Question: When the input to a causal LTI system is? x[n] = ?1/3 (1/2) n u[n] ? 4/3 2 n u[? n ? 1], the z-transform

When the input to a causal LTI system is?

x[n] = ?1/3 (1/2)nu[n] ? 4/3 2nu[? n ? 1],

the z-transform of the output is

1+z! Y(2) = (1 - z') (1 + 2) (1 2:-1)

(a) Find the z-transform of x[n].

(b) What is the region of convergence of Y(z)?

(c) Find the impulse response of the system.

(d) Is the systems table?

1+z! Y(2) = (1 - z') (1 + 2) (1 2:-1)

Step by Step Solution

★★★★★

3.46 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b c d ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

30-E-T-E-D-S-P (132).docx

120 KBs Word File

Students Have Also Explored These Related Telecommunication Engineering Questions!

Q:

A causal LTI system has impulse response h [n], for which the z-transform is, (a) What is the region of convergence of H (z)? (b) Is the system stable? Explain. (c) Find the z-transform X(z) of an...

Q:

A causal LTI system has a transfer function (a) Find the poles and zeros of H(s), and from this determine if the filter is BIBO stable or not. (b) Draw a block diagram for such a system. (c) Find the...

Q:

The input to a causal linear time-invariant system is x[n] = u[?n ? 1] + (1/2) n u[n]. The z-transform of the output of this system is? (a) Determine H(z), the z-transform of the system impulse...

Q:

Let x[n] be a causal, N-point sequence that is zero outside the range 0 ? n ? N ? 1. When x[n] is the input to the causal LTI system represented by the difference equation? y[n] ? ? y[n ? 2] = x[n ?...

Q:

Consider the following problems related to steady state and frequency responses. (a) The input x(t)and the output y(t), x(t) = 4 cos(2Ï t) + 8 sin(3Ï t), y(t) = 2 cos(2Ï t). Determine...

Q:

The following problems relate to FIR and IIR systems. (a) The input and the output of a causal LTI discrete-time system are Determine the impulse response h[n]. (b) The transfer function H(z)of an...

Q:

6 This assignment is used to clarify the difference between Ch3 (Fourier Series) and Ch4 (Continuous-Time Fourier Transform). 1. Let ( t, 0t1 x(t) = 2 t, 1 t 2 be a periodic signal with fundamental...

Q:

Consider a causal LTI system with impulse response h[n], and input x[n] = x 1 [n] x 1 [n 2] + x 1 [n 4] where x 1 [n] = u[n] u[n 2]. The impulse response of the system is h[n] = u[n] u[n 2] (a) Use...

Q:

If the input x[n] to an LTI system is x[n] = u[n], the output is y[n] = (1/2) n1 u[n + 1]. (a) Find H(z), the z-transform of the system impulse response, and plot its pole-zero diagram. (b) Find the...

Q:

A causal LTI system excited by the input x(n) = (1/4) n u ( n ) + u(- n ? 1) produce an output y(n) with z-transform (a) Determine the system function H(z) and its ROC. (b) Determine the output y(n)...

Q:

Your firm where you are the new Chief Financial Officer (CFO) has had an interesting year. For the Show more Your firm where you are the new Chief Financial Officer (CFO) has had an interesting year....

Q:

Derrick Iverson is a divisional manager for Holston Company. His annual pay raises are largely determined by his divisions return on investment (ROI), which has been above 20% each of the last three...

Q:

6.50 Impact of x on the P-value. We can study the P-value by using the Statistical Significance applet. Set the null hypothesis to =0 , the alternative hypothesis to >0 , the sample size to n=10 ,...

Q:

The steel plate shown will support six 50-mm-diameter idler rollers mounted on the plate as shown. Two flat belts pass around the rollers, and rollers A and D will be adjusted so that the tension in...

Q:

Figure shows an approximate plot of stress versus strain for a spider-web thread, out to the point of breaking at a strain of 2.00. The vertical axis scale is set by a = 0.12 GN/m2, b = 0.30 GN/m2,...

Q:

A 700-N force P is applied at point A of a structural member. Replace P with (a) An equivalent force-couple system at C, (b) An equivalent system consisting of a vertical force at B and a second...

Q:

Let H be a Wiener process. Consider the geometric process S again: (a) Calculate dS t . (b) What is the ?expected rate of change? of S t ? (c) If the exponential term in the definition of S t , did...

Q:

The fork lift has a weight W1 and center of gravity at G. If the rear wheels are powered, whereas the front wheels are free to roll, determine the maximum number of crates, each of weight W2 that the...

Q:

What frequencies will a 1.80-m-long tube produce in the audible range at 20.0C if: (a) The tube is closed at one end? (b) It is open at both ends?

Q:

Consider the first-order SDM model shown in figure(a) Show that the quantization noise power in the signal hand {-B, B} is given by:(b) Using a two-term Taylor series expansion of the sine function...

Q:

Consider the second-order SDM model shown in figure. (a) Determine the signal and noise system functions H s (z) and H n (z), respectively. (b) Plot the magnitude response for the noise system...

Q:

Figure illustrates the basic idea for a lookup table based sinusoidal signal generator. The samples of the signal x ( n ) = cos(2?/N n) n = 0, 1 . . . N ? 1 are stored in memory. A digital sinusoidal...

Q:

x Y Z Corporation is considering acquiring ABC Company. x Y Z estimates that the acquisition will generate additional free cash flows of 1 . 2 million dollars per year, in perpetuity. XYZ...

Q:

Jasper Furnishings has $350 million in sales. The company expects that its sales will increase 13% this year. Jasper's CFO uses a simple linear regression to forecast the company's inventory level...

Q:

SOLVE EXCEL PLEASE 2. Brandon buys a piece of equipment for $15,000. He pays $5,000 for upgrades in year 1 and the equipment generates $2,000 in cash flow for year 1 . In year 2 the equipment...