Mel Spec

A Rust implementation of mel spectrograms aligned to the results from the whisper.cpp, pytorch and librosa reference implementations and suited to streaming audio.

Examples:

See wavey-ai/hush for live demo

Usage

To require the libary's main features:

use mel_spec::prelude::*

Mel filterbank that has parity with librosa:

Mel filterbanks, within 1.0e-7 of librosa and identical to whisper GGML model-embedded filters.

        let file_path = "./testdata/mel_filters.npz";
        let f = File::open(file_path).unwrap();
        let mut npz = NpzReader::new(f).unwrap();
        let filters: Array2<f32> = npz.by_index(0).unwrap();
        let want: Array2<f64> = filters.mapv(|x| f64::from(x));
        let sampling_rate = 16000.0;
        let fft_size = 400;
        let n_mels = 80;
        let hkt = false;
        let norm = true;
        let got = mel(sampling_rate, fft_size, n_mels, hkt, norm);
        assert_eq!(got.shape(), vec![80, 201]);
        for i in 0..80 {
            assert_nearby!(got.row(i), want.row(i), 1.0e-7);
        }

Spectrogam using Short Time Fourier Transform

STFT with overlap-and-save that has parity with pytorch and whisper.cpp.

The implementation is suitable for processing streaming audio and will accumulate the correct amount of data before returning fft results.

        let fft_size = 8;
        let hop_size = 4;
        let mut spectrogram = Spectrogram::new(fft_size, hop_size);

        // Add PCM audio samples
        let frames: Vec<f32> = vec![1.0, 2.0, 3.0];
        if let Some(fft_frame) = spectrogram.add(&frames) {
            // use fft result
        }

STFT Spectrogam to Mel Spectrogram

MelSpectrogram applies a pre-computed filerbank to an FFT result. Results are identical to whisper.cpp and whisper.py

        let fft_size = 400;
        let sampling_rate = 16000.0;
        let n_mels = 80;
        let mut mel = MelSpectrogram::new(fft_size, sampling_rate, n_mels);
        // Example input data for the FFT
        let fft_input = Array1::from(vec![Complex::new(1.0, 0.0); fft_size]);
        // Add the FFT data to the MelSpectrogram
        let mel_spec = stage.add(fft_input);

Creating Mel Spectrograms from Audio.

The library includes basic audio helpder and a pipeline for processing PCM audio and creating Mel spectrograms that can be sent to whisper.cpp.

It also has voice activity detection that uses edge detection (which might be a novel approach) to identify word/speech boundaries in real- time.

        // load the whisper jfk sample
        let file_path = "../testdata/jfk_f32le.wav";
        let file = File::open(&file_path).unwrap();
        let data = parse_wav(file).unwrap();
        let samples = deinterleave_vecs_f32(&data.data, 1);

        let fft_size = 400;
        let hop_size = 160;
        let n_mels = 80;
        let sampling_rate = 16000.0;

        let mel_settings = MelConfig::new(fft_size, hop_size, n_mels, sampling_rate);
        let vad_settings = DetectionSettings::new(1.0, 10, 5, 0, 100);

        let config = PipelineConfig::new(mel_settings, Some(vad_settings));

        let mut pl = Pipeline::new(config);

        let handles = pl.start();

        // chunk size can be anything, 88 is random
        for chunk in samples[0].chunks(88) {
            let _ = pl.send_pcm(chunk);
        }

        pl.close_ingress();

        while let Ok((_, mel_spectrogram)) = pl.rx().recv() {
          // do something with spectrogram
        }

Saving Mel Spectrograms to file

Mel spectrograms can be saved in Tga format - an uncompressed image format supported by OSX and Windows.

As these images directly encode quantized mel spectrogram data they represent a "photographic negative" of audio data that whisper.cpp can develop and print without the need for direct audio input.

tga files are used in lieu of actual audio for most of the library tests. These files are lossless in Speech-to-Text terms, they encode all the information that is available in the model's view of raw audio and will produce identical results.

Note that spectrograms must have an even number of columns in the time domain, otherwise Whisper will hallucinate. the library takes care of this if using the core methods.

     let file_path = "../testdata/jfk_full_speech_chunk0_golden.tga";
     let dequantized_mel = load_tga_8bit(file_path).unwrap();
     // dequantized_mel can be sent straight to whisper.cpp

❯ ffmpeg -hide_banner -loglevel error -i ~/Downloads/JFKWHA-001-AU_WR.mp3 -f f32le -ar 16000 -acodec pcm_f32le -ac 1 pipe:1  | ./target/debug/tga_whisper -t ../../doc/cutsec_46997.tga
...
whisper_init_state: Core ML model loaded
Got 1
 the quest for peace.

the quest for peace.

Voice Activity Detection

I had the idea of using the Sobel operator for this as speech in Mel spectrograms is characterised by clear gradients.

The general idea is to outline structure in the spectrogram and then find vertical gaps that are suitable for cutting - to allow passing new spectrograms to the model in near real-time.

It's particualrly good at separating speech activity - this is important, because anything resembling white noise is hallucinogenic to Whisper. The Voice Activity Detector module therefore drops frames that look to be gaps in speech.

This is still not perfect and definitely a downside of stream processing, at least with Whisper. However, pre-processing audio as spectrograms should be more robust than pre-processing raw audio - with raw audio it's necessary to look for attack transients to find boundaries, but it's not easy to tell if enegry changes are voice or something else. Mel spectrograms already provide a distinctive "voice" signature.

The graphic below shows part of JFK's speech and uses Sobel edge detection to find possible word/speech boundaries. As you can see, it works pretty well:

For reference, the settings used for this example are:

        let settings = DetectionSettings {
            min_energy: 1.0,
            min_y: 3,
            min_x: 5,
            min_mel: 0,
            min_frames: 100,
        };

Voice boundares for the entire inaugural address can be found in: testdata/jfk_full_speech_chunk0_golden.tga.

It does a good job of detecting when a window contains no speech, vs when it contains very short expressions - green means no speech detected - green as it means it's safe to cut without cutting a word in half.

A segment in the JFK speech that's noisy and somewhat strucutured - but not speech (I picked these by finding the most wild hallucinations in the transcript):

energy but no speech: vad result:

Word detection will discard this entire frame as the intersections are only a pixel or two wide - it needs at least 5 pixels of contiguous intersection in the time domain (and 3 in the frequency domain - see DetectionSettings above) to count the window as including speech.

A fleeting word: vad result:

This passes as speech.

More work needs to be done here, but it is a good start. Hallucinations remain a problem but this always happens when the model is passed mel spectrograms that don't contain actual speech. TODO: I think there are also probability metrics for tokens returned by the model that might help.

The current state of play, the full JFK speech with the above voice activity and word boundary settings, processing on a stream and sending to Whisper approx every and 1-second, can be found here:

jfk_transcript_golden.txt

It will be possible to tidy up hallucinations by checking the spectrograms and refining the boundary detection (each segment/line has a corresponding spectrogram saved - see examples).

Discussion

Mel spectrograms encode at 6.4Kb /sec (80 * 2 bytes * 40 frames)
Float PCM required by whispser audio APIs is 64Kb /sec at 16Khz - expensive to reprocess - resource intensive to keep PCM in-band for overlapping

whisper.cpp produces mel spectrograms with 1.0e-6 precision. However, these spectrograms are invariant to 8-bit quantisation: we can save them as 8-bit images and not lose useful information - not lose any actual information about the sound wave at all.

Heisenberg's Uncertainty Principle puts a limit on how much resolution a spectrogram can have - the more we zoom in on a wave, the more blurry it becomes.

Time stretching by overlapping (whisper uses a 60% overlap) mitigates this, to a point. But after that more precision doesn't mean more accuracy, and may actually cause noise:

Indeed, we only need 1.0e-1 precision to get accurate results, and rounding to 1.0e-1 seems more accurate for some difficult transcriptions.

Consider these samples from the jfk speech used in the original whisper.py tests:

[src/lib.rs:93] &mel_spectrogram[10..20] = [
    0.15811597,
    0.26561865,
    0.07558561,
    0.19564378,
    0.16745868,
    0.21617787,
    -0.29193184,
    0.12279237,
    0.13897367,
    -0.17434756,
]

[src/lib.rs:92] &mel_spectrogram_rounded[10..20] = [
    0.2,
    0.3,
    0.1,
    0.2,
    0.2,
    0.2,
    -0.3,
    0.1,
    0.1,
    -0.2,
]

Once quantised, the spectrograms are the same:

(top: not rounded, botton: rounded to 1.0e-1)

A lot has to do with how speech can be encapsulated almost entirely in the frequency domain, and how effectively the mel scale divides those frequencies into 80 bins. 8-bytes of 0-255 grayscale is probably overkill even to measure the total power in each of those bins - it could be compressed even further.

wavey-ai/mel-spec