Continuous-time filters - Continuous and Discrete Time Signals and Systems - page 344

The cheb1ord also returns wn , another design parameter referred to as the
Chebyshev natural frequency to use with cheby1 to achieve the design spec-
ifications. The syntax for cheb1ord is given by
>> [N,wn] = cheb1ord(wp,ws,rp,rs,'s');
To determine the coefficients of the numerator and denominator of the
Type I Chebyshev filter, M ATLAB uses the cheb1 function with the following
syntax:
>> [num,den] = cheby1(N,rp,wn,'s');
The transfer function H ( s ) can be determined using the library function tf as
follows:
>> H = tf(num,den);
For Example 7.7, the M ATLAB commands for designing the Butterworth filter
are given by
>> wp = 50; ws = 100; rp = 1; rs = 15;
% specify design parameters
>> [N,wn] = cheb1ord (wp,ws,rp,rs,'s');
% determine order and
% natural freq
>> [num,den] = cheby1 (N,rp,wn,'s');
% determine num and denom
% coeff.
>> Ht = tf(num,den); % determine transfer
% function
>> [H,w] = freqs(num,den); % determine magnitude
% spectrum
>> plot(w,abs(H)); % plot magnitude spectrum
Stepwise implementation of the above code returns the following values for
different variables:
Instruction II: N = 3; wn = 50;
Instruction III: num = [0 0 0 61413.3]; den =
[1.0000 49.417 3096 61413.3];
Instruction IV: Ht = 61413.3/ (sˆ3 + 49.417sˆ2 + 3096s
+ 61413.3);
The magnitude spectrum is the same as that given in Fig. 7.9.
7.3.3 Type II Chebyshev filters
The Type II Chebyshev filters, or the inverse Chebyshev filters, are monotonic
within the pass band and introduce ripples in the stop band. Such an imple-
mentation is preferred over the Type I Chebyshev filter in applications where a
constant gain is desired within the pass band.