Quasi-zero basis understand FFT Fast Fourier transformation and its implementation procedure (2)

Quasi-zero basis understand FFT Fast Fourier transformation and its implementation procedure (2)

In the previous article, we learned about the principles of DFT. FFT is a DFT-based algorithm that is more suitable for computer computation. In this article, we started to learn the principles of FFT.

First, let me take a macro look at FFT. If we regard the entire FFT algorithm as a black box, its input is the Time Waveform signal, such as the sound waveform (the horizontal axis is time, and the vertical axis is amplitude ). In addition, what FFT is faster than DFT? The following figure (1) illustrates the complexity of FFT and DFT Algorithms (for computers ).

Figure 1

From the above mathematical expression, we can see that the FFT of A 1024 sample point is 102.4 times that of the DFT block. If the Fourier transformation has a larger order of magnitude, the speed advantage of FFT will be more obvious. This is why the meaning of FFT is to be invented.

To understand FFT, we can take the following steps:

1. Learning "Danielson-Lanczos Lemma" requires a slightly complex mathematical formula, but this is a very important part of FFT,

2. Understand "twiddle factor ". The rotation factor has been mentioned in the last DFT article.

3. Master "Butterfly digoal ". Butterfly operation, which is also the most distinctive algorithm of FFT.

4. Master "reverse bit pattern". Because of my study in the UK, I don't know what Chinese is called. Readers can go to Baidu.