Convolution and polynomial multiplication
Convolve two vectors a and b.
conv(a, b, shape = c("full", "same", "valid"))a, b |
Input, coerced to vectors, can be different lengths or data types. |
shape |
Subsection of convolution, partially matched to |
The convolution of two vectors, a and b, represents the area of
overlap under the points as B slides across a. Algebraically,
convolution is the same operation as multiplying polynomials whose
coefficients are the elements of a and b.
The function conv uses the filter function, NOT
fft, which may be faster for large vectors.
Output vector with length equal to length (a) + length (b) -
1. When the parameter shape is set to "valid", the length of
the output is max(length(a) - length(b) + 1, 0), except when
length(b) is zero. In that case, the length of the output vector equals
length(a).
When a and b are the coefficient vectors of two polynomials,
the convolution represents the coefficient vector of the product
polynomial.
Tony Richardson, arichard@stark.cc.oh.us, adapted by John W.
Eaton.
Conversion to R by Geert van Boxtel,
G.J.M.vanBoxtel@gmail.com.
u <- rep(1L, 3) v <- c(1, 1, 0, 0, 0, 1, 1) w <- conv(u, v) ## Create vectors u and v containing the coefficients of the polynomials ## x^2 + 1 and 2x + 7. u <- c(1, 0, 1) v <- c(2, 7) ## Use convolution to multiply the polynomials. w <- conv(u, v) ## w contains the polynomial coefficients for 2x^3 + 7x^2 + 2x + 7. ## Central part of convolution u <- c(-1, 2, 3, -2, 0, 1, 2) v <- c(2, 4, -1, 1) w <- conv(u, v, 'same')
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