Rust: library for frequency spectrum analysis using FFT

A simple and fast no_std library to get the frequency spectrum of a digital signal (e.g. audio) using FFT. It follows the KISS principle and consists of simple building blocks/optional features. In short, this is a convenient wrapper around the great rustfft library.

I'm not an expert on digital signal processing. Code contributions are highly welcome! :)

How to use

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:

use spectrum_analyzer::{samples_fft_to_spectrum, FrequencyLimit};
use spectrum_analyzer::windows::hann_window;

fn main() {
    // This lib also works in `no_std` environments!
    let samples: &[f32] = get_samples(); // TODO you need to implement the samples source
    // apply hann window for smoothing; length must be a power of 2 for the FFT
    let hann_window = hann_window(&samples[0..4096]);
    // calc spectrum
    let spectrum_hann_window = samples_fft_to_spectrum(
        // (windowed) samples
        &hann_window,
        // sample rate
        44100,
        // optional frequency limit: e.g. only interested in frequencies 50 <= f <= 150?
        FrequencyLimit::All,
        // optional per element scaling function, e.g. `20 * log10(x)`; see doc comments
        None,
        // optional total scaling at the end; see doc comments
        None,
    );

    for (fr, fr_val) in spectrum_hamming_window.raw_data().iter() {
        println!("{}Hz => {}", fr, fr_val)
    }
}

Scaling the frequency values/amplitudes

As already mentioned, there are lots of comments in the code. Short story is: Type ComplexSpectrumScalingFunction can do anything whereas BasicSpectrumScalingFunction is easier to write, especially for Rust beginners.

Performance

Measurements taken on i7-8650U @ 3 Ghz (Single-Core) with optimized build

Operation	Time
Hann Window with 4096 samples	≈70µs
Hamming Window with 4096 samples	≈10µs
Hann Window with 16384 samples	≈175µs
Hamming Window with 16384 samples	≈44µs
FFT to spectrum with 4096 samples @ 44100Hz	≈240µs
FFT to spectrum with 16384 samples @ 44100Hz	≈740µs

Example visualization

In the following example you can see a basic visualization of frequencies 0 to 4000Hz for a layered signal of sine waves of 50, 1000, and 3777Hz @ 41000Hz sample rate. The peaks for the given frequencies are clearly visible. Each calculation was done with 2048 samples, i.e. ≈46ms.

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.

Hann window function on samples before FFT

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

Hamming window function on samples before FFT

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

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. But I'm not an expert on this.

Jikstra / spectrum-analyzer