Crate embedded_dsp 

embedded-dsp

A #![no_std] Rust digital signal processing library for microcontrollers, embedded systems, and real-time signal processing applications.

Algorithm modules are Cargo-feature gated (all enabled by the full feature, which is in default). types and math are always available. See the crate’s [features] table for the per-module flags.

Overview

embedded-dsp provides zero-allocation digital signal processing algorithms:

• Basic Math: Elementwise addition, subtraction, multiplication, dot product, scale, shift, clip, logic ops.
• Complex Math: Complex vector addition, multiplication, magnitude, magnitude squared, conjugate, dot product.
• Fast Math: Trigonometric (sin, cos, atan2), square root, division, log, exp.
• Fixed-Point (Q16.16): Saturating Q16.16 arithmetic and scanline interpolation (fixed-point feature).
• LUT trigonometry: Compile-time 256-entry sin/cos tables (lut feature).
• Statistics: Mean, variance, standard deviation, RMS, power, min/max, entropy, Kullback-Leibler, LogSumExp.
• Support: Vector copy, fill, type conversions (Q7, Q15, Q31, F32), sort, barycenter, weighted sum.
• Matrix: Matrix addition, subtraction, multiplication, scale, transpose, Gauss-Jordan inverse.
• Filtering: FIR, Biquad IIR Direct Form I and transposed DF-II (f32/q15/q31), LMS / leaky LMS / NLMS, Convolution, Correlation, single-pole recursive filters (f32/q15), Q15 DC blocker, O(1) recursive moving average, and a double-sampled State Variable Filter (simultaneous LP/HP/BP/notch/peak, sweepable cutoff/resonance).
• Filter Design: Biquad Lowpass, Highpass, Bandpass, Notch, Peaking EQ, Allpass, Butterworth, Chebyshev, and arbitrary-response (frequency-sampling) design.
• Filter Analysis: Frequency response (DTFT) evaluation for FIR/biquad filters, FIR group delay, and pole-based IIR stability checks.
• Resampling & Multi-rate: CIC Decimator & Interpolator, linear fractional resampler.
• Kalman Filtering: 1D/2D helpers, const-generic linear KalmanFilter<N, M>, and trait-based ExtendedKalmanFilter (EKF).
• Const Generics: Compile-time fixed-size FirFilter<N>, FirFilterQ15<N>, BiquadCascade<N>, BiquadCascadeQ15, and Matrix<R, C>.
• Transform: In-place Complex FFT (CFFT), packed Real FFT / inverse (rfft_q15/irfft_q15), DCT-IV, Bit reversal, Fixed-point FFT (Q15/Q31), Haar transform, Hartley transform, and a generalized wavelet transform (Daubechies-4).
• Companding: µ-law and A-law curves plus ITU-T G.711 u8 encode/decode.
• Audio: Goertzel single-frequency detector (f32/q15), peak/RMS envelope followers (f32/q15), Mel filterbank, and MFCC feature extraction.
• Spectral Analysis & PSD: Welch’s method power spectral density estimation (averaged periodograms), single-segment periodograms in linear and dB scale.
• Spatial & 2D Signal Processing: 2D DCT/IDCT, 2D Convolution, 2D Non-linear Filtering (Min/Max/Median), Sobel edge detection, 2D Histogram, MSE, PSNR.
• Controller: PID motor controller, Clarke/Park (f32 and q15).
• Interpolation: Linear, Bilinear, Cubic spline interpolation.
• Quaternion: Norm, normalization, product, conjugate, inverse, rotation matrix conversion, and nalgebra interop (nalgebra feature).
• Window: Hanning, Hamming, Blackman, Blackman-Harris, Bartlett, Welch, Flat-top generators (f32), plus Q15 Hanning/Hamming/Blackman/Bartlett.
• Distance: Euclidean, Cosine, Chebyshev, Manhattan, Minkowski, Jaccard, Hamming, Canberra, Bray-Curtis.

Re-exports

pub use audio::*;

pub use basic_math::*;

pub use beamforming::*;

pub use companding::*;

pub use complex_math::*;

pub use const_generics::*;

pub use controller::*;

pub use cordic::*;

pub use distance::*;

pub use dynamics::*;

pub use fast_math::*;

pub use filter_analysis::*;

pub use filter_design::*;

pub use filtering::*;

pub use fixed_point::*;

pub use interpolation::*;

pub use kalman::*;

pub use lut::*;

pub use matrix::*;

pub use nalgebra_interop::*;

pub use pipeline::*;

pub use pll::*;

pub use psd::*;

pub use quaternion::*;

pub use resampling::*;

pub use spatial::*;

pub use statistics::*;

pub use svf::*;

pub use support::*;

pub use transform::*;

pub use window::*;

pub use intrinsics::*;

pub use math::*;

pub use types::*;

Modules

audio

Audio analysis: the Goertzel single-frequency detector, peak/RMS envelope followers, a Mel filterbank, and MFCC feature extraction. These are DSP front-ends (e.g. for a keyword-spotting pipeline); classifiers and neural nets live in embedded-nn.

basic_math

Basic math operations (absolute value, addition, subtraction, multiplication, dot product, negation, offset, scale, shift, clip, logic ops).

beamforming

Acoustic Array Processing, Delay-and-Sum Beamforming, and GCC-PHAT TDoA Direction-of-Arrival Estimation.

companding

Audio companding: the non-linear µ-law and “A”-law compression curves used by the ITU-T G.711 telephony standard to compress a wide-dynamic-range linear audio sample down to a lower bit depth with minimal perceptual loss (Steven W. Smith, “The Scientist and Engineer’s Guide to DSP”, Ch. 22, Eq. 22-1 / 22-2).

complex_math

const_generics

Const generic safe wrappers for compile-time sized FIR filters, Biquads, and Matrices.

controller

Controller functions (PID motor control, Clarke transform, Park transform, Inverse Clarke, Inverse Park).

cordic

CORDIC (Coordinate Rotation Digital Computer) pure-integer arithmetic engine.

distance

Distance metrics between vectors (Euclidean, Cosine, Chebyshev, Manhattan, Minkowski, Jaccard, Hamming, Canberra, Bray-Curtis).

dynamics

Dynamics Range Control: Compressor, Limiter, Expander, and Noise Gate.

fast_math

Fast math functions (sin, cos, sin_cos, sqrt, vsqrt, divide, log, exp, atan2).

filter_analysis

Frequency-response, group-delay, and pole-based stability analysis for filters produced by crate::filter_design or hand-written FIR/biquad coefficients.

filter_design

Filter design routines for calculating biquad IIR coefficients (Low-pass, High-pass, Band-pass, Notch, Peaking, All-pass, Butterworth).

filtering

Digital filtering functions (FIR, Biquad IIR Direct Form I & II, LMS Adaptive Filter, Convolution, Correlation).

fixed_point

Q16.16 fixed-point math.

interpolation

Interpolation functions (Linear, Bilinear, Spline).

intrinsics

SIMD and DSP hardware acceleration intrinsics hooks.

kalman

Kalman filtering and state estimation algorithms for zero-allocation embedded applications.

lut

Lookup-table trigonometry.

math

Unified math abstraction providing floating-point mathematical operations using libm in no_std environments or std math when available.

matrix

Matrix operations (addition, subtraction, multiplication, scale, transpose, inverse, complex matrix multiplication).

nalgebra_interop

Conversions between the [w, x, y, z] quaternion representation used by crate::quaternion and nalgebra’s Quaternion/UnitQuaternion.

pipeline

Zero-allocation composable DSP pipeline and streaming abstraction.

pll

Phase-Locked Loops (PLL) and carrier recovery for power electronics, motor resolvers, and SDR.

psd

Power Spectral Density (PSD) estimation using Welch’s Method (Averaged Overlapped Periodogram) and Bartlett/standard periodograms.

quaternion

Quaternion math functions (norm, normalize, product, conjugate, inverse, rotation matrix conversion).

resampling

Multi-rate digital signal processing routines: Cascaded Integrator-Comb (CIC) decimation/interpolation and linear fractional resampling.

spatial

2D Spatial and Image Processing routines (2D DCT/IDCT, 2D Convolution, 2D Nonlinear Filters, Sobel Edge Detection, 2D Histogram, MSE/PSNR).

statistics

Statistics functions (mean, variance, standard deviation, RMS, power, min, max, absmax, absmin, entropy, Kullback-Leibler, LogSumExp).

support

Support functions (copy, fill, format conversions q7/q15/q31/f32, sort, barycenter, weighted sum).

svf

State Variable Filter with simultaneous lowpass, highpass, bandpass, notch, and peak outputs.

transform

Fast Fourier Transform (FFT), Real FFT (RFFT), Discrete Cosine Transform (DCT-IV), and Bit Reversal functions.

types

Data types, status codes, complex structures, and fixed-point helper types.

window

Window functions (Hanning, Hamming, Blackman, Blackman-Harris, Bartlett, Welch, Flat-top window generators).