#fft #spectrum #audio #dsp #frequencies

no-std spectrum-analyzer

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.

14 releases (4 breaking)

0.5.0 Apr 10, 2021
0.4.6 Apr 7, 2021
0.4.1 Mar 30, 2021
0.3.0 Mar 22, 2021
0.1.1 Mar 13, 2021

#28 in No standard library

Download history 67/week @ 2021-03-11 34/week @ 2021-03-18 56/week @ 2021-03-25 80/week @ 2021-04-01 56/week @ 2021-04-08

87 downloads per month
Used in lowpass-filter

MIT license

260KB
1K SLoC

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 several FFT implementations which you can choose from during compilation time via Cargo features.

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

The MSRV (minimum supported Rust version) is 1.51 Stable because this crate needs the "resolver" feature of Cargo to cope with build problems occurring in no_std-builds.

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

Please see file /EDUCATIONAL.md.

How to use (including no_std-environments)

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:

FFT implementation as compile time configuration via Cargo features

By default this crate uses the real-module from the great microfft-crate. It's the fastest implementation and as of version v0.5.0 there should be no valid reason why you should ever change this. The multiple features are there mainly for educational reasons and to support me while programming/testing.

Cargo.toml

# ONLY NEEDED FOR `no_std`-builds!
# fixes `no_std` build problems caused by wrong feature resolution of Cargo
# This works since Rust 1.51 (stable)
resolver = "2"

# by default feature "microfft-real" is used
spectrum-analyzer = "<latest>"

your_binary.rs

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,
        // sampling 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_hann_window.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 like BasicSpectrumScalingFunction 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 (rustfft/complex) to spectrum with 4096 samples ≈240µs
FFT (rustfft/complex) to spectrum with 16384 samples ≈740µs
FFT (microfft/real) to spectrum with 4096 samples ≈120µs

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 @ 44100Hz sampling 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. Visualization of spectrum 0-4000Hz of layered sine signal (50, 1000, 3777 Hz)) with no window function.

Spectrum with 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. Visualization of spectrum 0-4000Hz of layered sine signal (50, 1000, 3777 Hz)) with Hann window function.

Spectrum with 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. Visualization of spectrum 0-4000Hz of layered sine signal (50, 1000, 3777 Hz)) with Hamming window function.

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.

Good resources with more information

Also check out my blog post! https://phip1611.de/2021/03/programmierung-und-skripte/frequency-spectrum-analysis-with-fft-in-rust/

Dependencies

~0.4–1MB
~18K SLoC