I have data with a vertical coordinate named fy as the amplitude and a horizontal coordinate named fx as the frequency Please use python codes to plot a squared envelope spectrum for this data

Assuming that your data is stored in a NumPy array called data with the shape (n, m) where n is the number of frequency samples and m is the number of amplitude samples, you can use the following Python code to plot a squared envelope spectrum:

import numpy as np
import matplotlib.pyplot as plt

# Compute the envelope spectrum
envelope = np.abs(np.fft.fft(data, axis=1)) ** 2

# Plot the envelope spectrum
plt.imshow(envelope.T, aspect='auto', origin='lower', extent=(fx[0], fx[-1], fy[0], fy[-1]))
plt.xlabel('Frequency (Hz)')
plt.ylabel('Amplitude')
plt.colorbar()
plt.show()

In this code, we first use the np.fft.fft function to compute the Fourier transform of the data along the amplitude axis (axis=1). We then take the absolute value of the resulting complex values and square them to obtain the envelope spectrum.

Finally, we use the imshow function from matplotlib to plot the envelope spectrum as an image. We set the aspect parameter to 'auto' to ensure that the aspect ratio of the plot matches the aspect ratio of the data. We also set the origin parameter to 'lower' to ensure that the y-axis is oriented from low to high values. The extent parameter specifies the limits of the x and y axes, which should correspond to the minimum and maximum values of the fx and fy arrays, respectively. The xlabel and ylabel functions are used to label the x and y axes, and the colorbar function adds a colorbar to the plot. Finally, the show function displays the plot