DSP - What is the difference between CTFS and CTFT

[Faizan Tahir Butt]

DSP

What is the difference between Continuous Time Fourier Series(CTFS) and
Continuous Time Fourier Transform(CTFT)? and how both are co-related?

 

[ring0]

Re: DSP

The difference is in that continuous time Fourier series are used to represent periodic signal (the spectrum of such signal is discrete, that's why Fourier series consist of separate harmonics). Conversely, continuous time Fourier transform represents aperiodic, unlimited (in time) signal (which have continuous spectrum).

By the way:

Fourier Series: periodic, continuous in time domain -> aperiodic, discrete in frequency domain

Fourier Transform: aperiodic, continuous in time domain -> aperiodic, continuous in frequency domain

Discrete Time Fourier Transform: aperiodic, discrete in time domain -> periodic, continuous in frequency domain

Discrete Fourier Transform: periodic, discrete in time domain -> periodic, discrete in frequency domain

That is, a periodic signal has discrete spectrum, an aperiodic signal has continuous spectrum, a discrete signal has periodic spectrum and a continuous signal has aperiodic spectrum.

 

[xulfee]

DSP

fourier series is used to find coefficents of periodic signals where as fourier transform is used to see how any signal is going to seen in frequency domain