7.2. Solved exercises
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]) ;
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)')
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 ...