Question

Consider a square wave with period T =2 and x(t) = rect (t) for t ∈ [-1,1]. Using the common transform pairs, tables and properties, determine the FS coefficients of x(t)

Answer 1

To find the FS coefficients of a square wave function, we can use the common transform pairs and properties and evaluate an integral. The FS coefficients can be calculated using the formula and the period of the function.

Step-by-step explanation:

To find the Fourier Series (FS) coefficients of the given square wave function x(t) = rect(t) for t ∈ [-1,1], we can use the common transform pairs and properties. The square wave function can be represented as the summation of sine functions with different frequencies. Using the Fourier Transform table, the FS coefficients can be calculated.

For the rect function with period T = 2, the FS coefficients can be found by using the formula:

c_n = (1/T) ∫[[-T/2,T/2]] rect(t) e^(-jwn) dt

By evaluating this integral, we can determine the FS coefficients of the square wave function x(t).