The entire 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
print(torch.__version__)
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 transformation(x, real_sigma_interval=torch.arange(-1, 1 + 0.001, 0.001)):
x = x
d = []
for sigma in real_sigma_interval:
exp = torch.exp(sigma * torch.tensor(range(len(x))))
exp /= torch.sum(exp)
# Option 1
out_1 = exp.view(2, 1, 1) * x
# Option 2
out_2 = torch.einsum('i, ijk->ijk', [exp, x])
# Same result
# print(torch.all(out_1 == out_2))
# exponentiated_signal = exp * x.T
d.append(out_1)
return torch.tensor([torch.fft.rfft(k) for k in d])
if __name__ == '__main__':
signal = high_pass_filter()
print("X signal : ", signal)
print(signal.shape)
l = transformation(signal)
```

Here is my X dataset :

```
tensor([[[ 3.4059e-30+1.0762e-46j, 4.8306e-30-1.9032e-46j,
3.6210e-30-9.2822e-46j, ...,
-3.9725e-30-1.3303e-46j, 3.0239e-30-6.3144e-46j,
-3.3859e-30+5.0432e-46j],
[ 1.2419e-29+5.6312e-30j, 1.7369e-31+3.3395e-30j,
-5.4256e-30-1.0258e-30j, ...,
1.9680e-30+8.6273e-30j, 1.7434e-30-2.6541e-30j,
7.2166e-30+2.3827e-30j],
[ 1.1664e-30+3.6048e-30j, 5.4630e-30+2.5606e-30j,
-1.0161e-30-1.3846e-30j, ...,
-3.3588e-30+2.0733e-30j, -1.9508e-30-9.3269e-31j,
1.3305e-32-7.5297e-30j],
...,
[ 2.3808e-30+1.4374e-30j, -4.0271e-30+3.6610e-30j,
-7.3671e-30+2.4534e-30j, ...,
2.5958e-30-3.9952e-30j, 4.3275e-30-1.1570e-30j,
-2.1836e-30-4.2820e-30j],
[ 1.1664e-30-3.6048e-30j, 5.4630e-30-2.5606e-30j,
-1.0161e-30+1.3846e-30j, ...,
-3.3588e-30-2.0733e-30j, -1.9508e-30+9.3269e-31j,
1.3305e-32+7.5297e-30j],
[ 1.2419e-29-5.6312e-30j, 1.7369e-31-3.3395e-30j,
-5.4256e-30+1.0258e-30j, ...,
1.9680e-30-8.6273e-30j, 1.7434e-30+2.6541e-30j,
7.2166e-30-2.3827e-30j]],
[[-1.0756e-30+1.9013e-46j, 1.2508e-29-3.5579e-46j,
4.4410e-30-3.9580e-46j, ...,
5.8015e-30-7.1195e-46j, -4.0934e-30+2.1252e-45j,
1.0737e-29+2.8130e-45j],
[-6.4574e-30+8.5894e-30j, -2.3886e-31+9.6275e-30j,
-1.6730e-30-6.5154e-30j, ...,
-2.2550e-30-1.3787e-30j, 2.2739e-30-2.2057e-30j,
-7.7044e-31+1.0369e-30j],
[ 7.7674e-31+1.1331e-31j, -2.0076e-30+4.8946e-31j,
-1.1086e-30-3.7737e-30j, ...,
5.4034e-30+3.3697e-30j, -2.9261e-31-3.7502e-30j,
-6.2307e-31+2.5731e-30j],
...,
[-4.2135e-30-1.2409e-31j, -5.0822e-30-1.0209e-30j,
-4.2199e-30+2.1307e-30j, ...,
-8.1933e-30+3.8817e-30j, -1.7231e-30+8.7054e-31j,
-5.1156e-30+7.2661e-31j],
[ 7.7674e-31-1.1331e-31j, -2.0076e-30-4.8946e-31j,
-1.1086e-30+3.7737e-30j, ...,
5.4034e-30-3.3697e-30j, -2.9261e-31+3.7502e-30j,
-6.2307e-31-2.5731e-30j],
[-6.4574e-30-8.5894e-30j, -2.3886e-31-9.6275e-30j,
-1.6730e-30+6.5154e-30j, ...,
-2.2550e-30+1.3787e-30j, 2.2739e-30+2.2057e-30j,
-7.7044e-31-1.0369e-30j]]], dtype=torch.complex128)
```

shape : `torch.Size([2, 10, 5000])`