Question: Let x[n] denote a causal sequence; i.e., x[n] = 0, n < 0. Furthermore, assume that x[0] 0. (a) Show that there are no

Let x[n] denote a causal sequence; i.e., x[n] = 0, n < 0. Furthermore, assume that x[0] ≠ 0.

(a) Show that there are no poles or zeros of X(z) at z = ∞, i.e., that lim z→∞ X(z) is nonzero and finite.

(b) Show that the number of poles in the finite z-plane equals the number of zeros in the finite z-plane. (The finite z-plane excludes z = ∞.)

Step by Step Solution

★★★★★

3.40 Rating (175 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b Xz X00 znz 10 00 lim z... 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 (135).docx

120 KBs Word File

Students Have Also Explored These Related Telecommunication Engineering Questions!

Q:

Show that there are no 2 2 matrices A and B such that AB - BA = 12.

Q:

Show that there are no vectors u and v such that u = 1, v = 2, and u v = 3.

Q:

Let z be a nonzero complex number and n a negative integer (n = 1,2, . . .). Also, write z = reiθ and m = n = 1, 2, . . . . Using the expressions verify that (zm)1 = (z1)m and hence that...

Q:

Chapter 5 Discrete Markov process Suppose we have a sequence of random variables, {X0 , X1 , . . .} = {Xn } , which is also n=0 called a stochastic process. In this chapter, we study a commonly used...

Q:

1456HHSC attend all (a) In the quantum teleportation protocol, Alice and Bob are every in possession of one qubit of a couple in the joint country00i + statei. Explain how the protocol works. In...

Q:

(a) How does the use of condition codes complicate the implementation of a superscalar processor that supports out-of-order execution? [4 marks] (b) A branch predictor with a high prediction accuracy...

Q:

Let Dn be the demand for an item at a store on day n. Suppose that {Dn, n ? 0} is an i.i.d. sequence of random variables with common PMF: pk = P[Dn = k], k = 0, 1, 2, . . .. Suppose the store follows...

Q:

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Q:

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Q:

The volume of a right-circular cylinder of radiusr and height his V-h. Suppose the radius and height of the cylinder are changing with respect to time t dv dr (a) Find a relationship between and dt...

Q:

When a company acquires a subsidiary, and that subsidiary continues in legal existence and prepares separate financial statements, the parent will need to adopt some internal accounting method to...

Q:

For commercial solicitations, it is a good idea to offer a period of time within the solicitation period for potential offerors to submit written questions and / or to attend pre - proposal...

Q:

LEW Jewelry Co. uses gold in the manufacture of its products. LEW anticipates that it will need to purchase 500 ounces of gold in October 2012, for jewelry that will be shipped for the holiday...

Q:

In Figure observer S detects two flashes of light. A big flash occurs at x1 = 1200 m and, 5.00s later, a small flash occurs at x2 = 480 m. As detected by observer S', the two flashes occur at a...

Q:

Some physical systems possessing capacitance continuously distributed over space can be modeled as an infinite array of discrete circuit elements. Examples are a microwave waveguide and the axon of a...

Q:

Relativistic reversal of events figures a and b show the (usual) situation in which a primed reference frame passes an unprimed reference frame, in the common positive direction of the x and x' axes,...

Q:

The potential energy of two atoms in a diatomic molecule is approximated by V(r) = a/r12 - b/r2, where r is the spacing between atoms and a and b are positive constants. (a) Find the force F( r) on...

Q:

By what fraction will the frequencies produced by a wind instrument change when air temperature goes from 10.0C to 30.0C? That is, find the ratio of the frequencies at those temperatures.

Q:

Consider a signal x(n) with Fourier transform(a) Show that the signal x(n) can be recovered from its samples x(mD) if the sampling frequency ?x = 2?/D ? 2?m(fs = 1/D ? 2fm).(b) Show that x(n) can be...

Q:

In this problem we illustrate the concepts of sampling and decimation for discretetime signals. To this end consider a signal x(n) with Fourier transform X() as in Figure. (a) Sampling x(n) with a...

Q:

Design a decimator that downsamples an input signal x(n) by a factor D = 5. Use the Remez algorithm to determine the coefficients of the FIR filter that has 0.1-dB ripple in the passband {0 /5} and...

Q:

If Barbara Guarin is single and in the 25% tax bracket, calculate the tax associated with each of the following transactions. (Use the IRS regulations for capital gains in effect in 2008.) EXHIBIT...

Q:

You buy 50 shares of ABC stock at $30/share; stock currently pays $3/share in annual dividends. Price of the stock increases at 20%/year and dividends grow at 10%/year. If you participate in DRIP,...

Q:

Assume an economy in which there are three securities: Stock A with rA = 10% and A = 10%; Stock B with rB = 15% and B = 20%; and a riskless asset with rRF = 7%. Stocks A and B are perfectly negativly...