Consider a real sequence x n that has all the poles and zeros of its z transform inside the unit circle Determine, in terms of x n , a real sequence x 1 n not equal to x n , but for which x 1 0 x 0 , x 1 n x n , and the z transform of x 1 n has all its poles and zeros inside the unit circle

Question: Consider a real sequence x[n] that has all the poles and zeros of its z-transform inside the unit circle. Determine, in terms of x[n], a

Consider a real sequence x[n] that has all the poles and zeros of its z-transform inside the unit circle. Determine, in terms of x[n], a real sequence x₁[n] not equal to x[n], but for which x₁[0] = x[0], |x₁[n]| = |x[n]|, and the z-transform of x₁[n] has all its poles and zeros inside the unit circle.

Step by Step Solution

★★★★★

3.32 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The poles and zero... View full answer

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)

30-E-T-E-D-S-P (140).docx

120 KBs Word File

Students Have Also Explored These Related Telecommunication Engineering Questions!

Consider a finite-duration sequence x(n), 0 n 7, with z-transform X(z). We wish to compute X(z) at the following set of values: zk = 0.8ej[(2k/8)+(/8)] 0 k 7 (a) Sketch the points {zk} in the complex...

Consider the following problem. Maximize z = x1 + 2x2, Subject to and x1 0, x2 0. (a) Plot the feasible region and circle all the CPF solutions. (b) For each CPF solution, identify the pair of...

Consider the following problem. Maximize Z = x 1 x 2 + 2x 3 , Subject to and x 1 0, x 2 0, x 3 0 Let x 4 , x 5 , and x 6 denote the slack variables for the respective constraints. After you apply...

Consider a complex sequence x[n] = x r [n] + jx i [n], where x r [n] and x i [n] are the real part and imaginary part, respectively. The z-transform X(z) of the sequence x[n] is zero on the bottom...

Review Problems 3 Four FIR Filter Types Four types of FIR linear phase digital filters have coefficients h(n) for 0 n M. They are defined as follows: Type I: h(n) = h(M-n) and M even. Type II: h(n) =...

A modified discrete Fourier transform (MDFT) was proposed (Vernet, 1971) that computes samples of the z-transform on the unit circle offset from those computed by the DFT. In particular, with X M [k]...

In Section 11.3, we mention that a causal complex cepstrum x[n] is equivalent to the minimum-phase condition of Section 5.4. Remember that x[n] is the inverse Fourier transform of X(e j? ) as defined...

A discrete sequence {xn} can be converted into a continuous representation x(t) = ts X n= (t n ts) xn, where ts is the sampling period. (a) State two characteristic properties of Dirac's function. [2...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

A business borrows $2,000,000. Interest on the loan is 11% compounded daily. The first $1 million loan is to be paid back in 30 days, the other $1 million is to be paid back in one year plus 30 days....

In terms of many broad characters, if phenotypic variance is 750 and total genotypic variance is 75, what is the inheritance degree in a broad sense? a)10 b)100 C)75 D)1

Finding slope given two points on a line Find the slope of the line passing through the points ( 4 , - 6 ) and ( 3 , - 2 ) .

A homogeneous cube, each edge of which has a length l, is initially in a position of unstable equilibrium with one edge is contact with a horizontal plane. The cube is then given a small displacement...

Aluminum wire with a mass per unit length of 0.049 kg/m is used to form the circle and the straight members of the figure shown. Determine the mass moment of inertia of the assembly with respect to...

The homogeneous circular cylinder shown has a mass m, and the diameter OB of its top surface forms 45o angles with the x and z axes. (a) Determine the principal moments of inertia of the cylinder at...

Flow of a fluid in a network of tubes (Fig. 2B.12), a fluid is flowing in laminar flow from A to B through a network of tubes, as depicted in the figure. Obtain an expression for the mass flow rate w...

Find the frequency of small oscillations for a thin homogeneous plate if the motion takes place in the plane of the plate and if the plate has the shape of an equilateral triangle and is suspended...

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example, because its...

Prove the following expression for an interpolator of order I.(a) The impulse response h(n) can be expressedas hin) => Pi(n k) where * = 0. 1. 21.... P.(nil). PAin) = otherwise (b) H(2) may be...

Zoom-frequency analysis consider the system in figure(a) (a) Sketch the spectrum of the signal y(n) = y R (n) + jy l (n) if the input signal x(n) has the spectrum shown in figure(b). (b) Suppose that...

The power density spectrum of an AR process {x(n)} is given as where ?2R is the variance of the input sequence.(a) Determine the difference equation for generating the AR process when the excitation...

How many different possible tests can be made from a test bank of 20 questions if the test consists of 5 questions? (Ignore the order of questions.)

Question 2 (13 marks) Manchester College (MC) is a private university located in Winnipeg, Manitoba. MC offers programs toward a bachelors degree in science. Revenues consist of tuition fees,...

6. Suppose you are evaluating two mutually exclusive projects, Thing 1 and Thing 2 , with the following cash flows: (a) If the cost of capital on both projects is 5%, which project, if any, would you...