## Can any signal be represented by Fourier series?

Almost any periodic function can be represented by a Fourier series that converges.

## How do you find the Fourier series of a signal?

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.

Which type of signal is used in Fourier transform?

There are some naturally produced signals such as nonperiodic or aperiodic, which we cannot represent using Fourier series. To overcome this shortcoming, Fourier developed a mathematical model to transform signals between time (or spatial) domain to frequency domain & vice versa, which is called ‘Fourier transform’.

### What class of signals is the Fourier series valid for?

Fourier Series (FS) exists only for periodic signals.

### What is Fourier series in networking?

A Fourier series is a representation of a wave form or other periodic function as a sum of sines and cosines. It is named after the French mathematician and physicist Jean-Baptiste Joseph Fourier (1768–1830). Since sound waves are made up of sine waves, Fourier transforms are widely used in signal processing.

What are periodic and aperiodic signals?

A signal is said to be periodic signal if it has a definite pattern and repeats itself at a regular interval of time. Whereas, the signal which does not at the regular interval of time is known as an aperiodic signal or non-periodic signal.

#### What Fourier series do?

Fourier series is used to describe a periodic signal in terms of cosine and sine waves. In other other words, it allows us to model any arbitrary periodic signal with a combination of sines and cosines.

#### What is a aperiodic signal?

A non-periodic or aperiodic signal is one for which no value of T satisfies Equation 10.11. In principle this includes all actual signals since they must start and stop at finite times. However, aperiodic signals can be presented quantitatively in terms of periodic signals.

What is the Fourier series of a basis signal?

If we consider basis signals as complex exponentials, then the Fourier Series is known as Exponential Fourier Series . If the basis signals are sines and cosines then the Fourier Series is known as Trigonometric Fourier Series.

## What is the Fourier series representation of CT periodic signals?

Fourier Series Representation of CT Periodic Signals – smallest such T is the fundamental period – is thefundamental frequency Periodic with period T -periodic with period T -{a k } are the Fourier (series) coefficients -k= 0 DC -k= 1 first harmonic -k= 2 second harmonic ()t

## What is the Fourier series of convergence?

Still, convergence has some interesting characteristics: Book Chapter 3 : Section 1 Computer Engineering Department, Signal and Systems 16 – The Fourier series = x(t) at points where x(t) is continuous – The Fourier series = “midpoint” at points of discontinuity – As N→ ∞, x

What are the Fourier (series) coefficients for the first harmonic?

k } are the Fourier (series) coefficients -k= 0 DC -k= 1 first harmonic -k= 2 second harmonic ()t 0T2/ e