Suppose we cascade a differentiator and a smoother. The equations for the differentiator is w[n] = x[n]

Question:

Suppose we cascade a differentiator and a smoother. The equations for the differentiator is w[n] = x[n] ˆ’ x[n ˆ’ 1] where w[n] is the output and x[n] the input, and for the smoother the equation is

where y[n] is the output and w[n] the input.

(a) Obtain the difference equation relating the input x[n] to the output y[n] of the whole system.

(b) If x[n] = u[n], calculate y[n]. Assume zero initial conditions.

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

Step by Step Answer:

Related Book For book-img-for-question

Signals and Systems using MATLAB

ISBN: 978-0123948120

2nd edition

Authors: Luis Chaparro

See More Books

Question Posted: Dec 28, 2018 11:26 AM

See More Questions

Suppose we cascade a differentiator and a smoother systems characterized by the following input/output equations where the output of the differentiator and input to the smoother is w[n], while x[n]...
The input-output equation characterizing an amplifier that saturates once the input reaches certain values is where x(t) is the input and y(t) the output. (a) Plot the relation between the input x(t)...
The output of an ideal low-pass filter is (a) Assume the filter input is a periodic signal x[n]. What is its fundamental frequency Ï 0 ? What is the fundamental period N 0 ? (b) When the filter...
In Problems 530, a. Classify the sequences as arithmetic, geometric, Fibonacci, or none of these. b. If arithmetic, give d; if geometric, give r; if Fibonacci, give the first two terms; and if none...
The general form for a three-dimensional stress field is given by where the diagonal terms represent tensile or compressive stresses and the off-diagonal terms represent shear stresses. A stress...
Which of the following best describes the extent to which the SEC requires or permits the use of IFRS by U.S. public companies? a. U.S. public companies are required to use IFRS. b. U.S. public...
For each of the following situations, calculate the degrees of freedom \((d f)\), identify the critical values (assume \(\mathbf{a}=.05\) [two-tailed]), calculate the standard error of the mean \(s\)...
The owner of Waco Waffle House is considering an expansion of the business. He has identified two alternatives, as follows: ¢ Build a new restaurant near the mall. ¢ Buy and renovate an old...
In what ways do virtue ethics challenge traditional consequentialist and deontological frameworks in moral philosophy ?
1. How would you describe the current charity industry structure? How could it change if consolidation increases and what would be the benefits and disadvantages? 2. Which of Porters five forces are...
An LTI discrete-time system is characterized by the difference equation y[n] + ay[n 1] + by[n 2] = x[n] Determine for which of the the following sets of coefficients the system is BIBO stable (i) a...
The transfer function of a causal LTI discrete-time system is H(z) = (1 + z 1 )/(1 .5z 1 ). (a) Find the poles and zeros of H(z). Choose the correct region of con-vergence corresponding to H(z)from...
A kayaker paddles with a power output of 35.0 W to maintain a steady speed of 2.24 m/s. (a) Calculate the resistive force exerted by the water on the kayak. (b) If the kayaker doubles her power...
What do you think are some pressing questions for health communication researchers to investigate?
True or False: If \(F W(\mathrm{~A})>F W(\mathrm{~B})\), then \(D P B P(\mathrm{~A})
In Exercise 8.7, a nonminimum delay overlapped solution is possible by choosing \[\mathbf{C}_{l}(z)=\left[\begin{array}{cccc}D_{0}(z) & R_{1}(z) & 0 & 0 \\0 & R_{0}(z) & R_{1}(z) & 0 \\0 & 0 &...
True or False: If \(F W>0\) when the \(M A R R=20 \%\), then \(D P B P <5\) years.
Moving money forward in time while accounting for the time value of money is referred to as a. weighted average cost of capital. b. minimum attractive rate of return. c. discounting. d. compounding.
Minor Cars Ltd., a small company selling second-hand cars, has just been taken over by Major Vehicles plc, which runs a chain of garages. One implication is that the existing accounting systems of...
What is the mode?
Consider a version of deterministic quick-sort where we pick as our pivot the median of the d last elements in the input sequence of n elements, for a fixed, constant odd number d 3. What is the...
Describe and analyze an efficient method for removing all duplicates from a collection A of n elements.
Give an example input that requires merge-sort and heap-sort to take O(nlogn) time to sort, but insertion-sort runs in O(n) time. What if you reverse this list?
a) What is arbitrage? And what are the different types of arbitrage? B) Can arbitrage strategies be risky when price convergence is not guaranteed? Clearly describe and outline 1 real-life example to...
Explain each segments of Financial Services Industry which are the BANKS, INSURANCE, AND ASSET MANAGEMENT . Explain each. Explain the updates on the 3 segments of Financial Services Industry (banks,...
2. Currency pegging refers to the practice of locking a currency's exchange rate to another country's currency. As it has its own merits and drawbacks, express your opinion to agree or disagree on...

Suppose we cascade a differentiator and a smoother. The equations for the differentiator is w[n] = x[n]

Question:

y[n] = {y[n – 1]+ w[n]

Step by Step Answer:

a Replacing wn in the smoother equation b If xn un then ...View the full answer

Signals and Systems using MATLAB

Students also viewed these Computer science questions