Module nowcastlib.signals
Utils for working with signal processing
Expand source code
"""
Utils for working with signal processing
"""
import numpy as np
from nowcastlib.utils import find_closest_factor
def normalize_signal(input_signal):
"""
Rescales a signal such that it is 0-centered and has a max amplitude of 1.
Parameters
----------
input_signal : numpy.ndarray
The signal we wish to normalize.
Returns
-------
numpy.ndarray
The resulting normalized signal
"""
# centering it about 0
max_signal = np.max(input_signal)
min_signal = np.min(input_signal)
signal_range = max_signal - min_signal
mid_signal = max_signal - signal_range / 2
zero_c_signal = input_signal - mid_signal
# setting max = 1, min = -1
normed_signal = zero_c_signal / max(zero_c_signal)
return normed_signal
def gen_composite_red_noise(noise_length, component_length, normed=True):
"""
Generates a signal made of sub-signals of red noise.
Parameters
----------
noise_length : int
The desired output signal length
component_length : int
The desired length of each sub-signal red noise.
If `component_length` is not a factor of `noise_length`, the factor of
`noise_length` closest to `component_length` will be used
normed : bool, default True
Whether each sub-signal should be normalized, i.e. centered about 0 with a max
amplitude of 1.
Returns
-------
numpy.ndarray
A signal made of sub-signals of red noise.
"""
white_noise = np.random.randn(noise_length)
# reshape white noise into comps, then cumsum each component individually
white_noise = white_noise.reshape(
(-1, find_closest_factor(noise_length, component_length))
)
red_noise_comps = np.cumsum(white_noise, axis=1)
if normed:
red_noise_comps = np.apply_along_axis(normalize_signal, 1, red_noise_comps)
# remember to flatten before returning since we're actually working in 1D
return red_noise_comps.flatten()
def scale_noise(input_signal, noise_signal, snr_db):
"""
Appropriately scales a noise signal so that it can be applied to an input signal
as additive noise with a desired signal-to-noise ratio
Parameters
----------
input_signal : numpy.ndarray
The input signal to which we wish to add noise
noise_signal : numpy.ndarray
The noise signal that we wish to add to `input_signal`
snr_db : float
The desired signal-to-noise ratio in decibels (dB)
Returns
-------
numpy.ndarray
The appropriately scaled noise signal. Adding this signal to `input_signal`
will cause the resulting signal to have a SNR roughly equivalent to `snr_db`
"""
snr = 10 ** (snr_db / 10)
signal_energy = np.sum(input_signal ** 2)
noise_energy = np.sum(noise_signal ** 2)
noise_scalar = np.sqrt(signal_energy / (snr * noise_energy))
return noise_scalar * noise_signal
def add_noise(input_signal, noise_signal, snr_db):
"""
Adds a noise signal to an input signal at a given signal-to-noise ratio.
Parameters
----------
input_signal : numpy.ndarray
The input signal to which we wish to add noise
noise_signal : numpy.ndarray
The noise signal that we wish to add to `input_signal`
snr_db : float
The desired signal-to-noise ratio in decibels (dB)
Returns
-------
numpy.ndarray
The original signal with the addition of noise at the desired SNR
"""
additive_noise = scale_noise(input_signal, noise_signal, snr_db)
return input_signal + additive_noiseFunctions
def normalize_signal(input_signal)-
Rescales a signal such that it is 0-centered and has a max amplitude of 1.
Parameters
input_signal:numpy.ndarray- The signal we wish to normalize.
Returns
numpy.ndarray- The resulting normalized signal
Expand source code
def normalize_signal(input_signal): """ Rescales a signal such that it is 0-centered and has a max amplitude of 1. Parameters ---------- input_signal : numpy.ndarray The signal we wish to normalize. Returns ------- numpy.ndarray The resulting normalized signal """ # centering it about 0 max_signal = np.max(input_signal) min_signal = np.min(input_signal) signal_range = max_signal - min_signal mid_signal = max_signal - signal_range / 2 zero_c_signal = input_signal - mid_signal # setting max = 1, min = -1 normed_signal = zero_c_signal / max(zero_c_signal) return normed_signal def gen_composite_red_noise(noise_length, component_length, normed=True)-
Generates a signal made of sub-signals of red noise.
Parameters
noise_length:int- The desired output signal length
component_length:int- The desired length of each sub-signal red noise.
If
component_lengthis not a factor ofnoise_length, the factor ofnoise_lengthclosest tocomponent_lengthwill be used normed:bool, defaultTrue- Whether each sub-signal should be normalized, i.e. centered about 0 with a max amplitude of 1.
Returns
numpy.ndarray- A signal made of sub-signals of red noise.
Expand source code
def gen_composite_red_noise(noise_length, component_length, normed=True): """ Generates a signal made of sub-signals of red noise. Parameters ---------- noise_length : int The desired output signal length component_length : int The desired length of each sub-signal red noise. If `component_length` is not a factor of `noise_length`, the factor of `noise_length` closest to `component_length` will be used normed : bool, default True Whether each sub-signal should be normalized, i.e. centered about 0 with a max amplitude of 1. Returns ------- numpy.ndarray A signal made of sub-signals of red noise. """ white_noise = np.random.randn(noise_length) # reshape white noise into comps, then cumsum each component individually white_noise = white_noise.reshape( (-1, find_closest_factor(noise_length, component_length)) ) red_noise_comps = np.cumsum(white_noise, axis=1) if normed: red_noise_comps = np.apply_along_axis(normalize_signal, 1, red_noise_comps) # remember to flatten before returning since we're actually working in 1D return red_noise_comps.flatten() def scale_noise(input_signal, noise_signal, snr_db)-
Appropriately scales a noise signal so that it can be applied to an input signal as additive noise with a desired signal-to-noise ratio
Parameters
input_signal:numpy.ndarray- The input signal to which we wish to add noise
noise_signal:numpy.ndarray- The noise signal that we wish to add to
input_signal snr_db:float- The desired signal-to-noise ratio in decibels (dB)
Returns
numpy.ndarray- The appropriately scaled noise signal. Adding this signal to
input_signalwill cause the resulting signal to have a SNR roughly equivalent tosnr_db
Expand source code
def scale_noise(input_signal, noise_signal, snr_db): """ Appropriately scales a noise signal so that it can be applied to an input signal as additive noise with a desired signal-to-noise ratio Parameters ---------- input_signal : numpy.ndarray The input signal to which we wish to add noise noise_signal : numpy.ndarray The noise signal that we wish to add to `input_signal` snr_db : float The desired signal-to-noise ratio in decibels (dB) Returns ------- numpy.ndarray The appropriately scaled noise signal. Adding this signal to `input_signal` will cause the resulting signal to have a SNR roughly equivalent to `snr_db` """ snr = 10 ** (snr_db / 10) signal_energy = np.sum(input_signal ** 2) noise_energy = np.sum(noise_signal ** 2) noise_scalar = np.sqrt(signal_energy / (snr * noise_energy)) return noise_scalar * noise_signal def add_noise(input_signal, noise_signal, snr_db)-
Adds a noise signal to an input signal at a given signal-to-noise ratio.
Parameters
input_signal:numpy.ndarray- The input signal to which we wish to add noise
noise_signal:numpy.ndarray- The noise signal that we wish to add to
input_signal snr_db:float- The desired signal-to-noise ratio in decibels (dB)
Returns
numpy.ndarray- The original signal with the addition of noise at the desired SNR
Expand source code
def add_noise(input_signal, noise_signal, snr_db): """ Adds a noise signal to an input signal at a given signal-to-noise ratio. Parameters ---------- input_signal : numpy.ndarray The input signal to which we wish to add noise noise_signal : numpy.ndarray The noise signal that we wish to add to `input_signal` snr_db : float The desired signal-to-noise ratio in decibels (dB) Returns ------- numpy.ndarray The original signal with the addition of noise at the desired SNR """ additive_noise = scale_noise(input_signal, noise_signal, snr_db) return input_signal + additive_noise