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Unformatted text preview: Speech Recognition Speech Signal Representations February 11, 2012 Veton Kpuska 2 Speech Signal Representations Fourier Analysis Discretetime Fourier transform Shorttime Fourier transform Discrete Fourier transform Cepstral Analysis The complex cepstrum and the cepstrum Computational considerations Cepstral analysis of speech Applications to speech recognition MelFrequency cepstral representation Performance Comparison of Various Representations February 11, 2012 Veton Kpuska 3 DiscreteTime Fourier Transform Definition: Sufficient condition for convergence: Although x [ n ] is discrete, X (e j ) is continuous and periodic with period 2 . February 11, 2012 Veton Kpuska 4 DiscreteTime Fourier Transform Convolution/multiplication duality: February 11, 2012 Veton Kpuska 5 ShortTime Fourier Analysis (Time Dependent Fourier Transform) February 11, 2012 Veton Kpuska 6 Rectangular Window February 11, 2012 Veton Kpuska 7 Hamming Window February 11, 2012 Veton Kpuska 8 Comparison of Windows February 11, 2012 Veton Kpuska 9 Comparison of Windows (contd) February 11, 2012 Veton Kpuska 10 A Wideband Spectrogram February 11, 2012 Veton Kpuska 11 A Narrowband Spectrogram February 11, 2012 Veton Kpuska 12 Discrete Fourier Transform In general, the number of input points, N, and the number of frequency samples, M, need not be the same. If M>N , we must zeropad the signal If M<N , we must timealias the signal February 11, 2012 Veton Kpuska 13 Examples of Various Spectral Representations February 11, 2012 Veton Kpuska 14 Cepstral Analysis of Speech The speech signal is often assumed to be the output of an LTI system; i.e., it is the convolution of the input and the impulse response. If we are interested in characterizing the signal in terms of the parameters of such a model, we must go through the process of deconvolution. Cepstral, analysis is a common procedure used for such deconvolution. February 11, 2012...
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