Problem 2. Suppose the impulse response function h[n] of a DT system is: h[n] = (-−0.5)^u[n]. Determine the transfer function / eigenvalue H(z) of this DT system through its definition: assuming the input signal is the eigenfunction x[n] = z^, and calculate the absolute value and the phase angle of the eigenvalue H(z) at: 1 (a) z = √(1 + j) (Q5, Q6); (b) z = −0.5 + j; (Q7, Q8)

(a) The analog signal x(t) = sin(60rt) is sampled at 20 Hz. Derive and write down an expression for the sampled signal r[n]. What is the Nyquist frequency for this r(t)?

1. The CT signal x(t)=3cos (600πt) + 6cos2 (mπt) is critically sampled (Nyquist rate)by fs=4000 Hz. Find:i. The value of m.ii. The frequency components of the signal.iii. The frequency resolution (Δf) of the output spectrum if the sampled signal isprocessed by 64 point-DFT.iv. Define frequency resolution.

Problem 5 For the difference equation 0=2y[n+2]-3y[n+1]-2y[n]-4x[n+2]+2x[n+1] a. Put the difference equation in standard causal form_y[n]=... b. Draw a block diagram (i.e., flow diagram, or digital filter structure) implementing this difference equation. c. For the input x[n] = [n] and the system at rest (i.e., zero initial conditions), compute y[-1],y[0], y[1],y[2], and y[3] by hand directly from the difference equation. d. Find the transfer function H(z). e. Compute the unit pulse response h[n],via inverse z-transform. Confirm that [-1] through h[3] are identical to the samples of the unit pulse response computed above via direct iteration of the difference equation.

Please help with this problem and explain the steps to solve

*3. A continuous time signal, x(t) = sin(20t) + cos(40t), is sampled uniformly at intervals of T to obtain a discrete time signal, x(n) = sin(an/5) + cos(2rn/5). a) What is the value of T assuming no aliasing has occurred? b) Assume both frequency components have been aliased. In this case, is your choice of T unique? If not, specify some choices of T consistent with the information given.

The signal xc(t) = sin(2n (200)t) was sampled with sampling period T = 1/200 second to obtain a discrete-time signal x[n]. What is the resulting signal x[n]?

Consider the analog signal: x(t) = 3 cos 2000nt + 5 sin 6000nt + 10 cos 12000at. a) Find the Nyquist rate of this signal b) Assume that we sample this signal using a sampling rate of 5000 Hz. What is the discrete-time signal obtained after sampling? c) What is the analog signal ya(t) we can reconstruct from the samples if we use ideal interpolation? 9.

Affempt all Questions. A discrete-time signal x(n) is defined as x(n) = 0sns4 elsewhere (a) Determine its values and sketch the signal x(n). (b) Sketch the signals that result if we: (1) First fold x(n) and then delay the resulting signal by three samples. (2) First delay x(n) by three samples and then fold the resulting signal. A BI !!

An analog signal xa(t) = sin(480nt) + 3 sin(720nt) is sampled 600 times per second. 1. Determine the Nyquist sampling rate for xa(t). 2. Determine the folding frequency. 3. What are the frequencies, in radians, in the resulting discrete time signal x(1)? 4. If x(n) is passed through an ideal D/A converter, what is the reconstructed signal ya(t)?