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https://github.com/jurihock/qdft

Constant-Q Sliding DFT in C++, Rust and Python
https://github.com/jurihock/qdft

algorithms audio audio-processing constant-q constant-q-transform cpp cqt dft digital-signal-processing dsp fft library python qdft rust sdft signal-processing sliding-dft variable-q vqt

Last synced: about 2 months ago
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Constant-Q Sliding DFT in C++, Rust and Python

Host: GitHub
URL: https://github.com/jurihock/qdft
Owner: jurihock
License: mit
Created: 2023-01-05T22:17:29.000Z (almost 2 years ago)
Default Branch: main
Last Pushed: 2023-11-28T10:47:09.000Z (about 1 year ago)
Last Synced: 2024-10-13T16:31:06.480Z (2 months ago)
Topics: algorithms, audio, audio-processing, constant-q, constant-q-transform, cpp, cqt, dft, digital-signal-processing, dsp, fft, library, python, qdft, rust, sdft, signal-processing, sliding-dft, variable-q, vqt
Language: Python
Homepage:
Size: 2.48 MB
Stars: 31
Watchers: 2
Forks: 3
Open Issues: 7
Metadata Files:
- Readme: README.md
- License: LICENSE
- Citation: CITATION.cff

Awesome Lists containing this project

README

        # Constant-Q Sliding DFT in C++, Rust, and Python

![language](https://img.shields.io/badge/languages-C%2B%2B%20Rust%20Python-blue)

![license](https://img.shields.io/github/license/jurihock/sdft?color=green)

![pypi](https://img.shields.io/pypi/v/qdft?color=gold)

![creates](https://img.shields.io/crates/v/qdft?color=gold)

Forward and inverse Constant-Q Sliding DFT (QDFT) according to [[1]](#1) with following features:

- Arbitrary octave resolution ([quarter tone](https://en.wikipedia.org/wiki/Quarter_tone) by default)

- Built-in parameterizable cosine family window (Hann by default)

- Customizable time and frequency domain data type in C++

- Endless single or multiple sample processing at once

- Optional quality control parameter to smoothly reduce low frequency bandwidth and improve the time resolution

- Optional analysis latency control parameter

- Real-time analysis and synthesis capability

The Constant-Q Sliding Discrete Fourier Transform (QDFT) is a recursive approach to compute the Fourier transform sample by sample. This is an efficient implementation without the FFT calculus. Just define an arbitrary frequency range and octave resolution to obtain the corresponding DFT estimate. In contrast to the linear [SDFT](https://github.com/jurihock/sdft), frequency bins of the QDFT are logarithmically spaced. Thus, both high and low frequencies are resolved with the same quality, which is particularly useful for audio analysis. Based on the QDFT, a chromagram feature with detailed instantaneous frequency estimation is planned for the future release.

## WIP

- [x] Readme

- [ ] Docstrings

- [x] PyPI package [qdft](https://pypi.org/project/qdft)

- [x] Rust package [qdft](https://crates.io/crates/qdft)

- [ ] Sliding [chromagram](https://en.wikipedia.org/wiki/Chroma_feature) as a bonus (a draft is already included in the Python package)

## Basic usage

### C++

```c++

#include  // see also cpp folder

double sr = 44100;                             // sample rate in hertz

std::pair bw = { 50, sr / 2 }; // lowest and highest frequency in hertz to be resolved

double r = 24;                                 // octave resolution, e.g. number of DFT bins per octave

QDFT qdft(sr, bw, r); // create qdft plan for custom time and frequency domain data types

size_t n = ...;         // number of samples

size_t m = qdft.size(); // number of dft bins

float* x = ...; // analysis samples of shape (n)

float* y = ...; // synthesis samples of shape (n)

std::complex* dft = ...; // dft matrix of shape (n, m)

qdft.qdft(n, x, dft);  // extract dft matrix from input samples

qdft.iqdft(n, dft, y); // synthesize output samples from dft matrix

```

The time domain data type defaults to `float` and the frequency domain data type to `double`.

### Rust

```rust

use qdft::QDFT; // see also rust folder

// just a shortcut for our complex number type

#[allow(non_camel_case_types)]

type c64 = num::complex::Complex;

// zero number trait, e.g. c64::zero()

use num::Zero;

let samplerate = 44100.0;                 // sample rate in hertz

let bandwidth = (50.0, samplerate / 2.0); // lowest and highest frequency in hertz to be resolved

let resolution = 24.0;                    // octave resolution, e.g. number of DFT bins per octave

let latency = 0.0;                        // analysis latency adjustment between -1 and +1

let window = Some((0.5, -0.5));           // hann window coeffs

// create qdft plan for custom time and frequency domain data types

let mut qdft = QDFT::::new(

    samplerate,

    bandwidth,

    resolution,

    latency,

    window);

let n = ...;         // number of samples

let m = qdft.size(); // number of dft bins

let mut x = vec![f32::zero(); n]; // analysis samples of shape (n)

let mut y = vec![f32::zero(); n]; // synthesis samples of shape (n)

let mut dft = vec![c64::zero(); n * m]; // dft matrix of shape (n, m)

qdft.qdft(&x, &mut dft);  // extract dft matrix from input samples

qdft.iqdft(&dft, &mut y); // synthesize output samples from dft matrix

```

Alternatively use [ndarray](https://github.com/rust-ndarray/ndarray) instead of a flat array to allocate the DFT matrix, as shown in the `analysis.rs` example.

### Python

```python

from qdft import QDFT # see also python folder

sr = 44100        # sample rate in hertz

bw = (50, sr / 2) # lowest and highest frequency in hertz to be resolved

r = 24            # octave resolution, e.g. number of DFT bins per octave

qdft = QDFT(sr, bw, r) # create qdft plan

n = ...       # number of samples

m = qdft.size # number of dft bins (if need to know in advance)

x = ... # analysis samples of shape (n)

dft = qdft.qdft(x)  # extract dft matrix of shape (n, m) from input samples

y = qdft.iqdft(dft) # synthesize output samples from dft matrix

```

Feel free to obtain current version from [PyPI](https://pypi.org/project/qdft) by executing `pip install qdft`.

## Examples

| QDFT | Chroma12 |

| :--: | :------: |

| ![SDFT](https://github.com/jurihock/qdft/raw/main/python/examples/face.png) | ![STFT](https://github.com/jurihock/qdft/raw/main/python/examples/cmajor.png) |

| [face.py](https://github.com/jurihock/qdft/blob/main/python/examples/face.py) | [cmajor.py](https://github.com/jurihock/qdft/blob/main/python/examples/cmajor.py) |

| ![SDFT](https://github.com/jurihock/qdft/raw/main/python/examples/face.wav.png) | ![STFT](https://github.com/jurihock/qdft/raw/main/python/examples/cmajor.wav.png) |

## See also

If you're interested in Sliding DFT with *linear* frequency resolution, don't forget to browse my [jurihock/sdft](https://github.com/jurihock/sdft) project!

## References

1. Russell Bradford et al. (2008). Sliding with a Constant Q. International Conference on Digital Audio Effects. https://www.dafx.de/paper-archive/2008/papers/dafx08_63.pdf

2. Russell Bradford et al. (2005). Sliding is Smoother Than Jumping. International Computer Music Conference Proceedings. http://hdl.handle.net/2027/spo.bbp2372.2005.086

3. Eric Jacobsen and Peter Kootsookos (2007). Fast, Accurate Frequency Estimators. IEEE Signal Processing Magazine. https://ieeexplore.ieee.org/document/4205098

## License

[github.com/jurihock/qdft](https://github.com/jurihock/qdft) is licensed under the terms of the MIT license.

For details please refer to the accompanying [LICENSE](https://github.com/jurihock/qdft/raw/main/LICENSE) file distributed with it.