Signal Functions (20)

Apply a 2nd order Butterworth bandpass filter to a signal by cascading a highpass at lowCutoff and a lowpass at highCutoff.

Compute the discrete linear convolution of two arrays. The output length is len(a) + len(b) - 1.

Compute the cross-correlation of two arrays. When called with one argument, computes the autocorrelation. Equivalent to convolve(a, reverse(b)).

Compute the Discrete Cosine Transform (DCT-II) of a real-valued signal. DCT-II is defined as X[k] = sum_{n=0}^{N-1} x[n] * cos(pi*(2n+1)*k/(2N)). Computed directly in O(N^2). The DC component X[0] equals the sum of all input samples.

Compute the Discrete Sine Transform (DST-I) of a real-valued signal. X[k] = sum_{n=0}^{N-1} x[n] * sin(pi * (n+1) * (k+1) / (N+1)). Computed directly in O(N^2). Useful for PDEs with Dirichlet boundary conditions. The DST-I is its own inverse up to the scaling factor 2/(N+1), so idst(dst(x)) == x.

Compute one level of the Discrete Wavelet Transform (DWT). Decomposes the signal into approximation (lowpass) and detail (highpass) coefficients. Supported wavelets: "haar" (Haar wavelet) and "db2" (Daubechies-2). For "haar": approx[i] = (x[2i] + x[2i+1]) / sqrt(2), detail[i] = (x[2i] - x[2i+1]) / s

Compute the 2D Discrete Fourier Transform of a real-valued matrix. The 2D DFT is applied by computing a 1D DFT along each row, then along each column of the result. Returns a 2D array of complex numbers with properties re and im. The DC component (zero frequency) is at position [0][0].

Compute the Fourier transform of a real-valued signal with user-friendly output. Returns an object with frequencies, amplitudes, and phases arrays. Amplitudes are scaled by 1/N. Optionally accepts options.sampleRate (default: 1) for physical frequency bins, and options.output = "complex" to return t

Calculates the frequency response of a filter given its numerator and denominator coefficients.

Apply a 2nd order Butterworth highpass IIR filter to a signal. The cutoff and sampleRate must use the same time unit (e.g., both in Hz).

Compute the Hilbert transform of a real-valued signal. The Hilbert transform produces a 90-degree phase shift of the input. It is computed via DFT: multiply positive-frequency components by -i, zero out the DC and Nyquist, zero out negative frequencies, then take the imaginary part of the IDFT resul

Compute the Inverse Discrete Sine Transform (IDST-I). x[n] = (2/(N+1)) * sum_{k=0}^{N-1} X[k] * sin(pi * (n+1) * (k+1) / (N+1)). The IDST-I is self-inverse: applying it to the output of dst with scaling 2/(N+1) recovers the original signal. idst(dst(x)) == x within floating-point tolerance.

Reconstruct a real-valued signal from its Fourier spectrum. Accepts either a complex coefficient array (as returned by fourier with output:"complex") or a spectrum object { frequencies, amplitudes, phases } (as returned by the default fourier() call). Applies the inverse FFT with proper N-scaling.

Apply a 2nd order Butterworth lowpass IIR filter to a signal. The cutoff and sampleRate must use the same time unit (e.g., both in Hz).

Apply a median filter to a 1D signal. For each position, computes the median of the windowSize-element sliding window centered on that position. Edge samples use mirror (reflect) padding. windowSize must be a positive odd integer. The median filter is effective for removing impulse noise (spikes) wh

Estimate the power spectral density (PSD) of a signal using the periodogram method. Computes |FFT(x)|^2 scaled by window normalization. Returns the one-sided spectrum (DC to Nyquist) as an object with frequencies and power arrays. Options: sampleRate (default: 1), window type (default: "rectangular"

Resample a signal by a given factor using linear interpolation. A factor > 1 upsamples (increases length), a factor < 1 downsamples (decreases length). The output has round((N-1)*factor)+1 samples, mapping evenly between the first and last input samples. Non-integer factors are fully supported.

Compute the spectrogram (Short-Time Fourier Transform magnitude) of a signal. Slides a window across the signal, applies a window function, and computes the FFT magnitude at each position. Returns an object with times, frequencies, and magnitude (2D array indexed by [timeIndex][freqBin]). Options: h

Compute a window function of length n. Supported types: rectangular, hamming, hanning, blackman, kaiser. Default type is hamming.

Compute the transfer function of a zero-pole-gain model.