scirs2-fft

Fast Fourier Transform library for Rust, modeled after SciPy's fft module.

scirs2-fft provides a comprehensive suite of frequency-domain algorithms — FFT, RFFT, DCT/DST, STFT, NUFFT, sparse FFT, fractional FFT, wavelet packets, polyphase filter banks, and more — all in pure Rust using OxiFFT as the core FFT engine.

Installation

[dependencies]
scirs2-fft = "0.3.0"

With parallel processing:

[dependencies]
scirs2-fft = { version = "0.3.0", features = ["parallel"] }

Features (v0.3.0)

Core Transforms

DCT and DST Variants

• DCT types I, II, III, IV, V, VI, VII, VIII
• DST types I, II, III, IV, V, VI, VII, VIII
• Inverse transforms for all types
• MDCT (Modified DCT) and MDST
• N-dimensional DCT/DST

Window Functions Library

100+ window functions including:

• Standard: Hann, Hamming, Blackman, Bartlett, flat-top
• Kaiser, Gaussian, Tukey, Parzen, Bohman
• Nuttall, Blackman-Harris, Blackman-Nuttall
• DPSS (discrete prolate spheroidal sequences) for multi-taper
• Exponential, triangular, rectangular (boxcar)
• General cosine and general Hamming families
• Kaiser-Bessel derived (KBD)

Short-Time Fourier Transform

• stft / istft with configurable window, overlap, and boundary handling
• spectrogram (power spectral density)
• Normalized spectrogram for visualization
• Waterfall plot data generation (3D mesh, line stacks)
• Coherence and cross-spectral density

Sparse FFT (Sub-Linear Time)

• Sublinear sparse FFT (O(k log n) for k-sparse signals)
• Compressed sensing-based sparse FFT
• Iterative sparse FFT (robust to noise)
• Frequency pruning variant
• Prony method for damped sinusoid recovery
• MUSIC algorithm for super-resolution spectral estimation
• Batch sparse FFT (parallel CPU processing)
• GPU-accelerated sparse FFT (CUDA/ROCm/SYCL via feature flag)

Specialized Transforms

• Fractional Fourier Transform (FrFT) — 3 algorithm variants (Ozaktas-Arikan, Candan, sampling)
• Chirp-Z Transform (CZT) — FFT on arbitrary contours in the z-plane
• Non-Uniform FFT (NUFFT) types 1, 2, and 3 (Gaussian / sinc interpolation)
• Fast Hankel Transform (FHT)
• Hilbert transform (analytic signal)
• Hartley transform
• Number-theoretic Transform (NTT) over prime fields
• Bluestein's algorithm for prime-length FFT
• Mixed-radix FFT (arbitrary composite lengths)

Spectral Estimation

• Lomb-Scargle periodogram for irregularly sampled data
• MUSIC (Multiple Signal Classification) algorithm
• ESPRIT algorithm for frequency estimation
• Burg method (AR model-based PSD)
• Welch's method for PSD estimation
• Multitaper spectral analysis (DPSS windows)

Wavelet Packets

• Wavelet packet transform tree
• Best-basis selection (entropy criterion)
• Reconstruction from wavelet packet tree
• Available wavelet families: Daubechies, Symlets, Coiflets, Biorthogonal

Polyphase Filter Bank

• Analysis and synthesis polyphase filter banks
• Critically sampled and oversampled configurations
• Perfect reconstruction condition verification
• DFT modulated filter banks

Hilbert-Huang Transform (HHT)

• Empirical Mode Decomposition (EMD) into Intrinsic Mode Functions (IMFs)
• Instantaneous frequency and amplitude via Hilbert transform
• Ensemble EMD (EEMD) and Complete EEMD (CEEMDAN) for noise-assisted decomposition
• Hilbert spectrum visualization data

Multidimensional FFT Utilities

• Row-column decomposition for 2D FFT
• Separable N-dimensional FFT plans
• Mixed-radix N-dimensional FFT
• In-place 2D FFT with memory-efficient tiling

Convolution and Correlation

• Overlap-save and overlap-add convolution
• Circular convolution via FFT
• Cross-correlation and autocorrelation
• FFT-based polynomial multiplication

Plan Caching and Execution

• Automatic plan reuse for repeated same-size transforms (thread-safe cache)
• Parallel planner: create multiple plans concurrently
• Parallel executor: execute batch FFTs across worker threads
• Memory-efficient streaming FFT for large arrays

Usage Examples

Basic 1D FFT

use scirs2_fft::{fft, ifft, rfft};

let signal = vec![1.0_f64, 2.0, 3.0, 4.0, 3.0, 2.0, 1.0, 0.0];

// Complex FFT
let spectrum = fft(&signal, None)?;

// Inverse FFT
let recovered = ifft(&spectrum, None)?;

// Real FFT (more efficient for real inputs)
let real_spectrum = rfft(&signal, None)?;  // length = n/2 + 1

DCT

use scirs2_fft::dct::{dct, idct, DctType};

let data = vec![1.0_f64, 2.0, 3.0, 4.0];
let coeffs = dct(&data, DctType::II, None)?;   // DCT-II (most common)
let back = idct(&coeffs, DctType::II, None)?;

STFT and Spectrogram

use scirs2_fft::{stft, spectrogram, Window};

let fs = 44100.0_f64;
let signal: Vec<f64> = (0..44100).map(|i| (2.0 * std::f64::consts::PI * 440.0 * i as f64 / fs).sin()).collect();

// Short-Time Fourier Transform
let (freqs, times, stft_mat) = stft(&signal, Window::Hann, 1024, Some(512), None, Some(fs), None, None)?;

// Power spectral density spectrogram
let (freqs, times, psd) = spectrogram(&signal, Some(fs), Some(Window::Hann), Some(1024), Some(512), None, None, Some("density"), Some("psd"))?;

Fractional Fourier Transform

use scirs2_fft::fractional_ft::frft;

let signal: Vec<f64> = (0..256).map(|i| (0.1 * i as f64).sin()).collect();
// alpha = 0.5: halfway between time and frequency domain
let result = frft(&signal, 0.5, None)?;

Sparse FFT

use scirs2_fft::sparse_fft::{sparse_fft, SparseFFTAlgorithm};

// Signal with only a few significant frequency components
let result = sparse_fft(&signal, 5, SparseFFTAlgorithm::Sublinear, None)?;
println!("Dominant frequencies: {:?}", result.indices);
println!("Their amplitudes: {:?}", result.values);

Lomb-Scargle Periodogram

use scirs2_fft::spectral_analysis::lomb_scargle;

// Irregularly sampled time series
let times: Vec<f64> = vec![0.0, 0.3, 0.7, 1.1, 2.0, 3.5, 5.1];
let values: Vec<f64> = vec![1.0, 0.5, -0.3, -0.9, -0.2, 0.8, 0.4];
let frequencies: Vec<f64> = (1..=50).map(|i| i as f64 * 0.1).collect();

let power = lomb_scargle(&times, &values, &frequencies, true)?;

NTT (Number-Theoretic Transform)

use scirs2_fft::ntt::ntt;

let data: Vec<u64> = vec![1, 2, 3, 4, 5, 6, 7, 8];
let prime = 998_244_353_u64;  // NTT-friendly prime
let result = ntt(&data, prime)?;

Wavelet Packet Transform

use scirs2_fft::wavelet_packets::{WaveletPacketTree, WaveletFamily};

let signal: Vec<f64> = (0..256).map(|i| (i as f64 * 0.1).sin()).collect();
let tree = WaveletPacketTree::new(&signal, WaveletFamily::Daubechies(4), 4)?;
let best_basis = tree.best_basis()?;

Feature Flags

Links

• API Documentation
• SciRS2 Repository

License

Licensed under the Apache License 2.0. See LICENSE for details.