Question

Expand the following into complex Fourien

series and deternine the number of required terms to heve anaccuracy 99%
f(x)=[x1−x​x<1/2x>y/2​

Answer 1

To expand the given function into a complex Fourier series, find the coefficients using the formula for Fourier coefficients and truncate the series for desired accuracy.

Step-by-step explanation:

To expand the given function into a complex Fourier series, we need to find the coefficients of the series. The function is given as:

f(x) = [x(1−x)]x<1/2, x>y/2

To determine the coefficients, we can use the formula for the Fourier coefficients:

`c_n = (1/T) * ∫[f(x)e^(-iwnx)dx]`

Where T is the period of the function, and wn = 2πn/T are the frequencies. By evaluating the integral, we can find the coefficients and then truncate the series based on the desired accuracy.