A causal and stable LTI system S has its input x[n] and output y[n] related by the

Question:

A causal and stable LTI system S has its input x[n] and output y[n] related by the linear constant-coefficient difference equation,

Let the impulse response of S be the sequence h[n].

(a) Show that h[0] must be nonzero.

(b) Show that ?₁ can be determined from the knowledge of h[0] and h[1].

(c) If h[n] = (0.9)ⁿcos(?n/4) for 0 ? n ? 10, sketch the pole-zero plot for the system function of S, and indicate the region of convergence.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete Time Signal Processing

ISBN: 978-0137549207

2nd Edition

Authors: Alan V. Oppenheim, Rolan W. Schafer

See More Books

Question Posted: May 26, 2011 02:56 AM

See More Questions

Let S 1 be a causal and stable LTI system with impulse response h 1 [n] and frequency response H 1 (e j ). The input x[n] and output y[n] for S 1 are related by the difference equation y[n] y[n 1]...
Given that X and Y are related by the given equation, and that X = 3.0 0.1, estimate Y and its uncertainty. a. XY = 1 b. Y/X = 2 c. XY = 3 d. YX = 4
The impulse response of a causal LTI discrete-time system is (a) If the input of the system is a pulse x[n] = u[n] u[n 3], determine the length of the output of the system y[n]. Graphically calculate...
In which control account would you expect to find a provision for doubtful debts?
Are "Buy American" provisions good for (a) U.S. consumers, (b) U.S. producers?
The graph of f is given. State, with reasons, the numbers at which f is not differentiable. 6. 4-
Explain when it is appropriate to use a randomized block design.
Consider a two-stage rocket made up of two engine stages, each of inertia m when empty, and a payload of inertia m . Stages 1 and 2 each contain fuel of inertia m , so that the rocket's inertia...
3) (10 pts) Write a function NextMinute that receives one integer as the input argument, which is the current minute of the hour, and returns the next minute as the output argument. Please note that...
Dresden Press is a company that offers desktop publishing services to clients. The staff produces items such as newsletters, brochures, programs, and catalogs. A staff of ten full-time employees...
In Figure, h[n] is the impulse response of the LTI system within the inner box. The input to system h[n] is v[n], and the output is w[n]. The z-transform of h[n], H(z), exists in the following region...
When the input to an LTI system is x[n] = (1/2) n u[n] + 2 n u[ n 1], the output is y[n] = 6 (1/2) n u[n] 6 (3/4) n u[n]. (a) Find the system function H(z) of the system. Plot the poles and zeros...
What percentage does Coca-Cola's 2019 allowance for doubtful accounts represent as a percentage of its gross trade accounts receivables?
Can portfolio theory actually be applied by investors to improve their investment returns? Provide examples.
Describe some of the potential challenges currently facing the employees of this organisation. What are some ways in which leaders could keep their team motivated? Refer to at least one theory of...
In March 2020 you can get a 15-year term mortgage from TwinStar credit union to buy a house with a rate of 3.57% APR (given a credit score between 680 - 740 and a down payment of 20%). The lending...
Return on Investment (ROI) with the following information Current stock price: $45/share Original purchase price: $38/share Dividends received during the year: $2/share Discount brokerage fee: $9...
How could you define the grouping criteria used to organize resources in the different purchasing departments?
The growth in online and mobile shopping has forced many businesses to dramatically adjust their sales and marketing strategies. What kind of brick-and-mortar bookstores have survived the move to...
A 20-cm-square vertical plate is heated to a temperature of 30oC and submerged in glycerin at 10oC. Calculate the heat lost from both sides of the plate.
The frequencies to which the ear responds vary by a factor of 10 3 . Suppose the speedometer on your car measured speeds differing by the same factor of 10 3 , and the greatest speed it reads is 90.0...
Consider the two systems shown in figure(a) Sketch the spectra of the various signals if xa(t) has the Fourier transform shown in figure(b) and Fs = 2B. How are y1(t) and y2(t) related to xa(t)?(b)...
A continuous-time signal x a ( t ) with bandwidth B and its echo xa( t ? ? ) arrive simultaneously at a TV receiver. The received analog signal? s a (t) = x a ( t ) + ax a ( t ? ?) | a | s and H(z)...
A bandlimited continuous-time signal xa(t) is sampled at a sampling frequency Fs 2B. Determine the energy Ed of the resulting discrete-time signal x(n) as a function of the energy of the analog...
1. A clothes dryer rates at 4000 W runs for 1.50 hours each day. it uses utility power at 240 V. how much current does the dryer use? 2. For the clothes dryer in the previous question, how much does...
A particle undergoing simple harmonic motion has a potential energy given by E/J=3(y/m) as it oscillates back and forth along the y-axis. When the y-coordinate of the particle is 0.75 m, what is the...
A 480-g iron pan is heated on a stove to a temperature of 130 C. The pan is then dropped into a partially-filled sink of water at 20 C. The final temperature reached by the sink and the pan is 40 C....

A causal and stable LTI system S has its input x[n] and output y[n] related by the

Question:

10 y[n] + aky[n - k] = x[n] + Bx[n - 1]. k=1

Step by Step Answer:

a b c How can we extend hn for n 10 and still have it compatible with ...View the full answer

Discrete Time Signal Processing

Students also viewed these Telecommunication Engineering questions