What class of functions can be represented by a Fourier series?

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

Why do we use Fourier series of representation?

Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components. A periodic signal is just a signal that repeats its pattern at some period. The primary reason that we use Fourier series is that we can better analyze a signal in another domain rather in the original domain.

How does Fourier series make it easier to represent periodic signals?

Explanation: Fourier series makes it easier to represent periodic signals as it is a mathematical tool that allows the representation of any periodic signals as the sum of harmonically related sinusoids.

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.

How do you know if a function can be represented by a Fourier series?

Well there are 3 conditions for a Fourier Series of a function to be exist: 1. It has to be periodic. 2. It must be single valued, continuous.it can have finite number of finite discontinuities.

What functions can be Fourier Transform?

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 is the importance of Fourier series or Fourier transform in analyzing electronic circuits?

Fourier series are very vitally used to approximate a periodic waveform in electronics and electrical circuits. It is useful in mathematics as it is used extensively in calculators and computers for evaluating values of many functions [3].

Is Fourier transform only for periodic functions?

As such, the summation is a synthesis of another function. The discrete-time Fourier transform is an example of Fourier series. A Fourier series, however, can be used only for periodic functions, or for functions on a bounded (compact) interval.

What is the outcome of periodic convolution of signals in case of continuous time fourier series?

Explanation: This is a very important property of continuous time fourier series, it leads to the conclusion that the outcome of a periodic convolution is the multiplication of the signals in frequency domain representation.

Does a function need to be periodic to have a Fourier series?

What are the conditions for a Fourier series to exist?

Well there are 3 conditions for a Fourier Series of a function to be exist: 1. It has to be periodic. 2. It must be single valued, continuous.it can have finite number of finite discontinuities.

Is every function uniquely represented by a Fourier series?

Every function in can be uniquely represented in the sense of by a Fourier series. The deeper fact is Carleson’s theorem, which was one of the most difficult achievements in 20th century analysis, and tells us about the precise conditions for pointwise (actually, “pointwise almost everywhere”) convergence of Fourier series. – Ian Jul 30 ’15 at 0:53

What are the Fourier series formulas in calculus?

The above Fourier series formulas help in solving different types of problems easily. Example: Determine the fourier series of the function f (x) = 1 – x2 in the interval [-1, 1]. We know that, the fourier series of the function f (x) in the interval [-L, L], i.e. -L ≤ x ≤ L is written as:

Is the Fourier transform of a real function always real?

For a real function f(t), the Fourier transform will usually not be real. Indeed, theimaginarypart of the Fourier transform of a real function is