Signal Processing¶

Lightweight 1D signal-processing helpers used by the FFT / smoothing workflows: apodization windows, FFT zero-fill sizing, echo-centre detection, and a small Signal_Processing class for smoothing, baseline subtraction, and normalization. Every routine takes and returns plain NumPy arrays.

import numpy as np
import atomize.math_modules.signal_processing as sigproc

The module-level functions (apodization_window, zerofill_length, echo_center) are called directly; the smoothing / baseline / normalization helpers live on the Signal_Processing class.

Note

savitzky_golay() requires scipy (the math extra: pip install -e .[math]); everything else is NumPy-only.

apodization_window()¶

w = sigproc.apodization_window(n, name, param=8.6)

Returns an apodization window of length n to multiply onto a time-domain signal before an FFT. name is one of:

'None', 'Hann', 'Hamming', 'Blackman', 'Bartlett', 'Flat-top', 'Kaiser', 'Gaussian', 'Tukey'.

param is the shape parameter for the three parametric windows and is ignored by the rest:

Window	`param` meaning	Typical
`Kaiser`	β	8.6
`Gaussian`	σ as a fraction of `n`	0.15
`Tukey`	α taper fraction (`0` → rectangular, `1` → Hann)	0.5

signal = signal*sigproc.apodization_window(len(signal), 'Kaiser', 8.6)

zerofill_length()¶

n = sigproc.zerofill_length(length, choice)

Target FFT length for a zero-fill choice: 'None' (returns length), '×2' / '×4' / '×8' (or the ASCII 'x2'…), or 'Next pow₂' (the smallest power of two ≥ length). Feed the result to numpy.fft.fft(signal, n).

n = sigproc.zerofill_length(len(signal), '×4')
spectrum = np.fft.fft(signal, n)
freq = np.fft.fftfreq(n, dt)

echo_center()¶

k = sigproc.echo_center(envelope, window=0)

Returns the index of the echo centre in a 1D magnitude envelope. Pass an offset-invariant envelope such as sqrt(I**2 + Q**2) so the carrier modulation from a field/frequency offset has already cancelled and only the echo shape remains — then the centre is the envelope peak, refined by a local centre-of-mass and rounded to the nearest sample.

window is the half-width (in points) of the centre-of-mass window around the peak. With window <= 0 (default) it is sized automatically from the crest width: walk out from the peak until the envelope drops below 70 % of the peak height, then take the narrower of the two sides. Measuring from the crest (rather than a baseline-relative half-maximum) keeps the result on the peak even when the pre-echo baseline is elevated — there a half-maximum can sit at the baseline level, the window blows up, and a slow FID decay drags the centre-of-mass far past the true peak. A positive window forces that exact half-width.

This is used to start an FFT "from the centre of the echo": find k, drop the first k points, and the dead-time first-order phase ramp disappears.

env = np.sqrt(i**2 + q**2)
k = sigproc.echo_center(env)
spectrum = np.fft.fft((i + 1j*q)[k:], n)

Signal_Processing()¶

sp = sigproc.Signal_Processing()

Creates the helper object exposing the methods below.

savitzky_golay()¶

y_smooth = sp.savitzky_golay(y, window=11, order=3)

Savitzky–Golay smoothing (requires scipy). window must be odd and greater than order; it is auto-corrected (forced odd, clamped to the data length) if not. Raises RuntimeError when scipy is missing.

moving_average()¶

y_smooth = sp.moving_average(y, window=5)

Centred moving-average smoothing; edges are padded by reflection so the output has the same length as y. NumPy-only.

baseline_poly()¶

y_corr = sp.baseline_poly(x, y, order=1, region='all', npts=0)

Fits a polynomial of the given order and subtracts it from the full curve. region selects which points the polynomial is fitted to, so the baseline can be estimated from signal-free regions (e.g. the trace tails):

`region`	Points used for the fit
`'all'`	every point (default)
`'first'`	the first `npts` points
`'last'`	the last `npts` points
`'ends'`	the first and last `npts` points

npts is ignored when region='all' (or when it would select the whole curve).

# remove a linear baseline estimated from the first and last 50 points
y_corr = sp.baseline_poly(x, y, order=1, region='ends', npts=50)

normalize()¶

y_norm = sp.normalize(y, mode='minmax')

Normalizes y. mode:

`mode`	Result
`'minmax'`	rescaled to `[0, 1]`
`'max'`	divided by `max(\|y\|)`
`'area'`	divided by its absolute area (unit area)