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frequency.py
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Fri, May 23, 02:28

frequency.py
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import torch, math
from .interpolation1d import _Interpolate
from matplotlib import pyplot as plt
# -------- Hilbert-transform for demodulation ---------------
def hilbert(x):
'''
Perform Hilbert transform along the last axis of x.
Parameters:
-------------
x (Tensor) : The signal data.
The Hilbert transform is performed along last dimension of `x`.
Returns:
-------------
analytic (Tensor): A complex tensor with the same shape of `x`,
representing its analytic signal.
'''
x = torch.as_tensor(x).double()
N = x.shape[-1]
Xf = torch.fft.fft(x)
if (N % 2 == 0):
Xf[..., 1 : N//2] *= 2
Xf[..., N//2+1 : ] = 0
else:
Xf[..., 1 : (N+1)//2] *= 2
Xf[..., (N+1)//2 : ] = 0
return torch.fft.ifft(Xf)
def get_envelope_frequency(x, fs, ret_analytic = False, **kwargs):
'''
Compute the envelope and instantaneous freqency function of the given signal, using Hilbert transform.
The transformation is done along the last axis.
Parameters:
-------------
x (Tensor) :
Signal data. The last dimension of `x` is considered as the temporal dimension.
fs (real) :
Sampling frequencies in Hz.
ret_analytic (bool, optional) :
Whether to return the analytic signal.
( Default: False )
Returns:
-------------
(envelope, freq) when `ret_analytic` is False
(envelope, freq, analytic) when `ret_analytic` is True
envelope (Tensor) :
The envelope function, with its shape same as `x`.
freq (Tensor) :
The instantaneous freqency function measured in Hz, with its shape
same as `x`.
analytic (Tensor) :
The analytic (complex) signal, with its shape same as `x`.
'''
x = torch.as_tensor(x).double()
analytic = hilbert(x)
envelope = analytic.abs()
sub = torch.cat( (analytic[..., 1:] - analytic[..., :-1],
(analytic[..., -1]-analytic[..., -2]).unsqueeze(-1)
) , axis = -1 )
add = torch.cat( (analytic[..., 1:] + analytic[..., :-1],
2 * analytic[..., -1].unsqueeze(-1)
) , axis = -1 )
freq = 2 * fs * ((sub / add).imag)
freq[freq.isinf()] = 0
del sub, add
freq /= (2 * math.pi)
return (envelope, freq) if not ret_analytic else (envelope, freq, analytic)

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