Signal Analysis¶
Time-domain analysis tools for characterising signal properties, detecting features, and estimating pitch.
- pyminidsp.bessel_i0(x)[source]¶
Compute the zeroth-order modified Bessel function of the first kind.
Compute the zeroth-order modified Bessel function of the first kind, \(I_0(x)\). Used internally for Kaiser window generation, but also useful for filter design and statistical distributions.
- pyminidsp.sinc(x)[source]¶
Compute the normalized sinc function: sin(pi*x) / (pi*x), with sinc(0) = 1.
Compute the normalized sinc function:
\[\begin{split}\mathrm{sinc}(x) = \begin{cases} 1 & x = 0 \\ \frac{\sin(\pi x)}{\pi x} & x \ne 0 \end{cases}\end{split}\]Used in ideal filter design, interpolation, and resampling.
- pyminidsp.rms(a)[source]¶
Compute the root mean square (RMS) of a signal.
Compute the root mean square (RMS) of a signal — the standard measure of signal “loudness”:
\[\mathrm{RMS} = \sqrt{\frac{1}{N}\sum_{n=0}^{N-1} x[n]^2}\]Equivalently,
sqrt(power(a)). A unit-amplitude sine wave has RMS ≈ 0.707. A DC signal of value c has RMS = \(|c|\).signal = md.sine_wave(44100, amplitude=1.0, freq=440.0, sample_rate=44100.0) rms = md.rms(signal) # ≈ 0.707
- Parameters:
a (ArrayLike)
- Return type:
- pyminidsp.zero_crossing_rate(a)[source]¶
Compute the zero-crossing rate of a signal.
Count how often the signal changes sign, normalised by the number of adjacent pairs:
\[\mathrm{ZCR} = \frac{1}{N-1}\sum_{n=1}^{N-1} \mathbf{1}\bigl[\mathrm{sgn}(x[n]) \ne \mathrm{sgn}(x[n-1])\bigr]\]Returns a value in [0.0, 1.0]. High ZCR indicates noise or high-frequency content; low ZCR indicates tonal or low-frequency content.
signal = md.sine_wave(16000, freq=1000.0, sample_rate=16000.0) zcr = md.zero_crossing_rate(signal) # zcr ≈ 2 * 1000 / 16000 = 0.125
- Parameters:
a (ArrayLike)
- Return type:
- pyminidsp.autocorrelation(a, max_lag)[source]¶
Compute the normalised autocorrelation of a signal.
- Parameters:
a (ArrayLike) – Input signal.
max_lag (int) – Number of lag values to compute.
- Returns:
numpy array of autocorrelation values, length max_lag.
- Return type:
Compute the normalised autocorrelation — measures the similarity between a signal and a delayed copy of itself:
\[R[\tau] = \frac{1}{R[0]} \sum_{n=0}^{N-1-\tau} x[n]\,x[n+\tau]\]The output satisfies
out[0] = 1.0and|out[tau]| <= 1.0. A silent signal (all zeros) produces all-zero output.- Parameters:
a (ArrayLike) – Input signal.
max_lag (int) – Number of lag values to compute. Must be > 0 and < N.
- Returns:
Array of autocorrelation values, length max_lag.
- Return type:
signal = md.sine_wave(1024, freq=100.0, sample_rate=1000.0) acf = md.autocorrelation(signal, 50) # acf[0] = 1.0, acf[10] ≈ 1.0 (lag = one period of 100 Hz at 1 kHz)
- pyminidsp.peak_detect(a, threshold=0.0, min_distance=1)[source]¶
Detect peaks (local maxima) in a signal.
- Parameters:
- Returns:
numpy array of peak indices.
- Return type:
Detect peaks (local maxima) in a signal. A sample
a[i]is a peak if it is strictly greater than both immediate neighbours and above the given threshold. The min_distance parameter suppresses nearby secondary peaks.Peaks are found left-to-right. Endpoint samples are never peaks because they lack two neighbours.
- Parameters:
- Returns:
Array of peak indices.
- Return type:
import numpy as np signal = np.array([0, 1, 3, 1, 0, 2, 5, 2, 0], dtype=float) peaks = md.peak_detect(signal, threshold=0.0, min_distance=1) # peaks == [2, 6] (values 3 and 5)
- pyminidsp.f0_autocorrelation(signal, sample_rate, min_freq_hz=80.0, max_freq_hz=400.0)[source]¶
Estimate F0 using autocorrelation.
Estimate the fundamental frequency (F0) using autocorrelation. Searches for the strongest local peak in the normalised autocorrelation over lags corresponding to the requested frequency range:
\[f_0 = \frac{f_s}{\tau_\text{peak}}\]- Parameters:
- Returns:
Estimated F0 in Hz, or 0.0 if no reliable pitch is found.
- Return type:
- pyminidsp.f0_fft(signal, sample_rate, min_freq_hz=80.0, max_freq_hz=400.0)[source]¶
Estimate F0 using FFT peak picking.
Estimate F0 using FFT peak picking. The signal is internally Hann-windowed, transformed, then the dominant magnitude peak in the requested frequency range is mapped back to Hz:
\[f_0 = \frac{k_\text{peak} \cdot f_s}{N}\]Simple and fast, but generally less robust than
f0_autocorrelation()for noisy or strongly harmonic signals.
- pyminidsp.mix(a, b, w_a=0.5, w_b=0.5)[source]¶
Mix (weighted sum) two signals.
- Parameters:
- Returns:
numpy array of the mixed signal.
- Return type:
Mix (weighted sum) two signals element-wise:
\[\mathrm{out}[n] = w_a \cdot a[n] + w_b \cdot b[n]\]- Parameters:
- Returns:
Mixed signal array.
- Return type:
sine = md.sine_wave(1024, amplitude=1.0, freq=440.0, sample_rate=44100.0) noise = md.white_noise(1024, amplitude=0.1, seed=42) mixed = md.mix(sine, noise, w_a=0.8, w_b=0.2)