This page covers the Discrete Time Fourier Series (DTFS), detailing its derivation and properties related to expanding discrete-time periodic functions into harmonic complex sinusoids.

Discrete Fourier series representation of a periodic signal The Discrete Fourier Series (DFS) is an alternative representation of a periodic sequence x with period N.

Discrete time signals are fundamentally different from countinuous time signals in that they only exist at discrete instances of time and are undefined elsewhere.

In representing discrete-time periodic signals through the Fourier series, we again use harmonically related complex exponentials with fundamental frequencies that are integer …

In digital signal processing, a discrete Fourier series (DFS) is a Fourier series whose sinusoidal components are functions of a discrete variable instead of a continuous variable.

Any signal in practice is a discrete time signal but furthermore it is a signal for a finite number of samples. No wonder that the computational way to do frequency analysis is by using the DT …

This discrete-time Fourier series representation provides notions of frequency content of discrete-time signals, and it is very convenient for calculations involving linear, time-invariant systems …

Georg Ohm (already known for his work on electrical conduction) in-terpreted Seebeck's results using Fourier's recently described series. He held that the pulses generated by a siren …

Since multiplication in frequency is the same as convolution in time, that must mean that when you convolve any signal with an impulse, you get the same signal back again:

Discrete–time Fourier series have properties very similar to the linearity, time shifting, etc. properties of the Fourier transform. A table of some of the most important properties is …