Question

Use the duality property to find the Fourier transform of the sinc signal

x(t) = A [Sin (0.5t)]/ (0.5t) = Asinc (o.5t) -[infinity]< t< [infinity]
Use MATLAB to find the Fourier transforms for A = 10.

Answer 1

To find the Fourier transform of the sinc signal x(t) = A sinc(0.5t), you can use the duality property of the Fourier transform, which states that the Fourier transform of a function in the time domain is equal to the scaled and inverted complex conjugate of the Fourier transform of the same function in the frequency domain. The Fourier transform of the sinc function in the frequency domain is a rectangular pulse centered at frequency 0.5.

Step-by-step explanation:

To find the Fourier transform of the sinc signal x(t) = A sinc(0.5t), we can use the duality property of the Fourier transform. The duality property states that the Fourier transform of a function in the time domain is equal to the scaled and inverted complex conjugate of the Fourier transform of the same function in the frequency domain.

The Fourier transform of the sinc function in the frequency domain is a rectangular pulse centered at frequency 0.5. Let's denote this transform as X(f).

So, the Fourier transform of x(t) = A sinc(0.5t) is X(f) = A rect(2f) where rect(2f) is the rectangular pulse centered at frequency 0.5 and with amplitude A.