The basic idea of a Fourier series is that you use integer multiples of some fundamental frequency to represent any time domain signal.

Haykin page 253

Ok, so if the Fourier Transform (Non periodic, continuous in time, or non periodic, discrete in time) results in a continuum of frequencies, then uh, is there no fundamental frequency / concept of using integer multiples of some fundamental frequency?

  • 2
    $\begingroup$ Nope. Pretty much by definition, right? $\endgroup$ – Qiaochu Yuan Nov 7 '11 at 16:30
  • $\begingroup$ The Fourier series deals with discrete fundamentals and harmonics of periodic functions. The Fourier transform is a continuous generalization to non-periodic functions. $\endgroup$ – endolith Nov 8 '11 at 14:52

In order to talk about a fundamental frequency, you need a fundamental period. But the Fourier transform deals with integrable functions ($L^1$, or $L^2$ if you go further in the theory) defined on the whole real line, and they are not periodic (except the zero function).

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