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1) Graphically determine the convolution of the x[n] and the unit step sequence u[n]. Include a sketch of your answer.
2) For a causal, continuous time LTI system, determine the impulse response given the transfer function H(s):
H[s] = (5 + 2s)/(s2 - s -6)
3) Using time domain techniques, determine the impulse response of the following discrete time LTIC system (subject to zero initial state):
y[n+2] +0.5y[n+1] - 0.14y[n]=2x[n+2]+x[n+1]
4) Determine the inverse z-transform given:
X[z] = (1 - 1/2.z-1)/(1+ 3/4.z-1 +1/8.z-2) |z| > 1/2
5) Starting with the definition of the z-transform, show that the discrete time Fourier transform is equivalent to the unit circle in the z-plane.
Create and use an optimization model (preferably linear) of an engineering design - Your model should have 5 to 10 decision variables.
Write up the standard linear program for PhytoLife. Graph and show PhytoLife's feasible set and a cost line. Using graphical techniques show the most attractive point. Algebraically solve for PhytoLife's formula and its unit costs.
SAC wants the probability of failure to be no more than 20%. If launches will proceed at -10 degrees with no other missiles within 800 meters, how often should launch mechanisms be serviced?
A normal resting heart rate for adults ranges from 60 to 100 beats a minute," reports Dr. Edward Laskowski of the Mayo Clinic. Lower resting heart rates are generally associated with higher cardiovascular fitness.
How long will it take before it is considered dangerous to live in this mountain valley - atmospheric pollutants in a certain mountain valley grown according to a natural growth model
Let S be the surface parametrized by X: U → R3, where X(u, v)=(u, v, u2 - v2), Calculate the first fundamental form of S in terms of (u, v)
Simple differential equation modelling the smoke layer depth (y) in a large atrium provided with dynamic smoke extraction system.
Determine whether or not there exists a solution to the following linear Diophantine equation - Determine whether or not there exists a solution to the linear Diophantine equation.
Find the exact solution to the initial value problem and estimate the errors in the predicted value of ya(1) and yb (1) and suggest a value of step size for each method that would provide a value of y(1) accurate to 0.5%.
You are planning to save for retirement over the next 24 years. To do this, you will invest $638 per month in a stock account and $228 per month in a bond account. The return of the stock account is expected to be 9 %, and the bond account will pa..
If the option has N look-at dates, how many (pseudo-)random numbers will be needed per path? What if the jumps are not log-normal?
Write down a dual formulation of this linear program - describe how the dual formulation can be used to obtain a feasibility cut in the L-shaped method.
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