## 6.003 HOMEWORK 1 SOLUTION

### 6.003 HOMEWORK 1 SOLUTION

By Robbert de Ruijter. Signals and Systems Fall 32 The second row of pictures were blurred by passing each column of pixels through a system with the pole at 0. Each is one-sixth of a full circle, so the period of the response should be 6, which it is. Maybe you find this result surprising. Signals and Systems Fall 20 e. Find the output signal Y analytically in two ways: Switching the order of the tanks switches the order of the factors in the system functional but does not change the product. Signals and Systems Fall 32 The second row of pictures were blurred by passing each column of pixels through a system with the pole at 0. Now solve it by approximating the square root in the quadratic formula. How big is too big? One-third of the drug remains in the bloodstream after 8 hours one dosing interval. As the number of delays increases, the poles move ever closer to the unit circle, with no pole ending up outside the unit circle. So it becomes infinitely thin and infinitely high.

The block diagrams have similar parts, but the topologies are completely different.

# eea homework solutions

And the three right-hand panels show this pattern. Signals and Systems Fall 16 The pole—zero plot in part b was the simplest because one can tell at a glance what the behav- ior of the poles are, just by looking at their location relative to the unit circle and to the positive real axis.

Make sure the pole loca- tions are consistent with your answers to parts a and c!

JUDY SYFERS I WANT A WIFE ESSAY Here is a feedback-control system: Finding modes The following block diagram describes the relation between two discrete-time signals: So only diagrams A and B are possible. Indeed, it gives the output signal hoemwork, 5, 19, 65. Switching the order of the tanks switches the order of the factors in the system functional but does not change the product. Deter- mine the difference equation and block diagram representations for this system.

Eea solutoon 7 solutions. So it is not possible to make a differentiator soluion passive elements. Thus both poles are oscillatory and neither growing nor decaying. Homewok responses Find the impulse responses of the following systems: So it becomes infinitely thin and infinitely high. Impulse responses Find the impulse responses of the following systems: To understand the way that the solera system mixes and ages the wine, consider a thought experiment in which x[n] units of a tracer substance such as deuterium are added to the new crushed juice in year n.

It will not be collected. Since integration in time is dimensionally equivalent to multiplication by time because the dt has dimensions of timethe delta function itself has dimensions of inverse time.

So it is not possible to make a differentiator with passive elements. Give dimensional and extreme-cases arguments to show why the impulse response that you found is reasonable.

## 6.003 homework 2 solution – cdma homework solution

Hours While our primary goal in designing homework assignments is that these exercises should be educational, we know that they take time. Let W represent 6.030 input of the delay element. Then find the system functional in terms of the A operator, and expand the functional in powers of A. One way to check stability is to write a simulation.

Homework 6 Do all of the following warmups and problems, including the question about hours spent on the problem set. Eventually the mass catches up to it, the oscillations die, and the spring returns to its natural length. Comparing forward and backward Euler In this problem you compare the forward and backward Euler methods of converting homewwork contin- uous-time system into a discrete-time system.

Write a simula- tion to confirm your answers. Signals and Systems Fall 30 4. Eolution and Systems Fall 16 The pole—zero plot in part b was the simplest because one can tell at a glance what the behav- ior of the poles are, just by looking at their location relative to the unit circle and to the positive real axis.

Signals and Systems Fall 9 This schedule is an example of using a loading dose.

Due in recitation on Wednesday, 26 September An alternative, which we use here for variety, is to ask maxima to find the poles. Based on your evaluation of 0 y[n] for forward and backward Euler, which method do you prefer? Always sketch your results! 