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leiosleios
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adding draft for 1d chapter
1 parent 78cc189 commit 098c5b6

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‎contents/convolutions/1d/1d.md

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‎contents/convolutions/code/julia/1d_convolution.jl

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using DelimitedFiles
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using LinearAlgebra
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function convolve_cyclic(signal1::Array{T, 1},
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signal2::Array{T, 1}) where {T <: Number}
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# output size will be the size of sign
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output_size = max(length(signal1), length(signal2))
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# convolutional output
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out = Array{Float64,1}(undef,output_size)
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sum = 0
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for i = 1:output_size
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for j = 1:output_size
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if (mod1(i-j, output_size) <= length(signal2))
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sum += signal1[mod1(j, output_size)] * signal2[mod1(i-j, output_size)]
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end
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end
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out[i] = sum
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sum = 0
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end
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return out
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end
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function convolve_linear(signal1::Array{T, 1}, signal2::Array{T, 1},
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output_size) where {T <: Number}
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# convolutional output
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out = Array{Float64,1}(undef, output_size)
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sum = 0
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for i = 1:output_size
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for j = 1:i
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if j < length(signal1) && i-j+1 < length(signal2)
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sum += signal1[j] * signal2[i-j+1]
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end
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end
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out[i] = sum
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sum = 0
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end
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return out
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end
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function main()
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# Random distribution in x
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x = rand(100)
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# Gaussian signals
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y = [exp(-((i-50)/100)^2/.01) for i = 1:100]
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# Normalization is not strictly necessary, but good practice
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normalize!(x)
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normalize!(y)
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# full convolution, output will be the size of x + y
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full_linear_output = convolve_linear(x, y, length(x) + length(y))
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# simple boundaries
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simple_linear_output = convolve_linear(x, y, length(x))
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# cyclic convolution
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cyclic_output = convolve_cyclic(x, y)
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# outputting convolutions to different files for plotting in external code
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writedlm("full_linear.txt", full_linear_output)
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writedlm("simple_linear.txt", simple_linear_output)
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writedlm("cyclic.txt", cyclic_output)
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end

‎contents/convolutions/code/julia/conv.jl

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‎contents/convolutions/code/julia/convolutional_theorem.jl

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using FFTW
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using DelimitedFiles
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# using the convolutional theorem
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function convolve_fft(signal1::Array{T}, signal2::Array{T}) where {T <: Number}
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return ifft(fft(signal1).*fft(signal2))
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end
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function main()
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# Random distribution in x
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x = rand(100)
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# Gaussian signals
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y = [exp(-((i-50)/100)^2/.01) for i = 1:100]
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# Normalization is not strictly necessary, but good practice
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normalize!(x)
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normalize!(y)
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# cyclic convolution via the convolutional theorem
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fft_output = convolve_fft(x, y)
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# outputting convolutions to different files for plotting in external code
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writedlm("fft.txt", fft_output)
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end

‎contents/convolutions/code/julia/cyclic.txt

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‎contents/convolutions/code/julia/fft.txt

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