# 6.003 HOMEWORK 1 SOLUTION

Fit it with a simple function. Draw a block diagram and give the system functional. Impulse responses Find the impulse responses of the following systems: The feedforward functional is a cas- cade of three systems: Signals and Systems Fall 33 6. Assume that you take the medicine every 8 hours. Determine the steady-state value of tracer in the first barrel, i. It is therefore noncausal. A simple model of the body is a tank of blood from which drug exits at a rate proportional to its concentration and into which drug doses instantly arrive. Due in recitation on Wednesday, 19 September

It then plots the two results. Find the impulse response of the two systems numerically.

So it becomes infinitely thin and infinitely high. Then add the results to find the impulse response of the system. Periodic system In this problem you study this variant of the Fibonacci system: The worst pole is now closer the unit circle, solutlon the system is less stable.

Homework 5 Do all of the following warmups and problems, including the question about hours spent on the problem set.

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Results after unblurring are show below. Oslution can use a computer or, if you are skilled with series, you can do it analytically. Let xi [n] represent the amount of money you deposit in bank i during year n and yi [n] represent your balance in bank i. How many modes does the system have? How many modes does the system have? Click here to sign up.

MEI NUMERICAL METHODS COURSEWORK

Draw the block diagram .6003 give the system functional of a discrete- time system with this behavior. Signals and Systems Fall 20 e.

Find the impulse response of the two systems analytically and sketch the results. So the impulse response of this system is identical to the original system. Solutions will be posted in a few days for you to check yourself. Deter- mine the difference equation and block diagram representations for this system. It then plots the two results. The leaky tank has the same equation as the RC circuit see Recitation 1. Interpret your answer in terms of loading doses, whether for or against the idea.

Solve the difference equations numerically using Matlab, Octave, or Python and plot the results. At least the integral is not infinite and not zero; but it should be unity. Option 2, the Lorentzian shape, gets infinitely high and infinitely thin. Always sketch your results! Is the new system stable?

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