""" Various useful utilities (duh) """ import numpy as np import scipy.fft as ft def sampled_time(sample_rate=1, start=0, end=1, offset=0): return offset + np.arange(start, end, 1/sample_rate) def rot_vector(phi1=0.12345): """ Return a unit vector rotated by phi radians. """ unit = np.array([ phi1, phi1 - np.pi/2 ]) return np.cos(unit) def detect_edges(threshold, data, rising=True, falling=False): """ Detect rising/falling edges in data, returning the indices of the detected edges. https://stackoverflow.com/a/50365462 """ mask = np.full(len(data)-1, False) if rising: mask |= (data[:-1] < threshold) & (data[1:] > threshold) if falling: mask |= (data[:-1] > threshold) & (data[1:] < threshold) return np.flatnonzero(mask)+1 def sin_delay(f, t, t_delay=0, phase=0): return np.sin( 2*np.pi*f*(t - t_delay) + phase ) def time2phase(time, frequency=1): return 2*np.pi*frequency*time def phase2time(phase, frequency=1): return phase/(2*np.pi*frequency) def phase_modulo(phase, low=np.pi): """ Modulo phase such that it falls within the interval $[-low, 2\pi - low)$. """ return (phase + low) % (2*np.pi) - low def time_roll(a, samplerate, time_shift, sample_shift=0, int_func=lambda x: np.rint(x).astype(int), **roll_kwargs): """ Like np.roll, but use samplerate and time_shift to approximate the offset to roll. """ shift = int_func(time_shift*samplerate + sample_shift) return np.roll(a, shift, **roll_kwargs) ### signal generation def fft_bandpass(signal, band, samplerate): """ Simple bandpassing function employing a FFT. Parameters ---------- signal : arraylike band : tuple(low, high) Frequencies for bandpassing samplerate : float """ signal = np.asarray(signal) fft = ft.rfft(signal) freqs = ft.rfftfreq(signal.size, 1/samplerate) fft[(freqs < band[0]) | (freqs > band[1])] = 0 return ft.irfft(fft, signal.size), (fft, freqs) def deltapeak(timelength=1e3, samplerate=1, offset=None, peaklength=1): """ Generate a series of zeroes with a deltapeak. If offset is not specified, it puts it at a random location. Note: the series is regarded as periodic. Parameters ---------- timelength : float samplerate : float offset : float or tuple(float, float) Start of the peak peaklength : int Length of the peak """ N_samples = int(timelength * samplerate) if offset is None: offset = (None,None) if isinstance(offset, (tuple, list)): offset_min = 0 if offset[0] is None else offset[0] offset_max = N_samples if offset[-1] is None else offset[-1] offset = (np.random.random(1)*(offset_max - offset_min)+offset_min).astype(int) % N_samples position = (offset + np.arange(0, peaklength)).astype(int) % N_samples signal = np.zeros(N_samples) signal[position] = 1 return signal, position