Is Fourier series only applicable for periodic functions?

Fourier series is applicable only to periodic signals of period T. By setting T as very very large, we can turn a periodic signal to an aperiodic signal. This is Fourier Transform.

What is the Fourier transform of a non periodic signal?

Fourier transform require the signal to be periodic. Especially in image processing, images are not periodic (or most images don’t have periodic components) but people use 2D DFT to analyze their spectral features.

What is non periodic signal?

Non-periodic signals (also known as aperiodic signals), unlike periodic signals, do not have just one particular frequency. Instead, they are spread out over a continuous range of frequencies.

Which can be used for periodic and non periodic a Fourier series B Fourier transforms C Fourier series & transforms D None of the mentioned?

10. Which can be used for periodic and non periodic? Explanation: Fourier series is limited to only periodic signals where as Fourier transforms and laplace transforms can be used for both periodic and non periodic signals.

How do Fourier series represent periodic signals?

Fourier Series Representation of Continuous Time Periodic Signals

1. x(t)=cosω0t (sinusoidal) &
2. x(t)=ejω0t (complex exponential)
3. These two signals are periodic with period T=2π/ω0.
4. A set of harmonically related complex exponentials can be represented as {ϕk(t)}
5. Where ak= Fourier coefficient = coefficient of approximation.

What is the difference between Fourier series and non-periodic functions?

The Fourier series itself is a periodic function, so any function that equals its Fourier series must be periodic as well. A non-periodic function cannot equal its Fourier series, hence it is not that useful to use Fourier series to analyze non-periodic functions. On the other hand, a non-periodic function t

What is a Fourier series?

The most usual usage (as visible in the other answers and comments) is that “Fourier series” refers to that of a periodic function, or an extension-by-periodicity of a function on an interval to a periodic function on the line.

Can the Fourier series of a non-periodic signal be augmented?

Yes it can. To find the Fourier series of a non-periodic signal in the interval , just augment the signal at and for to make it periodic. What’s more, one can always make the augmented periodic signal always odd or always even. This is how half-range Fourier cosine and sine series work.

What is the difference between the Fourier series and the Laplace transform?

The Fourier series is applicable only to functions assumed to be periodic. A generalization called the Fourier transform is applicable to non periodic functions; the Laplace transform is applicable to functions defined only for non negative argument. Amazon doesn’t always show the best deal.