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bundles / scipy 1.17.1 / scipy / signal / _waveforms / sweep_poly

function

scipy.signal._waveforms:sweep_poly

source: /scipy/signal/_waveforms.py :473

Signature

def   sweep_poly ( t ,  poly ,  phi = 0 )

Summary

Frequency-swept cosine generator, with a time-dependent frequency.

Extended Summary

This function generates a sinusoidal function whose instantaneous frequency varies with time. The frequency at time t is given by the polynomial poly.

Parameters

t : ndarray

Times at which to evaluate the waveform.

poly : 1-D array_like or instance of numpy.poly1d

The desired frequency expressed as a polynomial. If poly is a list or ndarray of length n, then the elements of poly are the coefficients of the polynomial, and the instantaneous frequency is

f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]

If poly is an instance of numpy.poly1d, then the instantaneous frequency is

f(t) = poly(t)

phi : float, optional

Phase offset, in degrees, Default: 0.

Returns

sweep_poly : ndarray

A numpy array containing the signal evaluated at t with the requested time-varying frequency. More precisely, the function returns cos(phase + (pi/180)*phi), where phase is the integral (from 0 to t) of 2 * pi * f(t); f(t) is defined above.

Notes

If poly is a list or ndarray of length n, then the elements of poly are the coefficients of the polynomial, and the instantaneous frequency is:

f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]

If poly is an instance of numpy.poly1d, then the instantaneous frequency is:

f(t) = poly(t)

Finally, the output s is:

cos(phase + (pi/180)*phi)

where phase is the integral from 0 to t of 2 * pi * f(t), f(t) as defined above.

Array API Standard Support

sweep_poly has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

Compute the waveform with instantaneous frequency:: f(t) = 0.025*t**3 - 0.36*t**2 + 1.25*t + 2 over the interval 0 <= t <= 10. 
import numpy as np
from scipy.signal import sweep_poly
p = np.poly1d([0.025, -0.36, 1.25, 2.0])
t = np.linspace(0, 10, 5001)
w = sweep_poly(t, p)
✓
Plot it: 
import matplotlib.pyplot as plt
✓
plt.subplot(2, 1, 1)
plt.plot(t, w)
plt.title("Sweep Poly\nwith frequency " +
          "$f(t) = 0.025t^3 - 0.36t^2 + 1.25t + 2$")
plt.subplot(2, 1, 2)
plt.plot(t, p(t), 'r', label='f(t)')
plt.legend()
plt.xlabel('t')
✗
plt.tight_layout()
plt.show()
✓
fig-5f6ba4b0394bdcfc.png

See also

chirp

Aliases

  • scipy.signal.sweep_poly

Referenced by

This package