Signal processing

Nautilus.Signal provides fftfreq, the frequency of each bin of a discrete Fourier transform, in NumPy's numpy.fft.fftfreq order. Nautilus does not compute Fourier transforms, short-time transforms, or filters, because Chelis has no complex numbers; use fftfreq to label bins computed elsewhere.

fftfreq

import Nautilus.Signal (fftfreq)

def signal() -> tensor[8, f32] = to_tensor([0.0f32, 0.0f32, 0.0f32, 0.0f32, 0.0f32, 0.0f32, 0.0f32, 0.0f32])
freqs = fftfreq(signal(), 100.0f32)

signal = tensor(shape=[8], data=[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
freqs = tensor(shape=[8], data=[0.0, 12.5, 25.0, 37.5, -50.0, -37.5, -25.0, -12.5])

Signature: [n](x: &tensor[n, f32], sample_rate: f32) -> tensor[n, f32]

The input's values are ignored; only its length n is used. Bin i is i * sample_rate / n when i < n / 2, compared in floating point, and (i - n) * sample_rate / n otherwise. For even n the Nyquist bin n/2 is negative; for odd n bins 0 through (n - 1) / 2 are non-negative. Both match NumPy. fftfreq of a five-element tensor at sample_rate = 5.0 returns [0.0, 1.0, 2.0, -2.0, -1.0]. The result is in hertz when sample_rate is in samples per second. NumPy's second argument is the sample spacing d; pass sample_rate = 1 / d.

sample_rate should be positive. It is not checked: 0 gives all zeros (the upper half as -0.0), and a negative rate negates every bin.