DORDT COLLEGE ENGINEERING DEPARTMENT
DIGITAL SIGNAL PROCESSING -- EGR 366
(Spring 2006)
Click this note on cached pages and handouts if you are
having difficulty seeing the latest version of this page.
PROBLEM SETS (Last update:
------------ 4/17/06 3:49 pm)
+===============================================================+
|PS|ASSIGNED| DUE |RETURNED| Problems Assigned |
| #| / \ | |
|==+=======+=======+=======+====================================|
|10| 4/19 | 4/28 | | 5.1, 5.2 parts (a) and (c) only. |
| | | | | 5.3, 5.25, 6.8, 6.11 but do only |
| | | | | the decimation in time part. |
| | | | | |
| | | | | Hints: For some problems, e.g. 5.2,|
| | | | | Matlab can take the drudgery out |
| | | | | of the math. For 6.11 you can keep|
| | | | | the twiddle factors in exponential |
| | | | | form as multipliers until the last |
| | | | | step, when you expand them to |
| | | | | complex numbers to express the |
| | | | | results of the FFT. A further hint|
| | | | | on 6.11: X(2) = 0 and several other|
| | | | | terms are zero too. (Which ones?) |
| | | | | Note: The signal has _______ |
| | | | | symmetry in the time domain. |
|--+-------+-------+-------+------------------------------------|
| 9| 3/27 | 4/07 | 4/14#| 4.9, 4.10, 4.14, 4.15 |
| | | | | Hint on 4.14: What is the sum of |
| | | | | all the x(n) over all n? |
| | | | | Hints on 4.15: What is X(0) = ? |
| | | | | What is dX(w)/dw = when evaluated |
| | | | | at w = 0? (w = omega). |
| | | | | |
| | | | | On Monday, 4/3, the due date was |
| | | | | extended from 4/3 to 4/7. |
|--+-------+-------+-------+------------------------------------|
| 8| 2/27 | 3/06 | 3/29#| 4.4, 4.5, 4.8 |
| | | | | Note: In 4.4 the period, N = 6 |
|--+-------+-------+-------+------------------------------------|
| 7| 2/20 | 2/27 | 3/1? | Study for test on Wed. 2/22. |
| | | | | Also do 3.21 (a proof). |
| | | | | Hint: Assume the polynomial has a |
| | | | | complex root. Show that the |
| | | | | conjugate of the polynomial has |
| | | | | a root which is the conjugate of |
| | | | | the original root of the original |
| | | | | polynomial. Then show that the |
| | | | | original polynomial must have the |
| | | | | conjugate of the original root too.|
| | | | | Put these hints together to make a |
| | | | | complete proof. |
|--+-------+-------+-------+------------------------------------|
| 6| 2/15 | 2/20 | 2/27 | 3.1, 3.3, 3.7, 3.11, 3.15 |
| | | | | |
|--+-------+-------+-------+------------------------------------|
| 5| 2/06 | 2/13 | 2/21 | 2.62* parts (a) through (d) only. |
| | | | | |
| | | | | Hints: Try "help randn" in Matlab.|
| | | | | Crosscorrelation can be done via |
| | | | | matlab's "conv" function. |
| | | | | If x and y are equal size, |
| | | | | Rxy = conv(x, fliplr(y)); |
|--+-------+-------+-------+------------------------------------|
| 4| 2/01 | 2/06 | 2/15 | 2.22*, 2.25, 2.26 (assume relaxed),|
| | | | | 2.43 part (a) only. |
|--+-------+-------+-------+------------------------------------|
| 3| 1/23 | 1/30 | 2/03 | 2.11, 2.16, 2.20* |
| | | | | |
| | | | | Note: Part (a) of 2.16 is a proof.|
| | | | | For part (b) do at least sub-parts |
| | | | | 1, 2, and 3 by hand. For finite |
| | | | | numeric computations Matlab has a |
| | | | | command called "conv" which works |
| | | | | well for most of this problem. For|
| | | | | some parts Matlab cannot be used. |
| | | | | Do those parts by hand. |
|--+-------+-------+-------+------------------------------------|
| 2| 1/18 | 1/23 | 2/01 | 1.13, 1.14, 1.16*, 2.5, 2.10 |
| | | | | |
| | | | | See errata on 1.14 |
| | | | | |
| | | | | Hint for 1.16*--> You may use the |
| | | | | quantize.m file in your program. |
| | | | | Note: quantize.m requires limit.m |
| | | | | be stored in the same folder. |
|--+-------+-------+-------+------------------------------------|
| 1| 1/11 | 1/16 | 1/18 | 1.2, 1.5, 1.9, 1.15* |
+---------------------------------------------------------------+
* = A computer is highly recommended for solving this problem.
Notes: To save a copy of a *.m file, right-click the link and
then click on something like "save target as. . ." (the
exact procedure depends on your web browser.)
To read a *.m file with it's original formatting, after
clicking on the link select "View | Source" or similar
command from the top menu bar of your browser. (If this
exprience does not prove the value of white space, which
browsers typically remove, nothing will.)
Back to Prof. De Boer's home page