https://github.com/sinshu/fftflat
A fast FFT implementation in pure C#
https://github.com/sinshu/fftflat
audio dsp fft math numerics
Last synced: 11 months ago
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A fast FFT implementation in pure C#
- Host: GitHub
- URL: https://github.com/sinshu/fftflat
- Owner: sinshu
- License: other
- Created: 2023-10-20T10:12:11.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-12-02T00:48:56.000Z (over 1 year ago)
- Last Synced: 2025-03-18T13:15:17.733Z (over 1 year ago)
- Topics: audio, dsp, fft, math, numerics
- Language: C#
- Homepage:
- Size: 197 KB
- Stars: 18
- Watchers: 1
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE.md
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README
# FftFlat
The purpose of this library is to provide a fast FFT (Fast Fourier Transform) implementation, entirely in pure C#.
This library is adapted from [General Purpose FFT Package by Ooura](https://www.kurims.kyoto-u.ac.jp/~ooura/fft.html),
modified to be compatible with the .NET Standard complex number type.
> [!NOTE]
> This library was created as an FFT implementation for [NumFlat](https://github.com/sinshu/numflat),
> a general purpose numerical computing library written in pure C#.
> If you're interested in numerical computing with C#, please check out [NumFlat](https://github.com/sinshu/numflat).
## Features
* __Fast:__ More than four times as fast as the managed FFT implementation in Math.NET Numerics.
* __Lightweight:__ Small code size, with no dependencies other than .NET Standard 2.1.
## Installation
[The NuGet package](https://www.nuget.org/packages/FftFlat) is available:
```ps1
Install-Package FftFlat
```
If you don't want to add a DLL, copy [the .cs files](https://github.com/sinshu/fftflat/tree/main/FftFlat) to your project.
## Usage
First, add a `using` statement for the `FftFlat` namespace.
```cs
using FftFlat;
```
To perform FFT or IFFT, create an instance of `FastFourierTransform` and call the appropriate method.
```cs
var samples = new Complex[1024];
samples[0] = 1;
var fft = new FastFourierTransform(1024);
fft.Forward(samples);
```
## Important Notices
Ooura's original FFT implementation is based on a different definition from that used in Math.NET Numerics. FFtFlat adjusts this difference, ensuring its results match those of [Math.NET Numerics' FFT](https://numerics.mathdotnet.com/api/MathNet.Numerics.IntegralTransforms/Fourier.htm).
Normalization is only done during the IFFT.
This is similar to using `FourierOptions.AsymmetricScaling` for FFT in Math.NET Numerics.
Note that the `FastFourierTransform` object is not thread-safe.
If performing FFT across multiple threads, ensure a separate instance is provided for each thread.
## Demo
In this demo video, the spectrum is visualized in real-time as sound is played using `AudioStream` of [RayLib-CsLo](https://github.com/NotNotTech/Raylib-CsLo).
https://www.youtube.com/watch?v=KTpG_z_ejZ0
[](https://www.youtube.com/watch?v=KTpG_z_ejZ0)
## Performance
The following is a benchmark comparing this with other pure C# FFT implementations.
In this benchmark, the time taken to perform FFT and IFFT on a random signal was measured.
The FFT lengths used were powers of two, ranging from 256 to 8192.
### Complex FFT
| Method | Length | Mean | Error | StdDev | Median | Allocated |
|--------- |------- |-------------:|----------:|----------:|-------------:|----------:|
| FftFlat | 2048 | 17.664 μs | 0.0444 μs | 0.0415 μs | 17.664 μs | - |
| FftSharp | 2048 | 203.196 μs | 0.6797 μs | 0.6358 μs | 203.137 μs | - |
| MathNet | 2048 | 71.875 μs | 0.5197 μs | 0.4340 μs | 71.836 μs | 25660 B |
| FftFlat | 4096 | 36.990 μs | 0.2119 μs | 0.1983 μs | 37.014 μs | - |
| FftSharp | 4096 | 439.636 μs | 1.4182 μs | 1.3265 μs | 439.750 μs | - |
| MathNet | 4096 | 157.341 μs | 0.6241 μs | 0.5211 μs | 157.270 μs | 33650 B |
| FftFlat | 8192 | 83.777 μs | 0.1272 μs | 0.1128 μs | 83.769 μs | - |
| FftSharp | 8192 | 954.118 μs | 2.7325 μs | 2.5560 μs | 953.749 μs | - |
| MathNet | 8192 | 343.381 μs | 5.1914 μs | 4.8561 μs | 339.598 μs | 47481 B |
### Real FFT
| Method | Length | Mean | Error | StdDev | Median | Allocated |
|--------- |------- |-------------:|----------:|----------:|-------------:|----------:|
| FftFlat | 2048 | 10.303 μs | 0.0359 μs | 0.0336 μs | 10.296 μs | - |
| FftSharp | 2048 | 208.290 μs | 0.6072 μs | 0.5679 μs | 208.354 μs | 98416 B |
| MathNet | 2048 | 77.546 μs | 0.5357 μs | 0.4749 μs | 77.576 μs | 90663 B |
| FftFlat | 4096 | 22.647 μs | 0.1032 μs | 0.0966 μs | 22.640 μs | - |
| FftSharp | 4096 | 454.185 μs | 1.5450 μs | 1.4452 μs | 454.305 μs | 196720 B |
| MathNet | 4096 | 179.540 μs | 1.2277 μs | 1.1484 μs | 179.667 μs | 165035 B |
| FftFlat | 8192 | 47.374 μs | 0.2011 μs | 0.1881 μs | 47.337 μs | - |
| FftSharp | 8192 | 1,034.310 μs | 3.5584 μs | 3.1544 μs | 1,034.975 μs | 393356 B |
| MathNet | 8192 | 417.383 μs | 0.5965 μs | 0.5288 μs | 417.317 μs | 309285 B |
## Todo
* ✅ FFT for power-of-two length samples
* ✅ Real FFT
* ⬜ Other transformations (such as cosine transform)
* ⬜ Support for 32-bit floating-point numbers
* ⬜ FFT for arbitrary length samples
## License
FftFlat is available under [the MIT license](LICENSE.md).