Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 561

w ¼ filter(B,1,x); % Anti-aliasing filtering
% Compute the single-sided amplitude spectrum for the filtered signal
W ¼ 2*abs(fft(w,N))/N;W(1) ¼ W(1)/2;
% Downsampling
y ¼ w(1:M:N);
NM ¼ length(y);
% Compute the single-sided amplitude spectrum for the downsampled signal
Y

¼ 2*abs(fft(y,NM))/NM;Y(1) ¼ Y(1)/2;

% Plot spectra
subplot(2,1,1);plot(f,W(1:1:N/2));grid; xlabel( Frequency (Hz) );

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subplot(2,1,2);plot(fsM,Y(1:1:NM/2));grid; xlabel( );

Now we focus on how to design an anti-aliasing FIR filter, or decimation filter. We will discuss this
topic via the following example.

Frequency (Hz)

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EXAMPLE 12.1
Consider a DSP downsampling system with the following specifications:
Sampling rate ¼ 6,000 Hz
Input audio frequency range ¼ 0e800 Hz
Passband ripple ¼ 0.02 dB
Stopband attenuation ¼ 50 dB
Downsample factor M ¼ 3
Determine the FIR filter length, cutoff frequency, and window type if the window method is used.
Solution:
The specifications are reorganized as
Anti-aliasing filter operating at the sampling rate ¼ 6,000 Hz
Passband frequency range ¼ 0e800 Hz
Stopband frequency range ¼ 1e3 kHz
Passband ripple ¼ 0.02 dB
Stopband attenuation ¼ 50 dB
Filter type ¼ FIR

The block diagram and specifications are depicted in Figure 12.4 .

y ()

x () w ()

Anti-aliasing
filter H(z)

3

6 6

2

f

0 0. 1 2 3

FIGURE 12.4
Filter specifications for Example 12.1.