FFT (Fast Fourier Transform) - a method for phase continuation

In summary, Finding a good query for narrow and sophisticated topics in search engines is not an easy task. When performing an FFT, the amplitude and phase spectra are obtained, with the latter ranging from -PI to PI. However, there may be discontinuities in the phase spectrum when it exceeds this range. One method to obtain a continuous phase spectrum is by duplicating and shifting the same phase spectrum multiple times by n*PI. This method has been seen in some paper works.
  • #1
petol
2
0
Hello everyone,
Finding a good query to find an answer in www search engines isn't as easy as I thought. The subject is very narrow and sophisticated.
When one performs a FFT, he/she/IT ;) gets the amplitude and phase spectra. The phase spectrum ranges from -PI to PI. Then, there are of course places where the phase spectrum is discontinuous because it exceeds the range. How to obtain such continuous phase spectrum? Does anyone know the idea for this?
Kind Regards
 
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  • #2
Maybe this picture will help. I duplicated the same phase spectrum several times and shifted n*PI each.
I'm looking for such method because I've seen it in some paper works.
 

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1. What is FFT?

FFT, or Fast Fourier Transform, is an algorithm used to quickly compute the discrete Fourier transform (DFT) of a sequence or signal. It is commonly used for analyzing the frequency components of a signal and is widely used in various fields including signal processing, image processing, and data compression.

2. How does FFT work?

FFT works by breaking down a signal into its individual frequency components through a series of mathematical operations. It takes a sequence of complex numbers as input and produces a sequence of complex numbers as output. The output sequence represents the same signal in the frequency domain, where the amplitude and phase of each frequency component can be analyzed.

3. What are the advantages of using FFT?

There are several advantages of using FFT over other methods for computing the discrete Fourier transform. First, it is much faster than traditional methods, making it more efficient for analyzing large amounts of data. Additionally, it is more accurate and less prone to rounding errors. It also has a wide range of applications, making it a versatile tool for scientists and engineers.

4. Can FFT be used for non-periodic signals?

Yes, FFT can be used for non-periodic signals by first adding padding zeros to the signal to make it periodic. This does not affect the accuracy of the results and allows FFT to be used for a wider range of signals. Additionally, there are other variations of FFT, such as the non-uniform FFT, which can handle non-periodic signals without the need for padding.

5. Are there any limitations to using FFT?

One limitation of using FFT is that it requires the signal to be evenly sampled. This means that the time intervals between each data point must be equal. If the signal is not evenly sampled, additional processing steps may be required. Another limitation is that FFT is most effective for signals with a large number of data points. For smaller data sets, other methods may be more suitable.

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