Module signal_processing 

Signal processing: FFT, windowing, filtering, spectral analysis, wavelets.

Provides Cooley-Tukey FFT/IFFT, windowing functions (Hann/Hamming/Blackman/Kaiser), PSD estimation (Welch/Bartlett), FIR/IIR filter design (Butterworth/Chebyshev/elliptic), convolution, correlation, Hilbert transform, spectrogram, and wavelet transforms.

Structs

Biquad

A single biquad (second-order) IIR section.

Complex64

A complex number with f64 real and imaginary parts.

FirFilter

FIR filter coefficients computed via the window method.

IirFilter

A cascade of biquad sections forming an IIR filter.

PsdResult

PSD estimation result containing frequency bins and power values.

Spectrogram

Spectrogram result: time bins, frequency bins, and STFT magnitude matrix.

Enums

WindowType

The type of window function to apply.

Functions

analytic_signal

Compute the analytic signal (x + j*H{x}) using FFT.

apply_window

Apply a window to a signal in-place.

auto_correlate

Auto-correlation of x.

bartlett_psd

Bartlett’s method for PSD estimation (non-overlapping segments).

bartlett_window

Compute the Bartlett (triangular) window of length n.

bessel_i0

Modified Bessel function of the first kind, order zero (I₀). Used for Kaiser window computation.

blackman_harris_window

Compute the Blackman-Harris window of length n.

blackman_window

Compute the Blackman window of length n.

butterworth_lowpass

Butterworth low-pass filter design (bilinear transform, biquad cascade).

chebyshev1_lowpass

Chebyshev Type I low-pass filter (biquad cascade).

complex_cepstrum

Compute the complex cepstrum of a signal.

convolve

Linear convolution of two real signals via FFT (overlap-add style).

cross_correlate

Cross-correlation of x with y (i.e. sum_t x[t] * y[t+lag]).

db2_decompose

Daubechies-4 (db2) single-level forward DWT.

db2_reconstruct

Daubechies-4 (db2) single-level inverse DWT.

downsample

Downsample a signal by integer factor down (decimate, no anti-aliasing).

fft

Compute FFT of a real-valued signal. Pads to the next power of two if needed.

fft_frequencies

Return the frequency bins (in Hz) for an FFT of length n sampled at fs Hz.

fft_inplace

In-place Cooley-Tukey FFT. n must be a power of two.

find_peaks

Detect local maxima in a signal.

find_peaks_above

Detect peaks above a threshold.

flat_top_window

Compute the flat-top window of length n.

generate_chirp

Generate a test chirp (frequency sweep) signal.

generate_sine

Generate a test sinusoidal signal.

generate_white_noise

Generate white Gaussian noise (Box-Muller transform).

group_delay

Compute group delay from the phase response.

haar_decompose

Haar wavelet decomposition (one level).

haar_dwt

Multi-level Haar DWT.

haar_idwt

Multi-level Haar inverse DWT.

haar_reconstruct

Haar wavelet reconstruction (one level).

hamming_window

Compute the Hamming window of length n.

hann_window

Compute the Hann window of length n.

hilbert_transform

Compute the Hilbert transform of a real signal.

ifft_inplace

In-place inverse FFT (IFFT).

ifft_real

Compute IFFT and return the real part of each element.

iir_magnitude_response

Compute the magnitude response of a cascade of biquads at frequency f (normalised 0..1).

instantaneous_amplitude

Compute the instantaneous amplitude (envelope) of a signal.

instantaneous_frequency

Compute the instantaneous frequency (Hz) given sample rate fs.

instantaneous_phase

Compute the instantaneous phase of a signal (radians).

istft

Inverse STFT using overlap-add.

kaiser_window

Compute the Kaiser window of length n with shape parameter beta.

magnitude_spectrum

Compute the magnitude spectrum (|X[k]|) from a real signal.

moving_average

Compute the moving average of a signal.

moving_rms

Compute the moving RMS of a signal.

normalize_energy

Normalize a signal to unit energy.

normalize_peak

Normalize a signal to unit peak amplitude.

normalized_cross_correlation

Normalized cross-correlation coefficient at each lag.

nuttall_window

Compute the Nuttall window of length n.

periodogram_psd

Simple periodogram PSD estimate.

phase_spectrum

Compute the phase spectrum (arg(X[k])) from a real signal.

power_spectrum

Compute the power spectrum (|X[k]|^2) from a real signal.

real_cepstrum

Compute the real cepstrum of a signal.

resample

Resample a signal from sample rate fs_in to fs_out using rational resampling.

resample_linear

Linear interpolation resampling.

rfft_frequencies

Return only the positive-frequency bins (0 to fs/2).

rms

Compute the RMS value of a signal.

signal_energy

Compute the energy of a signal.

signal_mean

Compute the mean of a signal.

signal_variance

Compute the variance of a signal.

snr_db

Compute the SNR (signal-to-noise ratio) in dB given signal and noise power.

spectrogram

Compute a short-time Fourier transform (STFT) spectrogram.

stft

Short-time Fourier transform: returns complex coefficients [frame][freq_bin].

total_harmonic_distortion

Compute the THD (total harmonic distortion) from a power spectrum.

unwrap_phase

Unwrap phase (correct for 2π discontinuities).

upsample

Upsample a signal by integer factor up (insert zeros between samples).

welch_psd

Welch’s method for PSD estimation.

window_coherent_gain

Compute the coherent gain of a window (mean).

window_power_gain

Compute the power gain of a window (mean of squares).

windowed

Apply a window and return the windowed signal.

zero_pad

Zero-pad a signal to length n.