Continuous-time filters - Continuous and Discrete Time Signals and Systems - page 352

Fig. 7.11. Magnitude spectrum
of the elliptic lowpass filter
designed in Example 7.9.

0.891 1

0.6

0.4

0.1778

0

0 50 100 150 200 250

cheby1 functions used to design Type I Chebyshev filters. The code to imple-
ment an elliptic filter for Example 7.9 is as follows:
>> wp = 50; ws = 100; rp = 1; rs = 15;
% specify design parameters
>> [N,wn] = ellipord (wp,ws,rp,rs,'s');
% determine order and
% natural freq
>> [num,den] = ellip(N,rp,rs,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 = 2; wn = 50;
Instruction III: num = [0.1778 0 2369.66];
den = [1.0000 48.384 2961.75];
Instruction IV: Ht = (0.1778sˆ2 + 2640)/(sˆ2 + 48.38s
+ 2962);
The magnitude spectrum is plotted in Fig. 7.11.

7.4 Frequency transformations

In Section 7.3, we designed a collection of specialized CT lowpass filters. In
this section, we consider the design techniques for the remaining three cat-
egories (highpass, bandpass, and bandstop filters) of CT filters. A common
approach for designing CT filters is to convert the desired specifications into
the specifications of a normalized or prototype lowpass filter using a frequency
transformation that maps the required frequency-selective filter into a lowpass
filter. Based on the transformed specifications, a normalized lowpass filter is
designed using the techniques covered in Section 7.3. The transfer function
H ( S ) of the normalized lowpass filter is then transformed back into the original
frequency domain. Transformation for converting a lowpass filter to a highpass