Howtosignalprocessing
- What is the Fourier transform of a periodic signal?
- Why Fourier series is used for periodic signals?
- Is Fourier series applicable for periodic signals?
- Are all Fourier transforms periodic?
What is the Fourier transform of a periodic signal?
The Fourier transform of periodic signals can be found using the concept of impulse function. Hence, The Fourier transform of a periodic function consists of a series of equally spaced impulses and these impulse are located at the harmonic frequencies of the signal.
Why Fourier series is used for periodic signals?
Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components. A periodic signal is just a signal that repeats its pattern at some period. The primary reason that we use Fourier series is that we can better analyze a signal in another domain rather in the original domain.
Is Fourier series applicable for periodic signals?
The Fourier series is applicable only to the periodic signals i.e. the signals which repeat itself periodically over an interval from (−∞to∞)and it cannot be applied to non-periodic signals.
Are all Fourier transforms periodic?
The Discrete Fourier Transform is always periodic, but we usually focus only on what's inside the Nyquist window and ignore the periodic copies outside. The regular Fourier Transform (function of continuous frequency) cannot be periodic, to my knowledge.
