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Implement Short-time Fourier transform and its inverse (#587)
* Initial stft implementation * Finish STFT * Cleanup * Bump AMDGPU compat * Install GPU backends only when testing them * Add spectrogram * Move audio documentation to its own page - Convert examples to doctests or evaluate during build time -More tests * Fixes * Use Makie for spectrogram plots * Add mel-scale filterbanks * Run doctests when building documentation instead of a separate CI stage * Minor fix * Move FFTW-dependent functions to extension
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| Original file line number | Diff line number | Diff line change |
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| @@ -1,3 +1,9 @@ | ||
| [deps] | ||
| CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" | ||
| Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" | ||
| FLAC = "abae9e3b-a9a0-4778-b5c6-ca109b507d99" | ||
| FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549" | ||
| Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" | ||
| NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd" | ||
| UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228" | ||
| FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" |
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| # Reference | ||
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| !!! note | ||
| Spectral functions require importing `FFTW` package to enable them. | ||
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| ## Window functions | ||
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| ```@docs | ||
| hann_window | ||
| hamming_window | ||
| ``` | ||
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| ## Spectral | ||
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| ```@docs | ||
| stft | ||
| istft | ||
| NNlib.power_to_db | ||
| NNlib.db_to_power | ||
| ``` | ||
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| ## Spectrogram | ||
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| ```@docs | ||
| melscale_filterbanks | ||
| spectrogram | ||
| ``` | ||
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| Example: | ||
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| ```@example 1 | ||
| using FFTW # <- required for STFT support. | ||
| using NNlib | ||
| using FileIO | ||
| using Makie, CairoMakie | ||
| CairoMakie.activate!() | ||
| waveform, sampling_rate = load("./assets/jfk.flac") | ||
| fig = lines(reshape(waveform, :)) | ||
| save("waveform.png", fig) | ||
| # Spectrogram. | ||
| n_fft = 1024 | ||
| spec = spectrogram(waveform; n_fft, hop_length=n_fft ÷ 4, window=hann_window(n_fft)) | ||
| fig = heatmap(transpose(NNlib.power_to_db(spec)[:, :, 1])) | ||
| save("spectrogram.png", fig) | ||
| # Mel-scale spectrogram. | ||
| n_freqs = n_fft ÷ 2 + 1 | ||
| fb = melscale_filterbanks(; n_freqs, n_mels=128, sample_rate=Int(sampling_rate)) | ||
| mel_spec = permutedims(spec, (2, 1, 3)) ⊠ fb # (time, n_mels) | ||
| fig = heatmap(NNlib.power_to_db(mel_spec)[:, :, 1]) | ||
| save("mel-spectrogram.png", fig) | ||
| nothing # hide | ||
| ``` | ||
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| |Waveform|Spectrogram|Mel Spectrogram| | ||
| |:---:|:---:|:---:| | ||
| |||| |
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| module NNlibFFTWExt | ||
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| using FFTW | ||
| using NNlib | ||
| using KernelAbstractions | ||
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| include("stft.jl") | ||
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| end |
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| function NNlib.stft(x; | ||
| n_fft::Int, hop_length::Int = n_fft ÷ 4, window = nothing, | ||
| center::Bool = true, normalized::Bool = false, | ||
| ) | ||
| kab = get_backend(x) | ||
| use_window = !isnothing(window) | ||
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| use_window && kab != get_backend(window) && throw(ArgumentError( | ||
| "`window` must be on the same device as stft input `x` ($kab), \ | ||
| instead: `$(get_backend(window))`.")) | ||
| use_window && !(0 < length(window) ≤ n_fft) && throw(ArgumentError( | ||
| "Expected `0 < length(window) ≤ n_fft=$n_fft`, \ | ||
| but got `length(window)=$(length(window))`.")) | ||
| hop_length < 0 && throw(ArgumentError( | ||
| "Expected `hop_length > 0`, but got `hop_length=$hop_length`.")) | ||
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| # Pad window on both sides with `0` to `n_fft` length if needed. | ||
| if use_window && length(window) < n_fft | ||
| left = ((n_fft - length(window)) ÷ 2) + 1 | ||
| tmp = KernelAbstractions.zeros(kab, eltype(window), n_fft) | ||
| tmp[left:left + length(window) - 1] .= window | ||
| window = tmp | ||
| end | ||
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| if center | ||
| pad_amount = n_fft ÷ 2 | ||
| x = pad_reflect(x, pad_amount; dims=1) | ||
| end | ||
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| n = size(x, 1) | ||
| (0 < n_fft ≤ n) || throw(ArgumentError( | ||
| "Expected `0 < n_fft ≤ size(x, 1)=$n`, but got `n_fft=$n_fft`.")) | ||
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| n_frames = 1 + (n - n_fft) ÷ hop_length | ||
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| # time2col. | ||
| # Reshape `x` to (n_fft, n_frames, B) if needed. | ||
| # Each row in `n_frames` is shifted by `hop_length`. | ||
| if n_frames > 1 | ||
| # TODO can be more efficient if we support something like torch.as_strided | ||
| ids = [ | ||
| row + hop_length * col | ||
| for row in 1:n_fft, col in 0:(n_frames - 1)] | ||
| x = x[ids, ntuple(_ -> Colon(), ndims(x) - 1)...] | ||
| end | ||
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| region = 1 | ||
| use_window && (x = x .* window;) | ||
| y = eltype(x) <: Complex ? fft(x, region) : rfft(x, region) | ||
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| normalized && (y = y .* eltype(y)(n_fft^-0.5);) | ||
| return y | ||
| end | ||
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| function NNlib.istft(y; | ||
| n_fft::Int, hop_length::Int = n_fft ÷ 4, window = nothing, | ||
| center::Bool = true, normalized::Bool = false, | ||
| return_complex::Bool = false, | ||
| original_length::Union{Nothing, Int} = nothing, | ||
| ) | ||
| kab = get_backend(y) | ||
| use_window = !isnothing(window) | ||
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| use_window && kab != get_backend(window) && throw(ArgumentError( | ||
| "`window` must be on the same device as istft input `y` ($kab), \ | ||
| instead: `$(get_backend(window))`.")) | ||
| use_window && !(0 < length(window) ≤ n_fft) && throw(ArgumentError( | ||
| "Expected `0 < length(window) ≤ n_fft=$n_fft`, \ | ||
| but got `length(window)=$(length(window))`.")) | ||
| hop_length < 0 && throw(ArgumentError( | ||
| "Expected `hop_length > 0`, but got `hop_length=$hop_length`.")) | ||
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| # TODO check `y` eltype is complex | ||
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| n_frames = size(y, 2) | ||
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| # Pad window on both sides with `0` to `n_fft` length if needed. | ||
| if use_window && length(window) < n_fft | ||
| left = ((n_fft - length(window)) ÷ 2) + 1 | ||
| tmp = KernelAbstractions.zeros(kab, eltype(window), n_fft) | ||
| tmp[left:left + length(window) - 1] .= window | ||
| window = tmp | ||
| end | ||
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| # Denormalize. | ||
| normalized && (y = y .* eltype(y)(n_fft^0.5);) | ||
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| region = 1 | ||
| x = return_complex ? ifft(y, region) : irfft(y, n_fft, region) | ||
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| # De-apply window. | ||
| use_window && (x = x ./ window;) | ||
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| # col2time. | ||
| expected_output_len = n_fft + hop_length * (n_frames - 1) | ||
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| ids = Vector{Int}(undef, expected_output_len) | ||
| in_idx, out_idx = 0, 0 | ||
| prev_e, v = 0, 0 | ||
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| for col in 0:(n_frames - 1) | ||
| for row in 1:n_fft | ||
| in_idx += 1 | ||
| v = row + hop_length * col | ||
| v > prev_e || continue | ||
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| out_idx += 1 | ||
| ids[out_idx] = in_idx | ||
| end | ||
| prev_e = v | ||
| end | ||
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| # In case of batched input, reshaped it (n_fft, n_frames, batch) -> (:, batch). | ||
| nd = ntuple(_ -> Colon(), ndims(x) - 2) | ||
| ndims(x) == 3 && (x = reshape(x, (:, size(x, 3)));) | ||
| x = x[ids, nd...] | ||
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| # Trim padding. | ||
| left = center ? (n_fft ÷ 2 + 1) : 1 | ||
| right = if isnothing(original_length) | ||
| center ? (size(x, 1) - n_fft ÷ 2) : expected_output_len | ||
| else | ||
| left + original_length - 1 | ||
| end | ||
| x = x[left:right, nd...] | ||
| return x | ||
| end |
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