Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 388

m(6) ¼ sqrt(y1336(206)^2 þ y1336(205)^2- .
2*cos(2*pi*34/205)*y1336(206)*y1336(205));
m(7) ¼ sqrt(y1477(206)^2 þ y1477(205)^2- .
2*cos(2*pi*38/205)*y1477(206)*y1477(205));
% Convert the magnitude of DFT coefficients to the single-side spectrum
m ¼ 2*m/205;
% Determine the threshold
th

sum(m)/4;
% Plot the DTMF spectrum with the threshold
f

¼

¼ [ 697 770 852 941 1209 1336 1477];

f1 ¼ [0 fs/2];

th [ th th];

subplot(2,1,2);stem(f,m);grid;hold; plot(f1,th);
xlabel( ' Frequency (Hz) ' ); ylabel( ' (b) Spectral values ' );
m ¼ round(m); % Round to the binary pattern
if m ¼¼ [ 1 0 0 0 1 0 0] disp( ' Detected Key 1 ' ); end
if m ¼¼ [ 1 0 0 0 0 1 0] disp( ' Detected Key 2 ' ); end
if m ¼¼ [ 1 0 0 0 0 0 1] disp( ' Detected Key 3 ' ); end
if m ¼¼ [ 0 1 0 0 1 0 0] disp( ' Detected Key 4 ' ); end
if m ¼¼ [ 0 1 0 0 0 1 0] disp( ' Detected Key 5 ' ); end
if m ¼¼ [ 0 1 0 0 0 0 1] disp( ' Detected Key 6 ' ); end
if m ¼¼ [ 0 0 1 0 1 0 0] disp( ' Detected Key 7 ' ); end
if m ¼¼ [ 0 0 1 0 0 1 0] disp( ' Detected Key 8 ' ); end
if m ¼¼ [ 0 0 1 0 0 0 1] disp( ' Detected Key 9 ' ); end
if m ¼¼ [ 0 0 0 1 1 0 0] disp( ' Detected Key * ' ); end
if m ¼¼ [ 0 0 0 1 0 1 0] disp( ' Detected Key 0 ' ); end
if m ¼¼ [ 0 0 0 1 0 0 1] disp( ' Detected Key # ' ); end

¼

8.12 SUMMARY OF INFINITE IMPULSE RESPONSE (IIR) DESIGN
PROCEDURES AND SELECTION OF THE IIR FILTER DESIGN METHODS IN
PRACTICE
In this section, we first summarize the design procedures of the BLT design, impulse-invariant design,
and pole-zero placement design methods, and then discuss the selection of the particular filter for
typical applications.
The BLT design method:

1. Given the digital filter frequency specifications, prewarp each digital frequency edge to the analog
frequency edge using Equations (8.18) and (8.19) .
2. Determine the prototype filter order using Equation (8.29) for the Butterworth filter or Equation
(8.35b) for the Chebyshev filter, and perform lowpass prototype transformation using the
lowpass prototype in Table 8.3 (Butterworth function) or Tables 8.4 and 8.5 (Chebyshev
function) using Equations (8.20) to (8.23).
3. Apply the BLT to the analog filter using Equation (8.24) and output the transfer function.
4. Verify the frequency responses, and output the difference equation.