Chapter 4

% Program 4_1

% 4-th Order Analog Butterworth Lowpass Filter Design

%

format long

% Determine zeros and poles

[z,p,k] = buttap(4);

disp('Poles are at');disp(p);

% Determine transfer function coefficients

[pz, pp] = zp2tf(z, p, k);

% Print coefficients in descending powers of s

disp('Numerator polynomial'); disp(pz)

disp('Denominator polynomial'); disp(real(pp))

omega = [0: 0.01: 5];

% Compute and plot frequency response

h = freqs(pz,pp,omega);

plot (omega,20*log10(abs(h)));grid

xlabel('Normalized frequency'); ylabel('Gain, dB');

% Program 4_2

% Program to Design Butterworth Lowpass Filter

%

% Type in the filter order and passband edge frequency

N = input('Type in filter order = ');

Wn = input('3-dB cutoff angular frequency = ');

% Determine the transfer function

[num,den] = butter(N,Wn,'s');

% Compute and plot the frequency response

omega = [0: 200: 12000*pi];

h = freqs(num,den,omega);

plot (omega/(2*pi),20*log10(abs(h)));

xlabel('Frequency, Hz'); ylabel('Gain, dB');

% Program 4_3

% Program to Design Type 1 Chebyshev Lowpass Filter

%

% Read in the filter order, passband edge frequency

% and passband ripple in dB

N = input('Order = ');

Fp = input('Passband edge frequency in Hz = ');

Rp = input('Passband ripple in dB = ');

% Determine the coefficients of the transfer function

[num,den] = cheby1(N,Rp,2*pi*Fp,'s');

% Compute and plot the frequency response

omega = [0: 200: 12000*pi];

h = freqs(num,den,omega);

plot (omega/(2*pi),20*log10(abs(h)));

xlabel('Frequency, Hz'); ylabel('Gain, dB');

% Program 4_4

% Program to Design Elliptic Lowpass Filter

%

% Read in the filter order, passband edge frequency,

% passband ripple in dB and minimum stopband

% attenuation in dB

N = input('Order = ');

Fp = input('Passband edge frequency in Hz = ');

Rp = input('Passband ripple in dB = ');

Rs = input('Minimum stopband attenuation in dB = ');

% Determine the coefficients of the transfer function

[num,den] = ellip(N,Rp,Rs,2*pi*Fp,'s');

% Compute and plot the frequency response

omega = [0: 200: 12000*pi];

h = freqs(num,den,omega);

plot (omega/(2*pi),20*log10(abs(h)));

xlabel('Frequency, Hz'); ylabel('Gain, dB');