How do you know if a function is neither even or odd?

Answer: For an even function, f(-x) = f(x), for all x, for an odd function f(-x) = -f(x), for all x. If f(x) ≠ f(−x) and −f(x) ≠ f(−x) for some values of x, then f is neither even nor odd. Let’s understand the solution.

Can a Fourier series be zero?

We can use symmetry properties of the function to spot that certain Fourier coefficients will be zero, and hence avoid performing the integral to evaluate them. Functions with zero mean have d = 0. Segments of non-periodic functions can be represented using the Fourier series in the same way.

Do all the functions have Fourier series?

Any function that is defined over the entire real line can be represented by a Fourier series if it is periodic.

What is the Fourier series for odd function?

Therefore, the Fourier series of the following odd function is given by. f(t)=∞∑n=1bnsinnπtL. Hence, the Fourier series of an odd periodic function contains only sine terms.

Is the function FX is even then which of the following is zero?

If the function f(x) is even, then which of the following is zero? Explanation: Since bn includes sin(nx) term which is an odd function, odd times even function is always odd. So, the integral gives zero as the result.

Can non-periodic functions have Fourier series?

The Fourier series of a non-periodic function is really the Fourier series of its periodic extension. For example, there is a Fourier series of f(x)=x on [0,π], which is actually the Fourier series of the sawtooth wave that is formed by periodically extending f(x)=x.

For which function Fourier series Cannot be applied?

For exp (-|t|) sin (25t), due to decaying exponential decaying function, it is not periodic. So Fourier series cannot be defined for it.

What is odd and even function in Fourier series?

4.6 Fourier series for even and odd functions A function is called even if f(−x)=f(x), e.g. cos(x). A function is called odd if f(−x)=−f(x), e.g. sin(x).