Question

Given a sinusoidal signal:

x(t) = Asin(2πft)

Find Fourier Transform (FT) of the sinusoidal x(t) given above and plot the spectrum with:

a. A = 2, f = 1000Hz

b. A = 2, f = 9000Hz

c. A = 5, f = 1000Hz

d. A = 10, f = 10000Hz

Answer 1

Hi,

To solve this question we start from the first principles, that is definition of Fourier Transform.

Now we use this general result to determine and plot the Fourier transform for each of the give functions

Answer (a) FT[x(t)] = (1/j) ( (f-1000) - (f-1000))

Answer (b) FT[x(t)] = (1/j) ( (f-9000) - (f-9000))

Answer (c) FT[x(t)] = (2.5/j) ( (f-1000) - (f-1000))

Answer (d) FT[x(t)] = (5/j) ( (f-10000) - (f-10000))

The plot of these four transforms is shown in the image below. These are drawn on the same image so that you can compared them easily.

Hope this helps.