Is This the Correct Approach for Fourier Transform and Gaussian Filter?

[Jamin2112]

Homework Statement

Homework Equations

Fourier transform, Gaussian filter

The Attempt at a Solution

First of all, someone in the class did it correctly and here's what they said:

Second of all, let me make sure I have a correct understanding of this.

We have a 20 x 262144 matrix (note that that 262144 = 64³) each row i, column j is the amplitude of the signal. We're supposed to fft and sum each row before dividing by 20, to get the average power at each frequency. Further, if you look at the code at the bottom you see that the 262144 columns are actually frequencies meant to be in a 64 x 64 x 64 matrix. So we have a 64 x 64 x 64 matrix, each index being a frequency and each containing an average power value. Find the location of the maximum power value. Do an inverse fft. Put a Gaussian filter around the frequency we found. Then look at the plot of the average signal with the filter.

Basically correct?

 

[mighty2000]

Hello! It seems like you have a good understanding of the problem and the steps involved in solving it. Let me break it down for you and provide some additional information.

First of all, the purpose of the Fourier transform is to convert a signal from the time domain to the frequency domain. This allows us to analyze the signal in terms of its frequency components. The Fourier transform of a signal will give us a spectrum, which is a plot of the signal's amplitude vs frequency.

In this case, we have a 20 x 262144 matrix, where each row represents a different signal and each column represents a different time point. To find the average power at each frequency, we need to first perform an FFT on each row of the matrix. This will give us a 20 x 262144 matrix in the frequency domain. We then need to sum the values in each column and divide by 20 to get the average power at each frequency. This will give us a 1 x 262144 matrix with the average power values at each frequency.

Next, we need to find the location of the maximum power value in this 1 x 262144 matrix. This will give us the frequency with the highest power. We then need to perform an inverse FFT on this frequency to get a signal in the time domain.

To filter out this frequency, we can use a Gaussian filter. This will essentially remove the frequency from the signal. Finally, we can plot the filtered signal and compare it to the original signal to see the effects of the filtering.

I hope this helps clarify the steps involved in solving this problem. Let me know if you have any further questions.