# Rust: library for frequency spectrum analysis using FFT

An easy to use and fast `no_std`

library (with `alloc`

) to get the frequency
spectrum of a digital signal (e.g. audio) using FFT.

The **MSRV** (minimum supported Rust version) is `1.63.0`

.

## I want to understand how FFT can be used to get a spectrum

Please see file /EDUCATIONAL.md.

## How to use (including `no_std`

-contexts)

Most tips and comments are located inside the code, so please check out the repository on GitHub! Anyway, the most basic usage looks like this:

### Cargo.toml

```
# by default feature "microfft-real" is used
[]
= "<latest version, see crates.io>"
```

### your_binary.rs

```
use ;
use hann_window;
use divide_by_N_sqrt;
/// Minimal example.
```

## Performance

*Measurements taken on i7-1165G7 @ 2.80GHz (Single-threaded) with optimized build*

I've tested multiple FFT implementations. Below you can find out why I decided
to use `microfft::real`

. It is not only the fastest, but also works in `no_std`

contexts.

Operation | Time |
---|---|

Hann Window with 4096 samples | ≈68µs |

Hamming Window with 4096 samples | ≈118µs |

FFT (`rustfft` ) to spectrum with 4096 samples |
≈170µs |

FFT (`microfft::real` ) to spectrum with 4096 samples |
≈90µs |

FFT (`microfft::complex` ) to spectrum with 4096 samples |
≈250µs |

## Example Visualizations

In the following examples you can see a basic visualization of the spectrum from `0 to 4000Hz`

for
a layered signal of sine waves of `50`

, `1000`

, and `3777Hz`

@ `44100Hz`

sampling rate. The peaks for the
given frequencies are clearly visible. Each calculation was done with `2048`

samples, i.e. ≈46ms of audio signal.

**The noise (wrong peaks) also comes from clipping of the added sine waves!**

### Spectrum *without window function* on samples

Peaks (50, 1000, 3777 Hz) are clearly visible but also some noise.

### Spectrum with *Hann window function* on samples before FFT

Peaks (50, 1000, 3777 Hz) are clearly visible and Hann window reduces noise a little. Because this example has few noise, you don't see much difference.

### Spectrum with *Hamming window function* on samples before FFT

Peaks (50, 1000, 3777 Hz) are clearly visible and Hamming window reduces noise a little. Because this example has few noise, you don't see much difference.

## Live Audio + Spectrum Visualization

Execute example `$ cargo run --release --example live-visualization`

. It will
show you how you can visualize audio data in realtime + the current spectrum.

## Building and Executing Tests

To execute tests you need the package `libfreetype6-dev`

(on Ubuntu/Debian).
This is required because not all tests are "automatic unit tests" but also tests
that you need to check visually, by looking at the generated diagram of the
spectrum.

## Trivia / FAQ

### Why f64 and no f32?

I tested f64 but the additional accuracy doesn't pay out the ~40% calculation overhead (on x86_64).

### What can I do against the noise?

Apply a window function, like Hann window or Hamming window.

## Good resources with more information

- Interpreting FFT Results: https://www.gaussianwaves.com/2015/11/interpreting-fft-results-complex-dft-frequency-bins-and-fftshift/
- FFT basic concepts: https://www.youtube.com/watch?v=z7X6jgFnB6Y
- „The Fundamentals of FFT-Based Signal Analysis and Measurement“ https://www.sjsu.edu/people/burford.furman/docs/me120/FFT_tutorial_NI.pdf
- Fast Fourier Transforms (FFTs) and Windowing: https://www.youtube.com/watch?v=dCeHOf4cJE0

Also check out my blog post.