What kind of functions have Fourier series?

What kind of functions have Fourier series?

A Fourier series is a way of representing a periodic function as a (possibly infinite) sum of sine and cosine functions.

Which condition is required for representing a function as a Fourier series?

4. What are the conditions called which are required for a signal to fulfil to be represented as Fourier series? Explanation: When the Dirichlet’s conditions are satisfied, then only for a signal, the fourier series exist. Fourier series is of two types- trigonometric series and exponential series.

What functions have Fourier transforms?

The Fourier Transform is a mathematical technique that transforms a function of time, x(t), to a function of frequency, X(ω). It is closely related to the Fourier Series.

What functions can be Fourier transformed?

The Fourier transform can also be generalized to functions of several variables on Euclidean space, sending a function of 3-dimensional ‘position space’ to a function of 3-dimensional momentum (or a function of space and time to a function of 4-momentum).

Do all functions have a Fourier transform?

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.

Which of the following function Cannot be expanded as a Fourier series?

→ 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.

Is the Fourier transform linear?

Linearity. The Fourier Transform is linear. The Fourier Transform of a sum of functions, is the sum of the Fourier Transforms of the functions. Also, if you multiply a function by a constant, the Fourier Transform is multiplied by the same constant.