Signals and Systems - Electrical Engineering

11.6 Realization of Discrete Filters 689

n = 0:N;

if wind == 1

window = boxcar(N + 1);

disp(‘ ***** RECTANGULAR WINDOW *****’)

elseif wind == 2

window = hanning(N + 1);

disp(‘ *****HANNING WINDOW *****’)

elseif wind == 3

window = hamming(N + 1);

disp(‘ ***** HAMMING WINDOW *****’)

else

window = kaiser(N + 1,4.55);

disp(‘ ***** KAISER WINDOW *****’)

end

% calculation of ideal impulse response

den = pi∗(n - N/2);

num = sin(wc*den);

% if N even, this prevents 0/0

if fix(N/2) == N/2,

num(N/2 + 1) = wc;

den(N/2 + 1) = 1;

end

b = (num./den).∗window’;

% frequency shifting

[H,w] = freqz(b,1,256); %% low-pass

if wo>0 & wo<1,

b = 2∗b.*cos(wo∗pi∗(n - N/2))/H(1);

elseif wo == 0,

b = b/abs(H(1));

elseif wo == 1;

b = b.∗cos(wo∗pi∗(n - N/2));

end

MATLAB provides the functionfir1to design FIR filters with the window method. As expected, the

results are identical for eitherfir1andfir. The reason for writingfiris to simplify the code and to

show how the modulation property can be used in the design of filters different from low-pass

filters. n

11.6 Realization of Discrete Filters

The realization of a discrete filter can be done in hardware or in software. In either case, the imple-
mentation of the transfer functionH(z)of a discrete filter requires delays, adders, and constant
multipliers as actual hardware or as symbolic components. Figure 11.25 depicts the operation of
each of these components as block diagrams.