By Andreas Spanias
An in-depth remedy of algorithms and criteria for perceptual coding of high-fidelity audio, this self-contained reference surveys and addresses all points of the sphere. insurance comprises sign processing and perceptual (psychoacoustic) basics, info on correct learn and sign versions, information on standardization and functions, and information on functionality measures and perceptual dimension platforms. It contains a finished bibliography with over six hundred references, machine workouts, and MATLAB-based tasks to be used in EE multimedia, desktop technology, and DSP courses. An ftp web site containing supplementary fabric akin to wave documents, MATLAB courses and workspaces for the scholars to resolve many of the numerical difficulties and machine workouts within the booklet are available at ftp://ftp.wiley.com/public/sci_tech_med/audio_signal
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Extra info for Audio Signal Processing and Coding
Rxx (−m) = rxx (m) rxx (0) |rxx (m)|. 9 The autocorrelation of a white noise signal is rww (m) = σw2 δ(m), where σw2 is the variance of the noise. The fact that the autocorrelation of white noise is the unit impulse implies that white noise is an uncorrelated signal. 31) to a white noise input of zero mean and unit variance is ryy (m) = E[y(n + m)y(n)] = δ(m + 2) + 2δ(m + 1) + 3δ(m) + 2δ(m − 1) + δ(m − 2). Cross-correlation is a measure of similarity between two signals. The crosscorrelation of a signal, x(n), relative to a signal, y(n), is given by rxy (m) = E[x(n + m)y(n)].
1 Transforms for Discrete-Time Signals Discrete-time signals are described in the transform domain using the z-transform and the discrete-time Fourier transform (DTFT). These two transformations have similar roles as the Laplace transform and the CFT for analog signals, respectively. 9) 21 DISCRETE-TIME SIGNAL PROCESSING where z is a complex variable. 10) then the z-transform becomes the discrete-time Fourier transform (DTFT). The DTFT is given by, ∞ X(e ) = j x(n)e−j n . 11) n=−∞ The DTFT is discrete in time and continuous in frequency.
DISCRETE-TIME RANDOM SIGNALS 39 that the reconstructed signal in the z-domain has the form 1 1 ˆ X(z) = (H0 (z)F0 (z) + H1 (z)F1 (z))X(z) + (H0 (−z)F0 (z) 2 2 + H1 (−z)F1 (z))X(−z). 49) The signal X(−z) in Eq. 49) is associated with the aliasing term. The aliasing term can be cancelled by designing ﬁlters to have the following mirror symmetries: F1 (z) = −H0 (−z). 51) T (z) = (H0 (z)F0 (z) + H1 (z)F1 (z)). 2 If T (z) = 1, then the ﬁlter bank allows perfect reconstruction. Perfect delayless reconstruction is not realizable, but an all-pass ﬁlter bank with linear phase characteristics can be designed easily.
Audio Signal Processing and Coding by Andreas Spanias
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