Table of Contents

## What is Fourier series representation of periodic signals?

The Fourier series represents periodic, continuous-time signals as a weighted sum of continuous-time sinusoids. It is widely used to analyze and synthesize periodic signals.

### Which of the following are types of representation of discrete-time sequences?

There are three ways to represent discrete time signals.

- Functional Representation.
- Tabular method of representation.
- Sequence Representation.

**Is discrete Fourier series periodic?**

In digital signal processing, the term Discrete Fourier series (DFS) is any periodic discrete-time signal comprising harmonically-related (i.e. Fourier) discrete real sinusoids or discrete complex exponentials, combined by a weighted summation. A specific example is the inverse discrete Fourier transform (inverse DFT).

**What is the Fourier series of a periodic function?**

A Fourier series (/ˈfʊrieɪ, -iər/) is a sum that represents a periodic function as a sum of sine and cosine waves. The frequency of each wave in the sum, or harmonic, is an integer multiple of the periodic function’s fundamental frequency. Each harmonic’s phase and amplitude can be determined using harmonic analysis.

## What do you mean by DFT?

discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.

### What is Fourier series in signal and system?

The Fourier Series is a specialized tool that allows for any periodic signal (subject to certain conditions) to be decomposed into an infinite sum of everlasting sinusoids. This may not be obvious to many people, but it is demonstrable both mathematically and graphically.

**What are the different types of representation of discrete?**

Representation of a Discrete Time Signal

- Graphical Representation.
- Functional Representation.
- Tabular Representation.
- Sequence Representation.

**How do you find the representation of a Fourier series?**

To find the coefficients a0, an and bn we use these formulas:

- a0 = 12L. L. −L. f(x) dx.
- an = 1L. L. −L. f(x) cos(nxπL) dx.
- bn = 1L. L. −L. f(x) sin(nxπL) dx.

## What is the discrete Fourier series expansion of the periodic sequence?

Hence Eq. (2.108) is recognized as the discrete Fourier series expansion of the periodic sequence {x ( n )}, and { X ( k )} are just the discrete Fourier series coefficients scaled by N. Conventional frequency domain interpretation permits an identification of X (0)/ N as the “DC” value of the signal.

### How many types of Fourier series representations are there?

There are two types of Fourier series representations, both are equivalent to each other. Depending on the type of signal, most convenient representation is chosen. J. B. J. Fourier demonstrated that a periodic function f (t) can be expressed as a sum of sinusoidal functions.

**What is the Fourier transform in frequency spectrum analysis?**

As with the discrete Fourier series, the DFT produces a set of coefficients, which are sampled values of the frequency spectrum at regular intervals. The number of samples obtained depends on the number of samples in the time sequence. A time sequence x ( n) is transformed into a sequence X (ω) by the discrete Fourier transform.

**What is discrete Fourier series (DFS)?**

Discrete Fourier Series Computational schemes can only be applied to discrete signals, and the continuous signals acquired by measurements are thus digitized. The DFS is the Fourier tool suitable for decomposing discrete periodic signals of the form: (52a)x(n) = x(n + N)