What are the limitations of Fourier Theorem?
Fourier transforms deal with signals that don’t have compact support and can be thought of as a translation between functions of the same type: it’s a unitary map on an inner product space. Fourier series don’t have this property which makes them so much harder to study in full detail.
What is Fouriers Theorem?
FOURIER THEOREM A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which has specific AMPLITUDE and PHASE coefficients known as Fourier coefficients.
Which of the following Cannot be the Fourier series expansion of a periodic function?
Which of the following cannot be the Fourier series expansion of a periodic signal? Since x2(t) is not periodic, so it cannot be expanded in Fourier series.
What is the condition for the existence of Fourier series for a signal?
In mathematics, the Dirichlet conditions are sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at each point where f is continuous. These conditions are named after Peter Gustav Lejeune Dirichlet. The conditions are: f must be absolutely integrable over a period.
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.
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.
Which type of function can be expanded as Fourier series?
periodic function
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.
Which is not Dirichlets condition for Fourier series?
There are maxima and minima not possible in dirichlet’s conditions. Explanation: Maxima and minima are possible if they are infinite number as stated by the second dirichlet’s condition. In any finite interval, x(t) is of bounded variation.
What are Dirichlet’s conditions for convergence of Fourier series representation?
f must be absolutely integrable over a period. f must have a finite number of extrema in any given bounded interval, i.e. there must be a finite number of maxima and minima in the interval.