Is FFT the Proper Method for Transforming Green Function in MATLAB?

In summary, the conversation revolved around using the FFT function in MATLAB for a non-periodic Green function. The participants discussed the necessity of zero-padding and windowing for non-periodic functions, as well as issues with ordering and high order components. The conclusion was that zero-padding is necessary for non-periodic functions, and that high order components can occur when the function has jumps or is not continuous across the boundaries.
  • #1
Zahra G
6
0
Hi everybody.
I have a (1×N) Green function in MATLAB. I want to use the FFt function for Green function to transform the time domain. Does the FFT command work correctly for Green function using: A=fft(Green function, nfft). Here nfft is the number of transformed points. Is it necessary that N=nfft ?
 
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  • #2
Why don't you try and tell us the result? Then we can analyze if something goes as not expected.
 
  • #3
I tried and I wanted to be sure that using fft command is true for non-periodic function like Green function or not?
 
  • #4
The FFT function in Matlab is really no different than other implementations of discrete Fourier transform. Hence, when you are using if for a non-periodic function (which in real life is almost always) you need to consider things like zero-padding (which is usually a good idea for non-periodic functions) and windowing ( should not really be needed here). One common -and not so obvious- problem is the way the elements in the resulting FFT are ordered. You may or mat not have to use the fftshift command, depending on what you are doing.
 
  • #5
Thank you.
 
  • #6
I would like to know that if my Green function was nonzero in almost energies (because the energy interval is from -infinity to infinity) is it necessary that I have zero padding?
Another question is that when I use the FFT without zero padding, my function goes to high orders. For example, if the value of the function is 0.4 the fft goes it to 10e03. Is it ordinary or not?
 
  • #7
The proper use of the FFT implies that the function is periodic. The zero padding ensure that the function can be interpreted as "periodic" because when you shift the computational windows you can match them because they all go to zero at the boundary. Using FFT without padding implies that you function is truly periodic, it is continuous across the left-right boundary, left boundary value is equal to the right boundary value. When you have jumps in the function, inside the computational domain or because the left boundary values is different from the right one, then you will see those high order components.
 

1. What is a Green function in FFT?

A Green function is a mathematical tool used in the field of signal processing to represent the response of a system to an input signal. It is particularly useful in Fourier analysis and can be used to efficiently calculate the Fourier transform of a signal using the Fast Fourier Transform (FFT) algorithm.

2. How does FFT using Green function work?

In FFT using Green function, the input signal is first convolved with the Green function to obtain the response of the system. This response is then transformed using FFT to obtain the Fourier transform of the signal. This method is faster than traditional FFT as it eliminates the need for computing multiple Fourier transforms of the input signal.

3. What are the advantages of using FFT with Green function?

The main advantage of using FFT with Green function is the speed of calculation. By convolving the input signal with the Green function, the number of Fourier transforms needed to be computed is reduced, resulting in a faster calculation. Additionally, FFT using Green function can handle non-periodic signals, which is useful in many real-world applications.

4. Are there any limitations to using FFT with Green function?

One limitation of using FFT with Green function is that it requires the system to be linear and time-invariant. This means that the system's response must be the same regardless of when the input signal is applied. Additionally, FFT using Green function may not be suitable for signals with sharp discontinuities or high-frequency components.

5. How is FFT with Green function used in practical applications?

FFT with Green function is commonly used in various fields such as image processing, audio signal processing, and communication systems. It is particularly useful in scenarios where fast and efficient calculation of the Fourier transform is required, such as in real-time signal processing applications. It is also used in scientific research and engineering for analyzing and simulating dynamic systems.

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