spectrum-analyzer 0.2.2

/*
MIT License

Copyright (c) 2021 Philipp Schuster

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
//! 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.

#![no_std]

// use alloc crate, because this is no_std
// #[macro_use]
extern crate alloc;
// use std in tests
#[cfg(test)]
#[macro_use]
extern crate std;

use alloc::vec::Vec;

use rustfft::algorithm::Radix4;
use rustfft::num_complex::Complex32;
use rustfft::{Fft, FftDirection};

pub use crate::frequency::{Frequency, FrequencyValue};
pub use crate::limit::FrequencyLimit;
pub use crate::spectrum::{FrequencySpectrum, SpectrumTotalScaleFunctionFactory};
use core::convert::identity;

mod frequency;
mod limit;
mod spectrum;
#[cfg(test)]
mod tests;
pub mod windows;

/// Takes an array of samples (length must be a power of 2),
/// e.g. 2048, applies an FFT (using library `rustfft`) on it
/// and returns all frequencies with their volume/magnitude.
///
/// * `samples` raw audio, e.g. 16bit audio data but as f32.
///             You should apply an window function (like Hann) on the data first.
///             The final frequency resolution is `sample_rate / (N / 2)`
///             e.g. `44100/(16384/2) == 5.383Hz`, i.e. more samples => better accuracy
/// * `sampling_rate` sampling_rate, e.g. `44100 [Hz]`
/// * `frequency_limit` Frequency limit. See [`FrequencyLimit´]
/// * `per_element_scaling_fn` Optional per element scaling function, e.g. `20 * log(x)`.
///                            To see where this equation comes from, check out
///                            this paper:
///                            https://www.sjsu.edu/people/burford.furman/docs/me120/FFT_tutorial_NI.pdf
/// * `total_scaling_fn` See [`crate::spectrum::SpectrumTotalScaleFunctionFactory`].
///
/// ## Returns value
/// New object of type [`FrequencySpectrum`].
pub fn samples_fft_to_spectrum(
    samples: &[f32],
    sampling_rate: u32,
    frequency_limit: FrequencyLimit,
    per_element_scaling_fn: Option<&dyn Fn(f32) -> f32>,
    total_scaling_fn: Option<SpectrumTotalScaleFunctionFactory>,
) -> FrequencySpectrum {
    // With FFT we transform an array of time-domain waveform samples
    // into an array of frequency-domain spectrum samples
    // https://www.youtube.com/watch?v=z7X6jgFnB6Y

    // FFT result has same length as input

    // convert to Complex for FFT
    let mut buffer = samples_to_complex(samples);

    // a power of 2, like 1024 or 2048
    let fft_len = samples.len();

    // apply the fft
    let fft = Radix4::new(fft_len, FftDirection::Forward);
    fft.process(&mut buffer);

    // we only need the first half of the results with FFT
    // because of Nyquist theorem. 44100hz sampling frequency
    // => 22050hz maximum detectable frequency

    // This function:
    // 1) calculates the corresponding frequency of each index in the FFT result
    // 2) filters out unwanted frequencies
    // 3) calculates the magnitude (absolute value) at each frequency index for each complex value
    // 4) optionally scales the magnitudes
    // 5) collects everything into the struct "FrequencySpectrum"
    fft_result_to_frequency_to_magnitude_map(
        buffer,
        sampling_rate,
        frequency_limit,
        per_element_scaling_fn,
        total_scaling_fn,
    )
}

/// Converts all samples to a complex number (imaginary part is set to two)
/// as preparation for the FFT.
///
/// ## Parameters
/// `samples` Input samples.
///
/// ## Return value
/// New vector of samples but as Complex data type.
#[inline(always)]
fn samples_to_complex(samples: &[f32]) -> Vec<Complex32> {
    samples
        .iter()
        .map(|x| Complex32::new(x.clone(), 0.0))
        .collect::<Vec<Complex32>>()
}

/// Transforms the complex numbers of the first half of the FFT results (only the first
/// half is relevant, Nyquist theorem) to their magnitudes.
///
/// ## Parameters
/// * `fft_result` Result buffer from FFT. Has the same length as the samples array.
/// * `sampling_rate` sampling_rate, e.g. `44100 [Hz]`
/// * `frequency_limit` Frequency limit. See [`FrequencyLimit´]
/// * `per_element_scaling_fn` Optional per element scaling function, e.g. `20 * log(x)`.
///                            To see where this equation comes from, check out
///                            this paper:
///                            https://www.sjsu.edu/people/burford.furman/docs/me120/FFT_tutorial_NI.pdf
/// * `total_scaling_fn` See [`crate::spectrum::SpectrumTotalScaleFunctionFactory`].
///
/// ## Return value
/// New object of type [`FrequencySpectrum`].
#[inline(always)]
fn fft_result_to_frequency_to_magnitude_map(
    fft_result: Vec<Complex32>,
    sampling_rate: u32,
    frequency_limit: FrequencyLimit,
    per_element_scaling_fn: Option<&dyn Fn(f32) -> f32>,
    total_scaling_fn: Option<SpectrumTotalScaleFunctionFactory>,
) -> FrequencySpectrum {
    let maybe_min = frequency_limit.maybe_min();
    let maybe_max = frequency_limit.maybe_max();

    let samples_len = fft_result.len();

    // collect frequency => frequency value in Vector of Pairs/Tuples
    let frequency_vec = fft_result
        .into_iter()
        // take first half; half of input length
        .take(samples_len / 2)
        // get (index, complex)-pairs
        .enumerate()
        // calc index => corresponding frequency
        .map(|(fft_index, complex)| {
            (
                fft_index_to_corresponding_frequency(fft_index, samples_len as u32, sampling_rate),
                complex,
            )
        })
        // #######################
        // ### BEGIN filtering: results in lower calculation and memory overhead!
        // check lower bound frequency (inclusive)
        .filter(|(fr, _complex)| {
            if let Some(min_fr) = maybe_min {
                // inclusive!
                *fr >= min_fr
            } else {
                true
            }
        })
        // check upper bound frequency (inclusive)
        .filter(|(fr, _complex)| {
            if let Some(max_fr) = maybe_max {
                // inclusive!
                *fr <= max_fr
            } else {
                true
            }
        })
        // ### END filtering
        // #######################
        // calc magnitude: sqrt(re*re + im*im) (re: real part, im: imaginary part)
        .map(|(fr, complex)| (fr, complex.norm()))
        // apply optionally scale function
        .map(|(fr, val)| (fr, per_element_scaling_fn.unwrap_or(&identity)(val)))
        // transform to my thin convenient orderable  f32 wrappers
        .map(|(fr, val)| (Frequency::from(fr), FrequencyValue::from(val)))
        .collect::<Vec<(Frequency, FrequencyValue)>>();

    // create spectrum object
    let fs = FrequencySpectrum::new(frequency_vec);
    // optionally scale
    if let Some(total_scaling_fn) = total_scaling_fn {
        fs.apply_total_scaling_fn(total_scaling_fn)
    }
    fs
}

/// Calculate what index in the FFT result corresponds to what frequency.
///
/// ## Parameters
/// * `fft_index` Index in FFT result buffer. If `samples.len() == 2048` then this is in `{0, 1, ..., 1023}`
/// * `samples_len` Number of samples put into the FFT
/// * `sampling_rate` sampling_rate, e.g. `44100 [Hz]`
///
/// ## Return value
#[inline(always)]
fn fft_index_to_corresponding_frequency(
    fft_index: usize,
    samples_len: u32,
    sampling_rate: u32,
) -> f32 {
    // Explanation for the algorithm:
    // https://stackoverflow.com/questions/4364823/

    // samples                    : [0], [1], [2], [3], ... , ..., [2047] => 2048 samples for example
    // FFT Result                 : [0], [1], [2], [3], ... , ..., [2047]
    // Relevant part of FFT Result: [0], [1], [2], [3], ... , [1023]
    //                               ^                         ^
    // Frequency                  : 0Hz, .................... Sampling Rate/2
    //                              0Hz is also called        (e.g. 22050Hz @ 44100H sampling rate)
    //                              "DC Component"

    // frequency step/resolution is for example: 1/1024 * 44100
    // 1024: relevant FFT result, 2048 samples, 44100 sample rate

    fft_index as f32 / samples_len as f32 * sampling_rate as f32
}