spectrum_analyzer/

lib.rs

/*
MIT License

Copyright (c) 2023 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.
*/
//! 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.
//!
//! ## Examples
//! ### Scaling via dynamic closure
//! ```rust
//! use spectrum_analyzer::{samples_fft_to_spectrum, FrequencyLimit};
//! // get data from audio source
//! let samples = vec![0.0, 1.1, 5.5, -5.5];
//! let res = samples_fft_to_spectrum(
//!         &samples,
//!         44100,
//!         FrequencyLimit::All,
//!         Some(&|val, info| val - info.min),
//! );
//! ```
//! ### Scaling via static function
//! ```rust
//! use spectrum_analyzer::{samples_fft_to_spectrum, FrequencyLimit};
//! use spectrum_analyzer::scaling::divide_by_N_sqrt;
//! // get data from audio source
//! let samples = vec![0.0, 1.1, 5.5, -5.5];
//! let res = samples_fft_to_spectrum(
//!         &samples,
//!         44100,
//!         FrequencyLimit::All,
//!         // Recommended scaling/normalization by `rustfft`.
//!         Some(&divide_by_N_sqrt),
//! );
//! ```

#![deny(
    clippy::all,
    clippy::cargo,
    clippy::nursery,
    clippy::must_use_candidate,
    clippy::undocumented_unsafe_blocks,
    // clippy::restriction,
    // clippy::pedantic
)]
// now allow a few rules which are denied by the above statement
// --> they are ridiculous and not necessary
#![allow(
    clippy::suboptimal_flops,
    clippy::redundant_pub_crate,
    clippy::fallible_impl_from,
    clippy::float_cmp
)]
#![deny(missing_docs)]
#![deny(missing_debug_implementations)]
#![deny(rustdoc::all)]
#![no_std]

#[cfg_attr(test, macro_use)]
#[cfg(test)]
extern crate std;

#[macro_use]
extern crate alloc;

pub use crate::frequency::{Frequency, FrequencyValue};
pub use crate::limit::FrequencyLimit;
pub use crate::limit::FrequencyLimitError;
pub use crate::spectrum::FrequencySpectrum;

use crate::error::SpectrumAnalyzerError;
use crate::fft::{Complex32, FftImpl};
use crate::scaling::SpectrumScalingFunction;
use alloc::vec::Vec;

pub mod error;
mod fft;
mod frequency;
mod limit;
pub mod scaling;
mod spectrum;
pub mod windows;

// test module for large "integration"-like tests
#[cfg(test)]
mod tests;

/// Takes an array of samples (length must be a power of 2),
/// e.g. 2048, applies an FFT (using the specified FFT implementation) on it
/// and returns all frequencies with their volume/magnitude.
///
/// By default, no normalization/scaling is done at all and the results,
/// i.e. the frequency magnitudes/amplitudes/values are the raw result from
/// the FFT algorithm, except that complex numbers are transformed
/// to their magnitude.
///
/// * `samples` raw audio, e.g. 16bit audio data but as f32.
///   You should apply a 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/frequency resolution. The amount of samples must
///   be a power of 2. If you don't have enough data, provide zeroes.
/// * `sampling_rate` The used sampling_rate, e.g. `44100 [Hz]`.
/// * `frequency_limit` The [`FrequencyLimit`].
/// * `scaling_fn` See [`SpectrumScalingFunction`] for details.
///
/// ## Returns value
/// New object of type [`FrequencySpectrum`].
///
/// ## Examples
/// ### Scaling via dynamic closure
/// ```rust
/// use spectrum_analyzer::{samples_fft_to_spectrum, FrequencyLimit};
/// // get data from audio source
/// let samples = vec![0.0, 1.1, 5.5, -5.5];
/// let res = samples_fft_to_spectrum(
///         &samples,
///         44100,
///         FrequencyLimit::All,
///         Some(&|val, info| val - info.min),
///  );
/// ```
/// ### Scaling via static function
/// ```rust
/// use spectrum_analyzer::{samples_fft_to_spectrum, FrequencyLimit};
/// use spectrum_analyzer::scaling::scale_to_zero_to_one;
/// // get data from audio source
/// let samples = vec![0.0, 1.1, 5.5, -5.5];
/// let res = samples_fft_to_spectrum(
///         &samples,
///         44100,
///         FrequencyLimit::All,
///         Some(&scale_to_zero_to_one),
///  );
/// ```
///
/// ## Panics
/// * When `samples.len()` isn't a power of two less than or equal to `16384` and `microfft` is used
pub fn samples_fft_to_spectrum(
    samples: &[f32],
    sampling_rate: u32,
    frequency_limit: FrequencyLimit,
    scaling_fn: Option<&SpectrumScalingFunction>,
) -> Result<FrequencySpectrum, SpectrumAnalyzerError> {
    // everything below two samples is unreasonable
    if samples.len() < 2 {
        return Err(SpectrumAnalyzerError::TooFewSamples);
    }
    // do several checks on input data
    if samples.iter().any(|x| x.is_nan()) {
        return Err(SpectrumAnalyzerError::NaNValuesNotSupported);
    }
    if samples.iter().any(|x| x.is_infinite()) {
        return Err(SpectrumAnalyzerError::InfinityValuesNotSupported);
    }
    if !samples.len().is_power_of_two() {
        return Err(SpectrumAnalyzerError::SamplesLengthNotAPowerOfTwo);
    }
    let max_detectable_frequency = sampling_rate as f32 / 2.0;
    // verify frequency limit: unwrap error or else ok
    frequency_limit
        .verify(max_detectable_frequency)
        .map_err(SpectrumAnalyzerError::InvalidFrequencyLimit)?;

    // 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
    // (but when we interpret the result, we don't need all indices)

    // applies the f32 samples onto the FFT algorithm implementation
    // chosen at compile time (via Cargo feature).
    // If a complex FFT implementation was chosen, this will internally
    // transform all data to Complex numbers.
    let fft_res = FftImpl::calc(samples);

    // 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_spectrum(
        samples.len(),
        &fft_res,
        sampling_rate,
        frequency_limit,
        scaling_fn,
    )
}

/// Transforms the FFT result into the spectrum by calculating the corresponding frequency of each
/// FFT result index and optionally calculating the magnitudes of the complex numbers if a complex
/// FFT implementation is chosen.
///
/// ## Parameters
/// * `samples_len` Length of samples. This is a dedicated field because it can't always be
///   derived from `fft_result.len()`. There are for example differences for
///   `fft_result.len()` in real and complex FFT algorithms.
/// * `fft_result` Result buffer from FFT. Has the same length as the samples array.
/// * `sampling_rate` The used sampling_rate, e.g. `44100 [Hz]`.
/// * `frequency_limit` The [`FrequencyLimit`].
/// * `scaling_fn` See [`SpectrumScalingFunction`] for details.
///
/// ## Return value
/// New object of type [`FrequencySpectrum`].
#[inline]
fn fft_result_to_spectrum(
    samples_len: usize,
    fft_result: &[Complex32],
    sampling_rate: u32,
    frequency_limit: FrequencyLimit,
    scaling_fn: Option<&SpectrumScalingFunction>,
) -> Result<FrequencySpectrum, SpectrumAnalyzerError> {
    let maybe_min = frequency_limit.maybe_min();
    let maybe_max = frequency_limit.maybe_max();

    let frequency_resolution = fft_calc_frequency_resolution(sampling_rate, samples_len as u32);

    // collect frequency => frequency value in Vector of Pairs/Tuples
    let frequency_vec = fft_result
        .iter()
        // See https://stackoverflow.com/a/4371627/2891595 for more information as well as
        // https://www.gaussianwaves.com/2015/11/interpreting-fft-results-complex-dft-frequency-bins-and-fftshift/
        //
        // The indices 0 to N/2 (inclusive) are usually the most relevant. Although, index
        // N/2-1 is declared as the last useful one on stackoverflow (because in typical applications
        // Nyquist-frequency + above are filtered out), we include everything here.
        // with 0..=(samples_len / 2) (inclusive) we get all frequencies from 0 to Nyquist theorem.
        //
        // Indices (samples_len / 2)..len() are mirrored/negative. You can also see this here:
        // https://www.gaussianwaves.com/gaussianwaves/wp-content/uploads/2015/11/realDFT_complexDFT.png
        .take(samples_len / 2 + 1)
        // to (index, fft-result)-pairs
        .enumerate()
        // calc index => corresponding frequency
        .map(|(fft_index, fft_result)| {
            (
                // Calculate corresponding frequency of each index of FFT result.
                //
                // Explanation for the algorithm:
                // https://stackoverflow.com/questions/4364823/
                //
                // N complex samples          : [0], [1], [2], [3], ... , ..., [2047] => 2048 samples for example
                //   (Or N real samples packed
                //   into N/2 complex samples
                //   (real FFT algorithm))
                // Complex FFT Result         : [0], [1], [2], [3], ... , ..., [2047]
                // Relevant part of FFT Result: [0], [1], [2], [3], ... , [1024]      => indices 0 to N/2 (inclusive) are important
                //                               ^                         ^
                // Frequency                  : 0Hz, .................... Sampling Rate/2 => "Nyquist frequency"
                //                              0Hz is also called        (e.g. 22050Hz for 44100Hz sampling rate)
                //                              "DC Component"
                //
                // frequency step/resolution is for example: 1/2048 * 44100 = 21.53 Hz
                //                                             2048 samples, 44100 sample rate
                //
                // equal to: 1.0 / samples_len as f32 * sampling_rate as f32
                fft_index as f32 * frequency_resolution,
                // in this .map() step we do nothing with this yet
                fft_result,
            )
        })
        // #######################
        // ### BEGIN filtering: results in lower calculation and memory overhead!
        // check lower bound frequency (inclusive)
        .filter(|(fr, _fft_result)| {
            maybe_min.is_none_or(|min_fr| {
                // inclusive!
                // attention: due to the frequency resolution, we do not necessarily hit
                //            exactly the frequency, that a user requested
                //            e.g. 1416.8 < limit < 1425.15
                *fr >= min_fr
            })
        })
        // check upper bound frequency (inclusive)
        .filter(|(fr, _fft_result)| {
            maybe_max.is_none_or(|max_fr| {
                // inclusive!
                // attention: due to the frequency resolution, we do not necessarily hit
                //            exactly the frequency, that a user requested
                //            e.g. 1416.8 < limit < 1425.15
                *fr <= max_fr
            })
        })
        // ### END filtering
        // #######################
        // FFT result is always complex: calc magnitude
        //   sqrt(re*re + im*im) (re: real part, im: imaginary part)
        .map(|(fr, complex_res)| (fr, complex_to_magnitude(complex_res)))
        // transform to my thin convenient orderable f32 wrappers
        .map(|(fr, val)| (Frequency::from(fr), FrequencyValue::from(val)))
        // collect all into a sorted vector (from lowest frequency to highest)
        .collect::<Vec<(Frequency, FrequencyValue)>>();

    // A valid frequency limit can still miss all FFT bins, or leave only one.
    // Statistics and interpolation require at least two frequency points.
    if frequency_vec.len() < 2 {
        return Err(SpectrumAnalyzerError::FrequencyLimitTooNarrow);
    }

    let mut working_buffer = vec![(0.0.into(), 0.0.into()); frequency_vec.len()];

    // create spectrum object
    let mut spectrum = FrequencySpectrum::new(
        frequency_vec,
        frequency_resolution,
        samples_len as u32,
        &mut working_buffer,
    );

    // optionally scale
    if let Some(scaling_fn) = scaling_fn {
        spectrum.apply_scaling_fn(scaling_fn, &mut working_buffer)?
    }

    Ok(spectrum)
}

/// Calculate the frequency resolution of the FFT. It is determined by the sampling rate
/// in Hertz and N, the number of samples given into the FFT. With the frequency resolution,
/// we can determine the corresponding frequency of each index in the FFT result buffer.
///
/// For "real FFT" implementations
///
/// ## Parameters
/// * `samples_len` Number of samples put into the FFT
/// * `sampling_rate` sampling_rate, e.g. `44100 [Hz]`
///
/// ## Return value
/// Frequency resolution in Hertz.
///
/// ## More info
/// * <https://www.researchgate.net/post/How-can-I-define-the-frequency-resolution-in-FFT-And-what-is-the-difference-on-interpreting-the-results-between-high-and-low-frequency-resolution>
/// * <https://stackoverflow.com/questions/4364823/>
#[inline]
fn fft_calc_frequency_resolution(sampling_rate: u32, samples_len: u32) -> f32 {
    sampling_rate as f32 / samples_len as f32
}

/// Maps a [`Complex32`] to its magnitude as `f32`. This is done by calculating
/// `sqrt(re*re + im*im)`. This is required to convert the complex FFT results
/// back to real values.
///
/// ## Parameters
/// * `val` A single value from the FFT output buffer of type [`Complex32`].
fn complex_to_magnitude(val: &Complex32) -> f32 {
    // calculates sqrt(re*re + im*im), i.e. magnitude of complex number
    let sum = val.re * val.re + val.im * val.im;
    let sqrt = libm::sqrtf(sum);
    debug_assert!(!sqrt.is_nan(), "sqrt is NaN!");
    sqrt
}