cconv - Modulo-N circular convolution
Syntax
c = cconv(a,b,n)
Description
Circular convolution is used to convolve two discrete Fourier
transform (DFT) sequences. For very long sequences, circular convolution
may be faster than linear convolution.
c = cconv(a,b,n) circularly
convolves vectors a and b. n is
the length of the resulting vector. If you omit n,
it defaults to length(a)+length(B)-1. When n
= length(a)+length(B)-1, the circular convolution is equivalent
to the linear convolution computed with conv.
You can also use cconv to compute the circular
cross-correlation of two sequences (see the example below).
Examples
The following example calculates a modulo-4 circular convolution.
a = [2 1 2 1];
b = [1 2 3 4];
c = cconv(a,b,4)
c =
14 16 14 16 The following example compares a circular correlation, where n uses
the default value, and a linear convolution. The resulting norm is
a value that is virtually zero, which shows that the two convolutions
produce virtually the same result.
a = [1 2 -1 1];
b = [1 1 2 1 2 2 1 1];
c = cconv(a,b) % Circular convolution
cref = conv(a,b) % Linear convolution
norm(c-cref)
ans =
9.7422e-016
The following example uses cconv to compute
the circular cross-correlation of two sequences. The result is compared
to the cross-correlation computed using xcorr.
a = [1 2 2 1]+i;
b = [1 3 4 1]-2*i;
c = cconv(a,conj(fliplr(b)),7) % Compute using cconv
cref = xcorr(a,b) % Compute using xcorr
c =
Columns 1 through 5
-1.0000 + 3.0000i 2.0000 +11.0000i 7.0000 +18.0000i
8.0000 +21.0000i 6.0000 +18.0000i
Columns 6 through 7
1.0000 +10.0000i -1.0000 + 3.0000i
cref =
Columns 1 through 5
-1.0000 + 3.0000i 2.0000 +11.0000i 7.0000 +18.0000i
8.0000 +21.0000i 6.0000 +18.0000i
Columns 6 through 7
1.0000 +10.0000i -1.0000 + 3.0000i
References
[1] Orfanidis, S.J., Introduction
to Signal Processing, Englewood Cliffs, NJ: Prentice-Hall,
Inc., 1996. pp. 524–529.
See Also
conv
 | cceps | | cell2sos |  |
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