How does the Cooley-Tukey FFT algorithm work?

In summary, the Fast Fourier Transform (FFT) is a mathematical algorithm used to efficiently compute the discrete Fourier transform (DFT) of a sequence or signal. It differs from the regular Fourier Transform by using a divide-and-conquer approach to reduce computations. Its applications include signal processing, data compression, and image processing, but it has limitations in terms of data requirements and accuracy. There are alternative algorithms, but the FFT remains the most widely used and efficient method for computing the DFT in most applications.
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andrey21
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First of all I apologies if I am in the wrong part of the forum for this question but here it is:
How do I go about finding the Fast Fourier Transform (FFT) for a given data set?



Homework Equations



Ive tried using FFT Magnitude = FFT (Real numbers)^2 + FFT (imaginary numbers)^2

From this I have plotted the values gained and seems to be correct, any advice greatly appreciated
 
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1. What is the Fast Fourier Transform (FFT)?

The Fast Fourier Transform (FFT) is a mathematical algorithm used to efficiently compute the discrete Fourier transform (DFT) of a sequence or signal. It is commonly used in signal processing and data analysis to convert a signal from its original domain (often time or space) to a representation in the frequency domain.

2. How does the FFT differ from the regular Fourier Transform?

The FFT is an optimized version of the regular Fourier Transform, which uses a divide-and-conquer approach to reduce the number of computations needed. This makes it much faster and more efficient for calculating the DFT of large sequences or signals.

3. What are the applications of the FFT?

The FFT has a wide range of applications in various fields, including signal processing, data compression, image processing, and spectral analysis. It is also used in the design and analysis of digital filters and in solving differential equations.

4. What are the limitations of the FFT?

The FFT can only be applied to discrete data that is evenly spaced in time or space. It also assumes that the data is periodic, which may not always be the case in real-world applications. Additionally, it is only accurate for signals that are stationary or have a stable frequency content.

5. Are there any alternatives to the FFT?

Yes, there are alternative algorithms for calculating the DFT, such as the discrete cosine transform (DCT) and the Chirp Z-transform (CZT). However, the FFT remains the most widely used and efficient method for computing the DFT in most applications.

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