Applications of digital signal processing - Continuous and Discrete Time Signals and Systems - page 760

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5
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1

0.5

0

−0.5

−1 20

0 2 6 8 101214161820

4 0 5 10 15 20

k (s)

k (s)

(a) (b)

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Fig. 17.7. Frequency analysis of
the music signal stored in the
testaudio2.wav file.
(a) Time representation;
(b) spectrogram; (c) power
spectrum of the music signal.

0 5 10 15 20

f (kHz)

(c)

Example 17.4
Consider the audio signal stored in the bell.wav file, which was sampled
at a sampling rate of 22 050 samples/s and quantized using an 8-bit quantizer.
The power spectral density, shown in Fig. 17.8(b), illustrates that the signal
has frequency components across the entire 0-11 025 Hz frequency range.
We now process the audio signal with the lowpass, highpass, and bandpass
filters.

Lowpass filtering A lowpass FIR filter with a cut-off frequency of 3 kHz and
order 64 is designed using the fir1 M ATLAB library function. The following
M ATLAB code designs the lowpass filter:

>> filtLow = fir1(64,3000/ % Filter: Order = 64

(Fs/2)); % cutoff = 3kHz

>> w = 0:0.001*pi:pi; % discrete frequencies for

% spectrum

>> HLpf = freqz(filtLow,1,w); % transfer function

>> plot(w*Fs/(2*pi),20*log10 % magnitude spectrum

(abs(HLpf) + eps));

By default, the fir1 function uses the Hamming window. Since the fir1
function accepts normalized frequencies, the cut-off frequency is normalized
with half the sampling frequency. The magnitude spectrum of the resulting
lowpass filter is shown in Fig. 17.9(a).