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function y = fftfilt(b, x, varargin)
// Performs FFT-based FIR filtering using overlap-add method
//
// Calling sequence
// y = fftfilt(b,x)
// y = fftfilt(b,x,n)
//
// Parameters
// x: real|complex numbers - vector|matrix
// Input data to be filtered
// If x is a matrix, each column is treated as an independent observation.
// b: real|complex numbers - vector|matrix
// Filter coefficients
// If b is a matrix and x is a vector, each column is treated as an
// independent filter. If both x and b are matrices, each column of x
// if filtered using corresponding column of b.
// n: positive integer
// Parameter used to determine the length of the fft
//
// Description
// y = fftfilt(b,x) filters the data in vector x with the filter described
// by coefficient vector b.
// y = fftfilt(b,x,n) uses n to determine the length of the FFT.
//
// Examples
// 1) Filtering a sine wave
// x = sin(1:2000);
// b = [1 1/2];
// y = fftfilt(b,x);
// 2) Multiple filters (1,1/3) and (1/4,1/5);
// x = sin(1:2000);
// b = [1 1/4;1/3 1/5];
// y = fftfilt(b,x);
//
// Authors
// Ayush Baid
[numOutArgs,numInArgs] = argn(0);
// ** Checking number of arguments
if numInArgs<1 | numInArgs>3 then
msg = "fftfilt: Wrong number of input argument; 1-3 expected";
error(77,msg);
end
if numOutArgs~=1 then
msg = "fftfilt: Wrong number of output argument; 1 expected";
error(78,msg);
end
// variables to keep track if the input vectors are column vectors
transform_x = %f;
// ** checking the type of input arguments **
if isempty(b) then
y = zeros(size(x,1),size(x,2));
return;
end
// b should contain numeric entries
if ~(type(b)==1 | type(b)==8 | type(b)==17) then
msg = "fftfilt: Wrong type for argument #1 (b); Real or complex entries expected ";
error(53,msg);
end
// x should contain numeric entries
if ~(type(x)==1 | type(x)==8 | type(x)==17) then
msg = "fftfilt: Wrong type for argument #2 (x); Real or complex entries expected ";
error(53,msg);
end
temp = size(x,1);
// b and x must have compatible dimensions
inpType = 0;
if size(b,1)==1 | size(b,2)==1 then
// b is a vector; hence x can be a matrix
inpType = 1;
// if x is a vector; it should be a column vector
if size(x,1)==1 then
x = x(:);
transform_x = %t;
end
// covert b to column vector
b = b(:);
else
// b is a matrix, hence x should either be a vector or a matrix with
// same number of columns
if size(x,1)==1 | size(x,2)==1 then
inpType = 2;
if size(x,1)==1 then
x = x(:);
transform_x = %t;
end
else
// check compatibility
if size(b,2)~=size(x,2) then
msg = "fftfilt: Wrong size for arguments #1 (b) and #2 (x); Must have same number of columns";
error(60,msg);
end
inpType = 3;
end
end
// getting the length of data vector x
nx = size(x,1);
nb = size(b,1);
if numInArgs==2 then // the param n was not passed
// figure out the nfft (length of the fft) and L (length of fft inp block)to be used
if (nb>=nx | nb>2^20) then
// take a single fft
nfft = 2^nextpow2(nb+nx-1);
L = nx;
else
// estimated flops for the fft operation (2.5nlog n for n in powers of 2 till 20)
fftflops = [5, 20, 60, 160, 400, 960, 2240, 5120, 11520, 25600, 56320, 122880, 266240, 573440, 1228800, 2621440, 5570560, 11796480, 24903680, 52428800];
n = 2.^(1:20);
candidateSet = find(n>(nb-1)); // all candidates for nfft must be > (nb-1)
n = n(candidateSet);
fftflops = fftflops(candidateSet);
// minimize (number of blocks)*(number of flops per fft)
L = n - (nb - 1);
numOfBlocks = ceil(nx./L);
[dum,ind] = min( numOfBlocks .* fftflops ); //
nfft = n(ind);
L = L(ind);
end
else // nfft is given
if nfft < nb then
nfft = nb;
end
nfft = 2.^(ceil(log(nfft)/log(2))); // forcing nfft to a power of 2 for speed
L = nfft - nb + 1;
end
// performing fft on b
if nb<nfft then
// perform padding
temp = zeros(nfft-nb,size(b,2));
b = [b; temp];
end
B = fft(b,-1,1);
// replication x or b to match the number of columns
if inpType==1 & size(x,2)~=1 then
B = B(:,ones(1,size(x,2)));
elseif inpType==2 then
x = x(:,ones(1,size(b,2)));
end
y=zeros(size(x,1),size(x,2));
blockStartIndex = 1;
while blockStartIndex <= nx,
blockEndIndex = min(blockStartIndex+L-1, nx);
if blockEndIndex==blockStartIndex then
// just a scalar in the block
X = x(blockStartIndex(ones(nfft,1)),:);
else
block = x(blockStartIndex:blockEndIndex,:);
// performing padding
temp = nfft-(blockEndIndex-blockStartIndex)-1;
if temp>0 then
pad = zeros(temp,size(block,2));
block = [block; pad];
end
X = fft(block,-1,1);
end
Y = fft(X.*B,1,1);
yEndIndex = min(nx, blockStartIndex+nfft-1);
y(blockStartIndex:yEndIndex,:) = y(blockStartIndex:yEndIndex,:) + Y(1:(yEndIndex-blockStartIndex+1),:);
blockStartIndex = blockStartIndex+L;
end
// if both data and filter coeffs were real, the output should be real
if ~(or(imag(b(:))) | or(imag(x(:)))) then
y = real(y);
end
if inpType==1 & transform_x then
y = y';
end
endfunction
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