Reply by nagi_nov3 ●December 20, 20022002-12-20
can any one suggest me how to get the required result,Iam not getting
response
plz any one help me......... Software Implementation in Matlab or Octave
In Matlab or Octave, this type of filter can be implemented using the
filter function. For example, the following matlab3.1 code computes
the output signal y given the input signal x for a specific example
comb filter: g1 = (0.5)^3; % Some specific coefficients
g2 = (0.9)^5;
B = [1 0 0 g1]; % Feedforward coefficients, M1=3
A = [1 0 0 0 0 g2]; % Feedback coefficients, M2=5
N = 1000; % Number of signal samples
x = rand(N,1); % Random test input signal
y = filter(B,A,x); % Matlab and Octave compatible

The example coefficients, and , are chosen to place all filter zeros
at radius and all filter poles at radius in the complex plane (as
we shall see below).
The matlab filter function carries out the following computation for
each element of the y array: (3.2)
(3.3) for , where NA = length(A) and NB = length(B). Note that the indices
of x and y can go negative in this expression. By default, such terms
are replaced by zero. However, the filter function has an optional
fourth argument for specifying the initial state of the filter, which
includes past input and past output samples seen by the filter. This
argument is used to forward the filter's state across successive
blocks of data:
[y1,state] = filter(B,A,x1); % filter 1st block of data x1
[y2,state] = filter(B,A,x2,state); % filter 2nd block x2
...

For completeness, a direct matlab implementation of the built-in
filter function (Eq. (3.3)) is given in Fig. 3.2. While this code is
useful for study, it is far slower than the built-in filter function.
As a specific example, filtering samples of data using an order 100
filter on a 900MHz Athlon PC required 0.01 seconds for filter and
10.4 seconds for filterslow. Thus, filter was over a thousand times
faster than filterslow in this case. The complete test is given in
the following matlab listing:

x = rand(10000,1); % random input signal
B = rand(101,1); % random coefficients
A = [1;0.001*rand(100,1)]; % random but probably stable
tic; yf=filter(B,A,x); ft=toc
tic; yfs=filterslow(B,A,x); fst=toc

The execution times differ greatly for two reasons:
recursive feedback cannot be ``vectorized'' in general, and
built-in functions such as filter are written in C, precompiled, and
linked with the main program.

Figure 3.2: Matlab function for implementing a digital filter
directly. Do not use this in practice because it is much slower than
the built-in filter routine.
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function [y] = filterslow(B,A,x)
% FILTERSLOW: Filter x to produce y = (B/A) x .
% Equivalent to 'y = filter(B,A,x)' using
% a slow (but tutorial) method.

NB = length(B);
NA = length(A);
Nx = length(x);

xv = x(:); % ensure column vector

% do the FIR part using vector processing:
v = B(1)*xv;
if NB>1
for i=2:min(NB,Nx)
xdelayed = [zeros(i-1,1); xv(1:Nx-i+1)];
v = v + B(i)*xdelayed;
end;
end; % fir part done, sitting in v

% The feedback part is intrinsically scalar,
% so this loop is where we spend a lot of time.
y = zeros(length(x),1); % pre-allocate y
ac = - A(2:NA);
for i=1:Nx, % loop over input samples
t=v(i); % initialize accumulator
if NA>1,
for j=1:NA-1
if i>j,
t=t+ac(j)*y(i-j);
%else y(i-j) = 0
end;
end;
end;
y(i)=t;
end;

y = reshape(y,size(x)); % in case x was a row vector ----------------------------------
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