Question

Compute the Fourier Transforms for the following signals.

x(t)=sinc(20πt). Recall the definition sinc(ϕ)= ϕ/sin(ϕ) ,sinc(0)=1. Sketch X(Ω).

Answer 1

To compute the Fourier Transform of the given signal, x(t) = sinc(20πt). The Fourier Transform X(Ω) represents the frequency content of the signal. We can sketch X(Ω) by evaluating the integral and plotting the result.

Step-by-step explanation:

To compute the Fourier Transform of the signal x(t) = sinc(20πt), we can use the definition of the Fourier Transform:

X(Ω) = ∫[x(t)e^(-jΩt)]dt

For the given signal x(t) = sinc(20πt), the Fourier Transform X(Ω) is a complex-valued function that represents the frequency content of the signal. Since the sinc function is defined as sinc(ϕ) = ϕ/sin(ϕ), we can substitute it into the equation:

X(Ω) = ∫[(sinc(20πt))e^(-jΩt)]dt

To sketch X(Ω), we need to determine the frequency content of the signal by evaluating the integral and plotting the result as a function of Ω.