LaPlace transform: AttributeError: ‘ImmutableDenseNDimArray’ object has no attribute ‘expand’

[vincentladis]

Need help to compute the integrate equation of ∫x(t)*e^(-st) dt where x(t) is my original signal after ifft calculation. The result shows the follwing error AttributeError: 'ImmutableDenseNDimArray' object has no attribute 'expand' when we convert datas from tensors to numpy array. While using tensors data as the one after High pass filter here the problem TypeError: unsupported operand type(s) for *: 'Tensor' and 'exp'. How can I resolve this issue? Thanks in advance.
Here is my code:

`
import torch
import numpy as np
import matplotlib.pyplot as plt
import os
from scipy import signal
import math
import scipy
import sympy as sym

  os.environ["KMP_DUPLICATE_LIB_OK"] = "TRUE"

 f_s = 48000
  f_c = 16000
  f_l = 19000
  f_r = 17000
  b = f_l - f_r
  n_order = 5
  cut_off = 10


 def high_pass_filter():
    # generate a random signal
       array_list = np.random.randn(1, 100, 1000)

tensor_array = torch.from_numpy(array_list)

reshape_tensor = tensor_array.reshape(2, 10, -1)

reshape_img = reshape_tensor.reshape(-1)

# compute the fft
fft_signal = torch.fft.fft(reshape_tensor)
print(fft_signal)
reshape_fft_signal = fft_signal.reshape(-1)
normalize_cutoff = (((f_c - b)/cut_off) / 2) / (f_s/2)  # normalize cut_off
print("normalize : ", normalize_cutoff)
down = math.sqrt(1 + ((f_c / normalize_cutoff)**(2*n_order)))
print("down reponse : ", down)

butterworth = torch.tensor(1 / down)

G = torch.mul(butterworth, fft_signal)
G_reshape = G.reshape(-1)
output_filter = torch.fft.ifft2(G)
print(output_filter)
output_filter_reshape = output_filter.reshape(-1)

plt.figure()
plt.plot(reshape_img)
plt.figure()
plt.plot(reshape_fft_signal)
plt.figure()
plt.plot(G_reshape)
plt.figure()
plt.plot(output_filter_reshape)
# plt.show()
return output_filter


def pole_zero_plot(poles, zeros, ax=None):
      for pole in poles:
            plt.plot(complex(pole).real, complex(pole).imag, 'rx', markersize=10)
      for zero in zeros:
             plt.plot(complex(zero).real, complex(zero).imag, 'bo', markersize=10)

  if ax is None:
      ax = plt.gca()
  ax.set_aspect(1)

plt.axis([-2, 2, -2, 2])
plt.xlabel(r'$\Re\{s\}')
plt.ylabel(r'$\Im\{s\}')
plt.grid()


if __name__ == '__main__':
    sym.init_printing()

signal = high_pass_filter()
signal_numpy = signal.detach().numpy()

t = sym.symbols('t', real=True)
s = sym.symbols('s', complex=True)

X = sym.integrate(signal  * sym.exp(-s * t), (t, -sym.oo, sym.oo))
print(X)

s0 = sym.symbols('s0', complex=True)
#
X, a, cond = sym.laplace_transform(sym.exp(-s0 * t), t, s)
print(X, ";", a, ";", cond)
#
# # Convergence
#
sigma, omega = sym.symbols('sigma omega')
X = 1 / (s + s0)
X1 = X.subs({s: sigma + sym.I * omega, s0: 1 + sym.I})
sym.plotting.plot3d(abs(X1), (sigma, -2, 2), (omega, -2, 2),
                     xlabel=r'$\Re\{s\}$', ylabel=r'$\Im\{s\}$', title=r'$|X(s)|$')

poles = sym.roots(sym.denom(X), s)
# print(poles)
#
zeros = sym.roots(sym.numer(X), s)
print(zeros)
#
X2 = X.subs(s0, 1 + sym.I)
pole_zero_plot(sym.roots(sym.denom(X2), s), sym.roots(sym.numer(X2), s))

plt.show()

`

[oscarbenjamin]

I don't think you have copied your code in correctly.

In any case if signal is an array of numbers then what do you expect this to do:

X = sym.integrate(signal  * sym.exp(-s * t), (t, -sym.oo, sym.oo))

[vincentladis]

In the proper way, this line uses DiracDelta to multiply with the equation. In my case I switched DiracDelta to a generated signal which is the signal or signal_numpy in tensor or numpy shape, but raises errors. I want to calculate the impulse response of the signal via the transfer function of the temporal convolution of LAPlace transform from the latter. Is it possible to proceed through the steps in my script? If so, what type of signal do I need, simple equation or real data? I need you help, thanks

[oscarbenjamin]

I don't understand what you're trying to do but my guess is that you should be calculating this numerically rather than symbolically.

[hanspi42]

This discussion has fallen asleep, but @oscarbenjamin was totally correct.