# Sliding DFT discrete Fourier transform

1. Dec 14, 2008

### hxtasy

"Sliding DFT" discrete Fourier transform...

I was wondering if any of you had had experience with the sliding DFT algorithm. It is somewhat similar to the Goertzel algorithm.

I am having some trouble understanding the mathematics of the algorithm, and I also cannot seem to identify a useful application of it.

So far I have not found a lot of information online and I am hoping somebody that has encountered this in industry can help me out.

thanks,

-Hxtasy

2. Jan 1, 2009

### Xezlec

Re: "Sliding DFT" discrete Fourier transform...

It sounds like your problems cancel each other out!

I assume this is what you're talking about: http://www.comm.utoronto.ca/~dimitris/ece431/slidingdft.pdf

I read the paper, and it's really very simple. All it is saying is that if you have, for example, a 10-point DFT of samples 0-9 of a signal (let's call it x(n)), you can turn it into the 10-point DFT for samples 1-10 very easily. All you have to do is subtract x(0) and add x(10) to every point in the DFT, and then multiply each point k (from 0 to 9) in the DFT by e^(k*2*pi*j/10). That's it. Now you can repeat the process to get the DFT for samples 2-11, and so on.

This is useful if you want to analyze a signal by looking at a bunch of DFT's of little chunks in time. This is a very common way of analyzing signals. In fact, where I work, it's almost the only way anyone ever works with a signal. Looking at a set of DFT's for different points in time gives you a spectrum of the signal that changes with time. I can't think of a case where you wouldn't find that information useful. For example, a music player does something like this when it displays a spectrogram while it is playing.