U. Glaeser

All described masking effects are exploited for data compression in modern perceptual audio coders
(e.g., in the MUSICAM procedure, MPEG standards, etc.).
27.5 Principles of Audio Coding
In order to digitally process audio, it is first necessary to sample and quantize the data, i.e., to convert the
analog signal x c(t) into a digital form. This is realized in an analog-to-digital converter (ADC). The digital
data can then be compressed and encoded in a digital audio coder (transmitter), transmitted through a
communication channel, decoded in a receiver, and finally recovered in a digital-to-analog converter
(DAC). A general scheme of a digital audio processing system is shown in Fig. 27.16.
Sampling of a continuous-time signal
is a process of time discretization. It consists in representing the signal x c(t) with a series of samples
© 2002 by CRC Press LLC
(27.26)
(27.27)
referred to as the discrete-time signal or sampled-data signal. Uniform time discretization with sampling
period T s > 0 and rate
is defined by
x n
x n
x = xc(), t – ∞ < t < ∞
= x( n)
= xc( tn), n = 0, ±1, ±2,…
(27.28)
(27.29)
where τ > 0 is some (usually unavoidable) system delay.
It should be stressed that scaling coefficients b (k+1)n in Eq. (27.10) approximate signal samples, i.e.,
xn ≈ b (k+1)n, because for high enough scale k + 1 the scaling functions ϕ 2 act as “delta functions.”
Sampling period is in this case equal to .
According to the sampling theory, a low-band continuous-time signal xc(t − τ), i.e., the signal, whose
spectrum extends from zero to some maximum frequency, can be reconstructed on the basis of the discretetime
signal x(n), if the sampling rate Fs is greater or at least equal to the Nyquist sampling rate, which is
twice as high as the greatest frequency contained in the continuous-time signal spectrum, or in other
words, if the whole signal spectrum lies below Fs/2, called the Nyquist frequency. In practice, sampling rate
Fs has to be somewhat greater than the Nyquist sampling rate [37]. Typical sampling rates for audio are:
k+1 ( t– n)
Ts 1/2 k+1
=
FIGURE 27.16 General scheme of a digital audio processing system.
F s
=
1/T s
= x( n)
= xd( nTs) = xc( tn), tn = nTs – τ, n = 0, ± 1, ± 2,…