Continuous-time filters - Continuous and Discrete Time Signals and Systems - page 356

and elliptic implementations is included below. In each case, M ATLAB auto-
matically designs the highpass filter. No explicit transformations are needed.

>> % Matlab code for designing highpass filter
>> wp = 100; ws = 50; Rp = 1; Rs = 15;

% design
% specifications

>> % for Butterworth

% filter

>> [N, wc] = buttord(wp,ws,Rp,Rs,'s');

% determine order
% and cut off
>> [num1,den1] = butter(N,wc,'high','s');
% determine
% transfer
% function

>> H1 = tf(num1,den1);
>> %%%%% % Type I Chebyshev

% filter

>> [N, wn] = cheb1ord(wp,ws,Rp,Rs,'s');
>> [num2,den2] = cheby1(N,Rp,wn,'high','s');
>> H2 = tf(num2,den2);
>> %%%%%

% Type II Chebyshev
% filter

>> [N,wn] = cheb2ord(wp,ws,Rp,Rs,'s') ;
>> [num3,den3] = cheby2(N,Rs,wn,'high','s') ;
>> H3 = tf(num3,den3);
>> %%%%% % Elliptic filter
>> [N,wn] = ellipord(wp,ws,Rp,Rs,'s') ;
>> [num4,den4] = ellip(N,Rp,Rs,wn,'high','s') ;
>> H4 = tf(num4,den4);

In the above code, note that wp>ws . Also, an additional argument of 'high'
is included in the design statements for different filters, which is used to specify
a highpass filter. The aforementioned M ATLAB code results in the following
transfer functions for the different implementations:

Butterworth

s 4
s 4 + 2 . 004 10 2 s 3 + 2 . 008 10 4 s 2 + 1 . 179 10 6 s + 3 . 459 10 7 ;

H ( s ) =

s 3
s 3 + 252 . 1 s 2 + 2 . 012 10 4 s + 2 . 035 10 6 ;

Type I Chebyshev H ( s ) =

s 3 + 3 . 027 10 3 s
s 3 + 113 . 5 s 2 + 9 . 473 10 3 s + 3 . 548 10 5 ;

Type II Chebyshev H ( s ) =

0 . 8903 s 2 + 1501
s 2 + 81 . 68 s + 8441 .

elliptic H ( s ) =