Sliding DFT discrete Fourier transform

[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

 

[Xezlec]

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

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.

 

[oswaler]

I can provide some insight into the sliding DFT algorithm and its potential applications. The sliding DFT is a variation of the traditional discrete Fourier transform (DFT) that allows for efficient calculation of the DFT in real-time applications. It works by using a sliding window instead of the entire signal, which reduces the computational complexity and allows for faster processing.

One potential application of the sliding DFT is in signal processing, specifically in real-time audio or video processing. It can be used to analyze and filter incoming signals in real-time, which is useful in applications such as audio equalization or video compression. The sliding DFT also has applications in digital communications, where it can be used to extract and demodulate signals in real-time.

In terms of understanding the mathematics behind the algorithm, it is based on the principles of the DFT, which is a mathematical tool for analyzing the frequency components of a signal. The sliding DFT introduces a sliding window and uses the overlap-add method to efficiently calculate the DFT of the signal.

While there may not be a lot of information readily available online, there have been numerous studies and research papers published on the sliding DFT and its applications. I suggest looking into these resources for a deeper understanding of the algorithm and its potential uses.

Overall, the sliding DFT is a useful tool in real-time signal processing and has applications in various industries. I hope this helps in your understanding and potential use of the algorithm.