diff --git a/examples/spectrogram.livemd b/examples/spectrogram.livemd index a9b82c1..f8bf9e6 100644 --- a/examples/spectrogram.livemd +++ b/examples/spectrogram.livemd @@ -71,7 +71,7 @@ Generated kino_vega_lite app :ok ``` -## Loading the audio data +## Generating the audio data ```elixir # You can load an audio file here. For this example, @@ -141,135 +141,137 @@ VegaLite.new(width: 600, height: 600, title: "Audio Sample") ``` ```elixir -# Now we're going to obtain an spectrogram through STFT +defmodule Spectrogram do + alias VegaLite, as: Vl + import Nx.Defn + + def calculate_stft_and_plot_spectrogram( + input, + fs, + window_duration_ms, + plot_cutoff_frequency \\ 4000 + ) do + n_window = ceil(fs * window_duration_ms) + {spectrogram, f, t, max_f} = stft(input, fs: fs, n_window: n_window) + + max_f = Nx.to_number(max_f) + spectrogram = Nx.slice(spectrogram, [0, 0], [Nx.size(t), max_f]) + f = Nx.slice(f, [0], [max_f]) + + spectrogram + |> to_plot_data(f, t, plot_cutoff_frequency) + |> plot() + end + + defn stft(input, opts) do + fs = opts[:fs] + n_window = opts[:n_window] -# 40ms window -n_window = ceil(fs * 40.0e-3) -window = NxSignal.Windows.hann(n: n_window, is_periodic: true) + # ms to samples + window = NxSignal.Windows.hann(n: n_window, is_periodic: true) -# use the default overlap of 50% -{spectrum, t, f} = NxSignal.stft(data, window, sampling_rate: fs, fft_length: 1024) + # use the default overlap of 50% + {s, t, f} = NxSignal.stft(input, window, sampling_rate: fs, fft_length: 1024) -IO.inspect(f) + max_f = + Nx.select(f >= fs / 2, Nx.iota(f.shape), Nx.size(f) + 1) + |> Nx.argmin() -max_f = - Nx.select(Nx.greater_equal(f, fs / 2), Nx.iota(f.shape), Nx.size(f) + 1) - |> Nx.argmin() - |> Nx.to_number() + spectrogram = Nx.abs(s) + # to dBFS + spectrogram = 20 * Nx.log(spectrogram / Nx.reduce_max(spectrogram)) / Nx.log(10) -spectrogram = spectrum |> Nx.slice([0, 0], [Nx.size(t), max_f]) |> Nx.abs() + {spectrogram, f, t, max_f} + end -# normalize and plot in decibels -spectrogram = - spectrogram - |> Nx.divide(Nx.reduce_max(spectrogram)) - |> Nx.log() - |> Nx.multiply(20) - |> Nx.divide(Nx.log(10)) + defp to_plot_data(s, f, t, plot_cutoff_frequency) do + for t_idx <- 0..(Nx.size(t) - 1), + f_idx <- 0..(Nx.size(f) - 1), + Nx.to_number(f[[f_idx]]) <= plot_cutoff_frequency, + reduce: %{"t" => [], "f" => [], "s" => []} do + %{"t" => t_acc, "f" => f_acc, "s" => s_acc} -> + %{ + "t" => [Nx.to_number(t[[t_idx]]) | t_acc], + "f" => [Float.round(Nx.to_number(f[[f_idx]]), 3) | f_acc], + "s" => [Nx.to_number(s[[t_idx, f_idx]]) | s_acc] + } + end + end -f = Nx.slice(f, [0], [max_f]) + defp plot(dataset) do + Vl.new(title: "Spectrogram", width: 500, height: 500) + |> Vl.mark(:rect) + |> Vl.data_from_values(dataset) + |> Vl.encode_field(:x, "t", + type: :quantitative, + title: "Time (seconds)", + axis: [tick_min_step: 0.1], + grid: false + ) + |> Vl.encode_field(:y, "f", + type: :quantitative, + sort: "-x", + title: "Frequency (Hz)", + axis: [tick_count: 25], + grid: false + ) + |> Vl.encode_field(:color, "s", + aggregate: :max, + type: :quantitative, + scale: [scheme: "viridis"], + legend: [title: "dBFS"] + ) + |> Vl.config(view: [stroke: nil]) + end +end ``` ``` -#Nx.Tensor< - f32[frequencies: 1024] - [0.0, 43.06640625, 86.1328125, 129.19921875, 172.265625, 215.33203125, 258.3984375, 301.46484375, 344.53125, 387.59765625, 430.6640625, 473.73046875, 516.796875, 559.86328125, 602.9296875, 645.99609375, 689.0625, 732.12890625, 775.1953125, 818.26171875, 861.328125, 904.39453125, 947.4609375, 990.52734375, 1033.59375, 1076.66015625, 1119.7265625, 1162.79296875, 1205.859375, 1248.92578125, 1291.9921875, 1335.05859375, 1378.125, 1421.19140625, 1464.2578125, 1507.32421875, 1550.390625, 1593.45703125, 1636.5234375, 1679.58984375, 1722.65625, 1765.72265625, 1808.7890625, 1851.85546875, 1894.921875, 1937.98828125, 1981.0546875, 2024.12109375, 2067.1875, 2110.25390625, ...] -> +{:module, Spectrogram, <<70, 79, 82, 49, 0, 0, 26, ...>>, {:plot, 1}} +``` + +```elixir +Spectrogram.calculate_stft_and_plot_spectrogram(data, fs, 50.0e-3) ``` +```vega-lite 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(seconds)","type":"quantitative"},"y":{"axis":{"tickCount":25},"field":"f","grid":false,"sort":"-x","title":"Frequency (Hz)","type":"quantitative"}},"height":500,"mark":"rect","title":"Spectrogram","width":500} ``` -#Nx.Tensor< - f32[frequencies: 512] - [0.0, 43.06640625, 86.1328125, 129.19921875, 172.265625, 215.33203125, 258.3984375, 301.46484375, 344.53125, 387.59765625, 430.6640625, 473.73046875, 516.796875, 559.86328125, 602.9296875, 645.99609375, 689.0625, 732.12890625, 775.1953125, 818.26171875, 861.328125, 904.39453125, 947.4609375, 990.52734375, 1033.59375, 1076.66015625, 1119.7265625, 1162.79296875, 1205.859375, 1248.92578125, 1291.9921875, 1335.05859375, 1378.125, 1421.19140625, 1464.2578125, 1507.32421875, 1550.390625, 1593.45703125, 1636.5234375, 1679.58984375, 1722.65625, 1765.72265625, 1808.7890625, 1851.85546875, 1894.921875, 1937.98828125, 1981.0546875, 2024.12109375, 2067.1875, 2110.25390625, ...] -> -``` + +Notice how the first half of the spectrogram looks cleaner than the second one. This is due to the window length, that also interferes in how we can observe both our time and frequency resolutions. + +Below we can see what happens if we use different window durations (150ms, 100ms and 25ms respectively). ```elixir -alias VegaLite, as: Vl - -# Format the spectrogram into tabular data - -dataset = - for t_idx <- 0..(Nx.size(t) - 1), - f_idx <- 0..(Nx.size(f) - 1), - Nx.to_number(f[[f_idx]]) <= 4000, - reduce: %{"t" => [], "f" => [], "s" => []} do - %{"t" => t_acc, "f" => f_acc, "s" => s_acc} -> - %{ - "t" => [Nx.to_number(t[[t_idx]]) | t_acc], - "f" => [Float.round(Nx.to_number(f[[f_idx]]), 3) | f_acc], - "s" => [Nx.to_number(spectrogram[[t_idx, f_idx]]) | s_acc] - } - end +Spectrogram.calculate_stft_and_plot_spectrogram(data, fs, 150.0e-3) ``` +```vega-lite 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