# ASSIGNMENT SOLUTIONS

### a. If h 1 [n] and h 2 [n], the impulse responses of two LTID systems are related by h 2 [n] = (-1)…

a. If h1[n] and h2[n], the impulse responses of two LTID systems are related by h2[n] = (−1)nh1,[n], then show that How are the frequency response spectrum H2[ejΩ] related to…

### The bilinear transformation is defined by the rules s = 2(1 -z-) T (1+z-1). a. Show that this…

The bilinear transformation is defined by the rules s = 2(1 -z−)T(1+z-1). a. Show that this transformation maps the ω axis in the s plane to the unit circle z…

### Let x[n]=(-1) n u[n-n 0 ] +an u[-n]. Determine the constraints on the complex number a and the…

Let x[n]=(−1)nu[n−n0]+αnu[−n]. Determine the constraints on the complex number α and the integer n0 so that the z trans form X(z) exists with region of convergence .

### Using the definition, compute the bilateral z-transform, including the region of convergence…

Using the definition, compute the bilateral z-transform, including the region of convergence (ROC), of the following complex-valued functions:

### Determine the zero-state response of a system having a transfer function

Determine the zero-state response of a system having a transfer function

### Consider an LTID system described by the difference equation 4y[n + 2] – y[n] = x[n + 2]+x[n]. a….

Consider an LTID system described by the difference equation 4y[n + 2] − y[n] = x[n + 2]+x[n]. a. Plot the pole-zero diagram for this system. b. Plot the system's…

### An LTID filter has an impulse response function given by h[n]=d[n – 1] + d[n + 1]. Determine and…

An LTID filter has an impulse response function given by h[n]=δ[n − 1] + δ[n + 1]. Determine and carefully sketch the magnitude response |H(ejΩ)| over the range −π ≤…

### A causal, stable discrete system has the rather strange transfer function H(z)=cos(z-1). a. Write…

A causal, stable discrete system has the rather strange transfer function H(z)=cos(z−1). a. Write MATLAB code that will compute and plot the magnitude response of this system over an appropriate…

### Find the compact trigonometric Fourier series for periodic signals shown in Fig. 6.6. Sketch…

Find the compact trigonometric Fourier series for periodic signals shown in Fig. 6.6. Sketch their amplitude and phase spectra. Allow Cn to take on negative values if bn = 0…

### Determine whether the signal is periodic. If it is periodic, find the fundamental frequency and…

Determine whether the signal is periodic. If it is periodic, find the fundamental frequency and the period. What harmonics are present in x(t)?