# 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.

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

## How to use
```rust
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 implement
    // 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)
    }
}
```

### How to scale values
```rust
// e.g. like this
fn get_scale_to_one_fn_factory() -> SpectrumTotalScaleFunctionFactory{
    Box::new(
        move |min: f32, max: f32, average: f32, median: f32| {
            Box::new(
                move |x| x/max
            )
        }
    )
}
fn main() {
    // ...
    let spectrum_hann_window = samples_fft_to_spectrum(
        &hann_window,
        44100,
        FrequencyLimit::All,
        None,
        // optional total scaling at the end; see doc comments
        Some(get_scale_to_one_fn_factory()),
    );
}
```

## 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 noise.
![Visualization of spectrum 0-4000Hz of layered sine signal (50, 1000, 3777 Hz)) with no window function.](spectrum_sine_waves_50_1000_3777hz--no-window.png "Some noise due to clipping in original signal.")

### Hann window function on samples before FFT
Peaks (50, 1000, 3777 Hz) are clearly visible and overall noise is much smaller, but a few noisy peaks.
![Visualization of spectrum 0-4000Hz of layered sine signal (50, 1000, 3777 Hz)) with Hann window function.](spectrum_sine_waves_50_1000_3777hz--no-window.png "Much less noise but noisy peaks.")

### Hamming window function on samples before FFT
Peaks (50, 1000, 3777 Hz) are clearly visible and overall noise is smaller.
![Visualization of spectrum 0-4000Hz of layered sine signal (50, 1000, 3777 Hz)) with Hamming window function.](spectrum_sine_waves_50_1000_3777hz--no-window.png "Less overall noise.")

## 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.
