cconv | R Documentation |
Compute the modulo-n circular convolution.
cconv(a, b, n = length(a) + length(b) - 1)
a , b |
Input, coerced to vectors, can be different lengths or data types. |
n |
Convolution length, specified as a positive integer. Default:
|
Linear and circular convolution are fundamentally different operations.
Linear convolution of an n-point vector x, and an l-point vector y, has
length n + l - 1, and can be computed by the function conv
,
which uses filter
. The circular convolution, by contrast, is
equal to the inverse discrete Fourier transform (DFT) of the product of the
vectors' DFTs.
For the circular convolution of x
and y
to be equivalent to
their linear convolution, the vectors must be padded with zeros to length at
least n + l - 1
before taking the DFT. After inverting the product of
the DFTs, only the first n + l - 1
elements should be retained.
For long sequences circular convolution may be more efficient than linear
convolution. You can also use cconv
to compute the circular
cross-correlation of two sequences.
Circular convolution of input vectors, returned as a vector.
Leonardo Araujo.
Conversion to R by Geert van Boxtel,
G.J.M.vanBoxtel@gmail.com.
conv
, convolve
a <- c(1, 2, -1, 1)
b <- c(1, 1, 2, 1, 2, 2, 1, 1)
c <- cconv(a, b) # Circular convolution
cref = conv(a, b) # Linear convolution
all.equal(max(c - cref), 0)
cconv(a, b, 6)
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