Inverse STFT https://github.com/JuliaDSP/DSP.jl/pull/85

istft.jl

backward_plan2{T<:Union(Float32, Float64)}(X::AbstractArray{Complex{T}}, Y::AbstractArray{T}) =
    FFTW.Plan(X, Y, 1, FFTW.ESTIMATE | FFTW.PRESERVE_INPUT, FFTW.NO_TIMELIMIT).plan

function istft2{T<:Union(Float32, Float64)}(S::AbstractMatrix{Complex{T}}, wlen::Int, overlap::Int; nfft=nextfastfft(wlen), window::Union(Function,AbstractVector,Nothing)=nothing)
    winc = wlen-overlap
    win, norm2 = compute_window(window, wlen)
    if win != nothing 
      win² = win.^2
    end
    nframes = size(S,2)-1
    outlen = nfft + nframes*winc
    out = zeros(T, outlen)
    tmp2 = zeros(T, nfft)
    p = backward_plan2(S[:,1], tmp2)
    wsum = zeros(outlen)
    for k = 1:size(S,2)
        FFTW.execute(p, sub(S,1:size(S,1), k), tmp2)
        scale!(tmp2, FFTW.normalization(tmp2))
        if win != nothing
            ix = (k-1)*winc
            for n=1:nfft
                @inbounds out[ix+n] += tmp2[n]*win[n]
                @inbounds wsum[ix+n] += win²[n]
            end
        else
            copy!(out, 1+(k-1)*winc, tmp2, 1, nfft)
        end
    end
    if win != nothing
        for i=1:length(wsum)
            @inbounds wsum[i] != 0 && (out[i] /= wsum[i])
        end
    end
    out
end