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

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

So this is what we do:

1. Take our target function, multiply it by sine (or cosine) and integrate (find the area)
2. Do that for n=0, n=1, etc to calculate each coefficient.
3. And after we calculate all coefficients, we put them into the series formula above.

## What is a Fourier series approximation?

Fourier series (real or complex) are very good ways of approximating functions in a finite range, by which we mean that we can get a good approximation to the function by using only the first few modes (i.e. truncating the sum over n after some low value n = N).

What is Fourier series expansion of signal?

To represent any periodic signal x(t), Fourier developed an expression called Fourier series. This is in terms of an infinite sum of sines and cosines or exponentials. Fourier series uses orthoganality condition.

### Which of the following is not Dirichlet condition for the Fourier series expansion?

f(x) has a finite number of discontinuities in only one period is not a Dirichlet’s condition for the Fourier series expansion​.

### What is the value of BN in Fourier series?

The value of fourier coefficient bn of the fourier sine series f(x)=x^2 for x in (0,π) isπ^2/3. π^2/5.

What is half range expansion?

Half Range Expansion of a Fourier series:- Suppose a function is defined in the range(0,L), instead of the full range (- L,L). Then the expansion f(x) contains in a series of sine or cosine terms only . The series is termed as half range sine series or half range cosine series.

#### Is Fourier series and Fourier transform same?

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.

Which of the following are Dirichlet’s conditions for the Fourier series expansion?

Explanation: Dirichlet’s condition for Fourier series expansion is f(x) should be periodic, single valued and finite; f(x) should have finite number of discontinuities in one period and f(x) should have finite number of maxima and minima in a period.

## Which of the following is Dirichlet condition?

Dirichlet Conditions in Fourier Transformation are as follows: f(x) must absolutely integrable over a period, i.e., ∫ − ∞ ∞ ⁡ f(x) must have a finite number of extrema in any given interval, i.e. there must be a finite number of maxima and minima in the interval.