Which function Cannot be expanded as Fourier series?

x4(t) = 2 cos(1.5)t + sin(3.5)t first term has frequency w1 = 1.5π and 2nd term has frequency w2 = 3.5π. Since, \frac{ω_1}{ω_2} = \frac{3}{7}, which is rational. Since x2(t) is not periodic, so it cannot be expanded in Fourier series.

Which function can be expanded as Fourier series?

A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

Can Fourier series representation be used for non periodic signals?

Fourier series representation can be used in case of Non-periodic signals too. The Fourier series is the representation of periodic signals in terms of complex exponentials, or equivalently in terms of sine and cosine waveform leads to Fourier series.

Which of the following functions Cannot be expanded in Fourier series in the interval (-)?

→ The frequency of first term frequency of 2nd term is ω2 = 1. So, x(t) is a periodic or not periodic. Since function in (b) is non periodic. So does not satisfy Dirichlet conditionand cannot be expanded in Fourier series.

What are the conditions for any series to be a Fourier series?

The conditions are: f must be absolutely integrable over a period. f must be of bounded variation in any given bounded interval. f must have a finite number of discontinuities in any given bounded interval, and the discontinuities cannot be infinite.

What can be used for periodic and non periodic Fourier series?

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.

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.

Which of the following is not a Dirchlet’s condition for the Fourier series expansion?

(c) f(x) must have a finite number of discontinuities in any given bounded interval, and the discontinuities cannot be infinite. Hence, the correct option is (b) i.e.f(x) has finite number of discontinuities in only one period.

Which of the following function is not a periodic function?

We know, √cosx and sin-1 both are periodic. So, this function is also periodic. As we can see, T is dependent on the value of x and hence, is not a constant. So cos(x2) is not periodic.

What are Dirichlet conditions for Fourier series expansion?

Can non-periodic functions be represented by a Fourier series?

The periodic functions can be represented by a Fourier series. If you add up the Fourier series, you get a series that represents their sum. But their sum is not periodic, yet you have described it using a Fourier series. I thought that non-periodic functions can’t be represented by a Fourier series. Why isn’t this a contradiction?

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.

How do you calculate the Fourier expansion of a function?

In fact, a well known exercise demonstration of this is calculating the Fourier expansion of the function, f (x) = x. However, there are very important caveats. The most important of these is that the Fourier Series will only be valid in the interval used for the Fourier series.

Is the sum of the periodic functions periodic?

Assume their sum is not periodic. The periodic functions can be represented by a Fourier series. If you add up the Fourier series, you get a series that represents their sum. But their sum is not periodic, yet you have described it using a Fourier series.