Can Cosec X be expanded in Fourier series?

Short answer: No; this series diverges.

What functions Cannot be represented by a Fourier series?

= 2 cos ω. Explanation: For periodic even function, the trigonometric Fourier series does not contain the sine terms since sine terms are in odd functions. The function only has dc term and cosine terms of all harmonics. So, the sine terms are absent in the trigonometric Fourier series of an even function.

What exactly is 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.

What are the Fourier series coefficients?

1.1, av , an , and bn are known as the Fourier coefficients and can be found from f(t). The term ω0 (or 2πT 2 π T ) represents the fundamental frequency of the periodic function f(t).

Why do we study Fourier series?

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.

Which of the following is the Fourier series representation of the signal x t?

Explanation: Fourier series uses frequency domain representation of signals. X(t)=1/T∑Xnejnwt.

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:

What is the Fourier series representation?

The Fourier series representation of analytic functions is derived from Laurent expansions.

How do you find the Fourier series of even and odd functions?

Graphically, even functions have symmetry about the y-axis, whereas odd functions have symmetry around the origin. To find a Fourier series, it is sufficient to calculate the integrals that give the coefficients a 0, a n, and b n and plug them into the big series formula.

What is the difference between Laurent series and Fourier series?

What is the Fourier Series? A Fourier series is an expansion of a periodic function f (x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions. Laurent Series yield Fourier Series