fft - About Discrete Fourier Transform vs. Discrete Fourier Series

I am new to the field of signal processing. I am wondering what is the difference between DFS(Fourier Series) vs. DFT(Fourier Transform).

For common applications, usually we get a segment(length N) of digital waveform(like a audio segment), and then we apply FFT(DFT) and then do post-analysis with it.

I am wondering if we can use DFS(thus not using DFT at all) all the time and just assume the waveform segment is repeated with period N. Would this naive thinking/approach cause any problems?

Answer

There is no operational difference between what is commonly called the Discrete Fourier Series (DFS) and the Discrete Fourier Transform (DFT). On the USENET newsgroup comp.dsp, we have had fights about this topic multiple times (if Google Groups wasn't so badly broken and messed up, I might be able to point you to the threads) and, despite the deniers, there is no, none whatsoever, operational difference between what is sometimes labeled as the DFS but most commonly labeled as the DFT. (The "FFT" is essentially an efficient or fast method of calculating the DFT.)