [Lim and Oppenheim, 1979, Boll, 1991, Ephraim and Malah, 1984, Moorer and Berger, 1986], or with a uniform filter-bank that can be implemented by STFT [Sondhi et al., 1981, Vary, 1985, Lagadec and Pelloni, 1983], Note that in such cases the two interpretations (multirate filter-... 

An analysis/synthesis system based on a filter bank representation of the signal can be derived from the time-dependent short-time Fourier transform (STFT) [Nawab and Quatieri, 1988a]... 

J.Warren Sparse filter banks for binary subdivision schemes. pp427-438 in Mathematics of Surfaces VII (eds Goodman and Martin) 1997 Leif Kobbelt Using the discrete fourier transform to analyze the convergence of subdivision schemes. Applied and Computational Harmonic Analysis, Volume 5(1), pp68-91, 1998... 

Fig. 9.8. Time-frequency plane described by the STFT. The analysis can be viewed as a series of FTs defined on windowed segments of the signal (vertical bars) or as a filtering process implemented with a bandpass filter-bank (horizontal bars).

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