conv: Convolution and polynomial multiplication

In gsignal: Signal Processing

Convolution and polynomial multiplication

Description

Convolve two vectors a and b.

Usage

conv(a, b, shape = c("full", "same", "valid"))

Arguments

a, b	Input, coerced to vectors, can be different lengths or data types.
shape	Subsection of convolution, partially matched to "full" (full convolution - default), "same" (central part of the convolution of the same size as a), or "valid" (only those parts of the convolution that are computed without the zero-padded edges)

Details

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.

Value

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.

Author(s)

Tony Richardson, [e-mail], adapted by John W. Eaton.
Conversion to R by Geert van Boxtel, [e-mail].

Examples

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')

gsignal documentation built on Sept. 12, 2024, 6:27 a.m.