Consider the discrete-time signal x[n] shown below. Let its DTFT be denoted by X (ein). 4-3 -2 (a) Evaluate X(ejº) (b) Evaluate X(ejπ) (c) Evaluate SX (e³³)dN 5 3 1 -1 -3 x[n] 1 • 2 3 4 n where x[n] is zero outside the interval from −4 to +4. Perform the following calcula- tions (for some of them, you may not need to computing the DTFT itself): (d) What values can ZX(e) take? (e) Determine and sketch the signal whose DTFT is Im[X(e¹¹)] (f) Evaluate (X(en)) ² dn

sample per sece 4. Consider the signal x(t) = 10 – 20 cos (4nt +) + sin (1 where t is in seconds. Find the Nyquist rate of x(t) and the discrete-time signal x[n] obtained when sampling x(t) at twice the Nyquist rate. What is x[1]?

I would like you to help me with these study questions.PLEASE.

Find the transfer function Hp(s) (for the first order system)of the circuit shown in Figure  and determine its theoretical  gain (K) and time constant (τ).