DSP in 20 loc

dsp.jl

using LinearAlgebra: diag

# returns a `LinRange` representing `k`s which can 
# be passed into `diag`, starting from top right
function diags(m::AbstractMatrix)
	(nr, nc) = size(m) .- 1
	return reverse(-nr:nc)
end

# sum of values along diagonal, `diagsum(m, 0) == tr(m)`
diagsum(m::AbstractMatrix, k::Integer = 0) = sum(diag(m, k))

function xcorr(a::AbstractVector, b::AbstractVector)
	m = a * b'
	return diagsum.(Ref(m), diags(m))
end

conv(a::AbstractVector, b::AbstractVector) = xcorr(a, reverse(b))

# tests
using DSP
@assert DSP.xcorr(1:3, 1:5) == xcorr(1:3, 1:5)
@assert DSP.conv(1:3, 1:5) == conv(1:3, 1:5)