Q3. (a) Consider the continuous function f(t) = sin(2rnt). i) What is the period of fſt)? ii) What is the frequency of f(t)? The Fourier transform, F(µ), of fſt) is purely imaginary, and because the...

Solve 3a (i) (ii) (iii) (iv) (v)


Extracted text: Q3. (a) Consider the continuous function f(t) = sin(2rnt). i) What is the period of fſt)? ii) What is the frequency of f(t)? The Fourier transform, F(µ), of fſt) is purely imaginary, and because the transform of the sampled data consists of periodic copies of F(µ), the transform of the sampled data, F(H). will also be purely imaginary. Draw a diagram of Fourier transform of the function and answer the following questions based on your diagram (assume that sampling starts at t = 0). iii) What would the sampled function and its Fourier transform look like in general if f(t) is sampled at a rate higher than the Nyquist rate? iv) What would the sample function look like in general if f(t) is sampled at a rate lower than the Nyquist rate? v) What would the sample function look like if f(t) is sampled at the Nyquist rate with samples taken at t = 0,AT,2AT,K ?