Applications of digital signal processing - Continuous and Discrete Time Signals and Systems - page 754

10 50

5 25

0

0

−5

−25

k

−10 −50 W

0 0.1 p 0.2 p 0.3 p 0.4 p 0.5 p 0.6 p 0.7 p 0.8 p 0.9 pp

0 20 40 60 80 100 120 140 160 180 200

(a) (b)

30

Fig. 17.3. Estimating the power
spectrum of a random signal
using the periodogram
approach. (a) Original random
signal. (b) Power spectrum
obtained from periodogram with
no averaging. (c) Power
spectrum obtained from
periodogram with overlap and
averaging based on the Welch
method.

20

10

0

W

0 0.1 p 0.2 p 0.3 p 0.4 p 0.5 p 0.6 p 0.7 p 0.8 p 0.9 p p

(c)

window of size 301. Two consecutive windows have an overlap of 240 samples,
resulting in a total of 94 data windows. Each of these sequences is zero-padded
with 211 zero-valued samples and the DFT is calculated. The averaged power
spectrum is then obtained by averaging all 94 power spectra.
The resulting power spectra are shown in Figs. 17.3(b) and (c). Although both
spectra exhibit peaks at Ω

= 0 . 2 π and 0 . 4 π the estimate PxxNoAvg contains a
substantial amount of noise. Since the estimate PxxWelch averages the power
spectrum, most of the noise is canceled out. However, averaging also reduces
the magnitudes of peaks at Ω = 0 . 2 π and 0 . 4 π in PxxWelch . In the latter

case, the peaks are not as pronounced as the peaks in PxxNoAvg .

17.2 Digital audio

Since the 1980s, digital audio has become a very popular multimedia format
for several applications, including the audio CD, teleconferencing, and digital
movies. With the enormous growth of the World Wide Web (WWW), audio
processing techniques such as filtering, equalization, noise suppression, com-
pression, and synthesis are being used increasingly. In this section, we focus
on three aspects of audio processing: spectrum estimation, audio filtering, and
audio compression. We start by discussing how audio is stored in files and
played back in M ATLAB .

17.2.1 Digital audio fundamentals

Sound is a physical phenomenon induced by vibrations of physical matter, such
as the excitation of a violin string, clapping of hands, and movement of our vocal
tract. The vibrations in the matter are transferred to the surrounding air resulting