Tricky quadratics adapted from R. Signals and Systems Fall 30 4. I will only provide helpful solutions and not detailed solutions, but you have to write all the steps involved along. Results after unblurring are show below. 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.

So it is not possible to make a differentiator with passive elements. The only differ- ence is that the roles of x and y are reversed. An alternative, which we use here for variety, is to ask maxima to find the poles. This discrete-time analysis ignores the behavior between sampling intervals, i. Switching the order of the tanks switches the order of the factors in the system functional but does not change the product.

How many different modes does this system have? Mark the poles and zeros of the system on a pole—zero diagram.

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Solve your difference equations in part a numerically using Matlab, Octave, or Python to determine your balance in each bank during years 0 through Number of Number of Defective Items Defective Items Sample n in the Sample Sample n in the Sample 1 15 3 6 15 2 2 15 1 7 15 0 3 15 0 8 15 3 4 15 0 9 15 1 5 15 0 10 15 0 a.

To approximate the quadratic, take out the big part, which is b2: The dimensions of a delta function are not obvious, but its time integral is 1 by definition. Assume that one unit of tracer is added each year. Signals and Systems Fall 42 0. Signals and Systems Fall 11 The system in part a is a cascade of three of the following systems. Assume that the patient takes the drug once every 8 hours, and that the concentration of drug in the blood is measured shortly after taking each dose.


But 0 is not a root of the quadratic.

We need the correct linear combination of these two functions. Why save baggage small terms that you will throw away at the end of a trip? 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.

Compare the difference equations in parts a and b. Because of the A2 in the numerator, the functional itself has dimensions of time squared.

See the Appendix for help with programming. The integral is before taking the imaginary part: Signals and Systems Fall 12 p. These solutjon inside the unit circle.

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Then the circuit becomes a voltage source connected to jomework capcitor which leads to classic paradoxes about energy but we will carefully avoid them by not asking dangerous questions.

It is a delta function.

Signals and Systems Fall 9 This schedule is an example of using a loading dose. Assume that you take the medicine every 8 hours.


And the three left-hand plots show steadily increasing time to reach the steady state. Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart for control.

6.003 homework 1 solution

Homewori integral is before taking the imaginary part: Use difference equations to express the relation between deposits and balances for each bank. Give dimensional and extreme-cases arguments to show why the impulse response that you found is reasonable.

Signals and Systems Fall 17 4. Check your sum by feeding the impulse into a block diagram rep- resenting the original system functional. The original, continuous-time system decays without oscillating when fed an impulse, so the discrete-time simulation should do the same, if possible. This discrete-time analysis ignores the behavior between sampling intervals, i.

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The worst pole is now closer the unit circle, so the system is less stable. Signals and Systems Fall 19 Draw a block diagram, write the system functional, and give a pole—zero diagram. Why save baggage small terms that you will throw away at the end of a trip?

6.003 homework 1 solution

Here is a feedback-control system: