Why Fourier series is used for periodic signals only?

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.

Can we use Fourier series for non periodic signals?

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.

Which can be used for periodic and non periodic Fourier series or Fourier transform?

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.

Can we use Fourier transform for periodic signals?

NO, its Fourier series that is applicable to periodic functions only and Fourier series of that periodic function is a discrete exponential or sinusoidal or co-sinusoidal signal, so spectrum of Fourier series is always discrete and as i said earlier its applicable to only periodic signals so one can say that there is …

Why do we need Fourier transform in Fourier transform Infrared Spectroscopy?

Fourier transform infrared spectroscopy (FTIR) uses the mathematical process (Fourier transform) to translate the raw data (interferogram) into the actual spectrum. FTIR method is used to obtain the infrared spectrum of transmission or absorption of a fuel sample.

Do all periodic functions have a Fourier series?

If we impose some restrictions on what kind of functions can be considered a “signal,” then all periodic signals have a Fourier series. The function should be piecewise continuous.

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

Fourier series is an expansion of periodic signal as a linear combination of sines and cosines while Fourier transform is the process or function used to convert signals from time domain in to frequency domain.

Is Fourier transform Non periodic?

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.

How do you find the Fourier transform of a periodic signal?

Fourier Transform of a Periodic Signal Described by a Fourier Series Given a periodic function xT(t) and its Fourier Series representation (period= T, ω0=2π/T): xT (t) = +∞ ∑ n=−∞cnejnω0t x T (t) = ∑ n = − ∞ + ∞ c n e j n ω 0 t we can use the fact that we know the Fourier Transform of the complex exponential

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 the Fourier series based on?

We now know that the Fourier Series rests upon the Superposition Principle, and the nature of periodic waves. The sinusoidal components are integer multiples of the fundamental frequency of a periodic wave.

How do trigonometric Fourier series work?

What trigonometric Fourier series do is represent a time-domain periodic function as a time-domain sum of sinusoids; notice that when you represent a function as a Fourier series, you’re still in the time domain (although if you plot its amplitude spectrum and its phase spectrum, maybe we could say you’re in the frequency domain.)