ASSIGNMENT 2
1. Find the Fourier Transform of the signal (𝑡) = 𝑡𝑒−𝑎𝑡𝑢(𝑡) .
2. State the conditions for the convergence of Fourier Series.
3. State and prove Parseval’s theorem for DTFS. CO2
4. A signal x[n] has DTFT (𝑒𝑗𝜔 ) = 1 1−𝑎𝑒−𝑗𝜔 , |𝑎| ≤ 1. Determine the DTFT of [𝑛 + 2]𝑒𝑗𝜋2𝑛 .
5. Consider the discrete LTI system [𝑛] − 12 𝑦[𝑛 − 1] = 𝑥[𝑛] + 12 𝑥[𝑛 − 1]. Determine the frequency response of the
system.
6. Find continuous time Fourier series for a half wave rectifier system.
7. Compute the Fourier transform of the signal x(t) and plot the magnitude and phase
response. CO2 (𝑡)={1+𝑐𝑜𝑠𝜋𝑡 |𝑡|≤00 |𝑡| >0
8. The input and the output of a stable and causal LTI system are related by the differential
equation: 𝑑2𝑦(𝑡)𝑑𝑡2+6𝑑𝑦(𝑡)𝑑𝑡+8𝑦(𝑡)=2𝑥(𝑡)
(a) Find the impulse response of this system.
(b) What is the response of this system if (𝑡)=𝑡𝑒−2𝑡𝑢(𝑡)?