O'Reilly logo

Digital Signal Processing Using Matlab by André Quinquis

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

7.2. Solved exercises

EXERCISE 7.1.

Define in the Laplace domain the transfer function of an anti-aliasing filter, which attenuates with 0.5 dB at the frequency vp = 3,500 Hz and with 30 dB at the frequency va = 4,500 Hz.

Fp = 3500;Fs = 4500;
Wp = 2*pi*Fp; Ws = 2*pi*Fs;
[N, Wn] = buttord(Wp, Ws, 0.5, 30,'s');
[b,a] = butter(N, Wn, 's');
wa = 0: (3*Ws)/511:3*Ws;
h = freqs(b,a,wa) ;
plot (wa/(2*pi), 20*log10(abs(h))) ;grid
xlabel('Frequency [Hz]');
ylabel('Gain [dB]');
title('Frequency response');
axis ([0 3*Fs -60 5]) ;

images

Figure 7.4. Frequency response of an analog Butterworth lowpass filter

EXERCISE 7.2.

Consider a system with the impulse response h[n] = 0.9n. Plot the impulse response of this system sampled at 1 Hz for values of n between 0 and 50. Demonstrate that its time constant is equal to 10.

n=[0:50]; h=(0.9) .^n;
subplot(211); stem(n,h)
grid; xlabel('n'); ylabel('h(n)')
title('Impulse response')
hI=exp(-n/10);
subplot (212)
plot (n,h1, '+',n,h,'-r')
grid; xlabel('n') ;
legend('exp(-n/10)', 'h(n)')

images

Figure 7.5. Impulse response of the system from exercise 7.2

The system indicial response can be calculated using the function cumsum.m. The transfer function has a zero in 0 and a pole in 0.9. The impulse and indicial responses can also be calculated using the function filter.m ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required