Speech signals analysis

Gallagher, N. C., Jr., and Wise, G. L., A theoretical analysis of the properties of median filters, IEEE Trans. Acoustics, Speech, Signal Proc. 29, 1136 (1981). 

The purpose of this chapter is to describe the principles of signal analysis/synthesis based on a sine-wave representation and to describe its many speech and music applications. As stated, an important feature of the sinusoidal representation is that the aforementioned sound components can be expressed approximately by a sum of amplitude- and frequency-modulated sine waves. Moreover these sound components, as well as the source and filter contribution to their sine-wave representation, are separable by means of a sine-wave-based decomposition. This separability property is essential in applying sinusoidal analysis/synthesis in a number of areas. 

Crochiere, 1980] Crochiere, R. (1980). A weighted overlap-add method of short-time Fourier analysis/synthesis. IEEE Trans. Acoust., Speech, Signal Processing, ASSP-28(2) 99-102. 

A common starting point in speech analysis is to find the magnitude spectrum from a speech signal. We want this to be in a discrete form that is easy to calculate and store store in a computer, so we use the discrete Fourier transform (DFT) as our principle algorithm. In practice the fast Fourier transform (FFT) implementation is nearly always used due to its speed (see Section 10.2.4). 

Here we have expressed x n purely in terms of the coefficients and the current and previous values ofy[ ] if we compare this to equation 10.54, we see that this is just a standard FIR filter. Hence if we have the speech signal and the coefficients for a single frame, we can find x n by a standard FIR filter operation. Apart from a gain normahsation, this will be identical to the error signal x[ ]. The inverse filtering technique is usefiil because often we are required to find the error signal after the LP analysis has been performed, or for cases (explained below) where we wish to... 

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