2005-2006 Assignments

• Signals and Systems

Fall 2005 Homework Assignments

Assignments for this quarter will be listed here so that there is an easy place to look up the assignments. Below each assignment is the date that it was assigned.

HW #1

Look at the Wiki & add your personal page. Spend two hours.

- 9/26/05

HW #2

Find the first three orthogonormal polynomials on $[-1,1]$ (lowest order polynomials).

- 9/30/05

HW #3

1) Work on the Wiki for two hours this week.

2) Find the output of a periodic function,

$x(t)=\sum _{k=-\infty }^{\infty }\alpha _{k}e^{j\pi k{\frac {t}{T}}}$

to an RC filter with RC = T.

- 10/3/05

HW #4

Show how the real and imaginary parts of $\alpha _{k}$ in the complex Fourier Series are related to the coefficients in the sine/cosine Fourier Series.

10/5/05

HW #5

Individual Wiki pages on Fourier Transform.

10/13/05

HW #6

1) Find ${\mathcal {F}}[x(t)sin(2\pi f_{o}t+\theta )$.

2) Convolve $u(t)-u(t-3)$ with $cos(2\pi t)[u(t-1)-u(t-2)]$

10/14/05

HW #7

1) Find ${\mathcal {F}}[u(t)cos(2\pi f_{o}t)]$

2) Show $x(t)*\delta (t-t_{o})=x(t-t_{o})$.

10/19/05

HW #8

There were two assignments that were labeled as HW #8.

HW #8A

Show that

$\Phi _{n}(t)\equiv {\frac {sin\left({\frac {\pi (t-nT)}{T}}\right)}{\frac {\pi (t-nT)}{T}}}$

form an orthogonal basis set. Tell me what functions these span.

10/21/05

HW #8B

Do a Wiki page on how a 2x oversampling CD Player works.

10/24/05

HW #9

Handout on FIR filter.

11/2/05

HW #10

Put something on FIR filters on the Wiki.

11/7/05

HW #11

Work on the Wiki. Read someone else's contribution & fix or extend it a little. Continue with FIR and do a DFT section if you have time.

11/14/05

HW #12

Come see me to discuss your Wiki contributions. I will give you suggestions for edits, etc.

11/30/05

HW #13

Write a Wiki page on adaptive FIR filters. Spend at least 2 hours by sundown Friday.

11/30/05

Principle author: Jeffrey Wonoprabowo