What are the conditions for existence of Fourier series?

For the Fourier Series to exist, the following two conditions must be satisfied (along with the Weak Dirichlet Condition): In one period, f(t) has only a finite number of minima and maxima. In one period, f(t) has only a finite number of discontinuities and each one is finite.

What are the properties of Fourier series?

These are properties of Fourier series:

• Linearity Property.
• Time Shifting Property.
• Frequency Shifting Property.
• Time Reversal Property.
• Time Scaling Property.
• Differentiation and Integration Properties.
• Multiplication and Convolution Properties.
• Conjugate and Conjugate Symmetry Properties.

What happens when the Fourier transform data assumptions are violated?

If the assumptions are violated, the discrete data does not accurately reflect the actual harmonic signal, and the FFT of the signal is invalid.

For which Fourier series Cannot be defined?

For which of the following a Fourier series cannot be defined? For 1 which is a constant, Fourier series exists. For exp (-|t|) sin (25t), due to decaying exponential decaying function, it is not periodic. So Fourier series cannot be defined for it.

What do you mean by existence of Fourier series?

In mathematics, a Fourier series (/ˈfʊrieɪ, -iər/) is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. The discrete-time Fourier transform is an example of Fourier series. The process of deriving weights that describe a given function is a form of Fourier analysis.

Which of the following conditions is known as Dirichlet for Fourier series?

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.

What are Dirichlet conditions what are the properties of 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 is the advantage of Fourier series?

The main advantage of Fourier analysis is that very little information is lost from the signal during the transformation. The Fourier transform maintains information on amplitude, harmonics, and phase and uses all parts of the waveform to translate the signal into the frequency domain.

Who discovered Fourier series *?

Jean Baptiste Joseph Fourier
Explanation: The Fourier series is the representation of non periodic signals in terms of complex exponentials or sine or cosine waveform. This was discovered by Jean Baptiste Joseph Fourier in 18th century.

Is Fourier series periodic?