ELEG 306: Digital Signal Processing   

Homework

The solutions are made based on my results and some standard book solutions.  Unfortunately, these two sources cannot guarantee correct answers. If you can figure out the mistakes in the homework solutions, I will give bonus points based on you contribution. And I’ll keep updating corrected solutions. Thanks

 

 

1.2, 1.3, 1.4, 1.5

2.2, 2.3, 2.6 (parts a, c and d. For parts c and d, determine only if the system is time invariant or not), 2.7 (parts a, c, d, f, i, j and l), 2.17 using the graphical method, 2.19, 2.42 and 2.43 (parts a and c).

 

Homework 1    solution

Homework 2  solution

Solve 2.67 using Matlab. Please, plot h(n) for 0≤n≤49 rather than 0≤n≤99 as the book says.

 

Computer Assignment 1 (Due September 22)

3.1, 3.3, 3.4 (except (f)), 3.6, 3.7 and 3.8

Note: In 3.7, you are asked to calculate the convolution. If you didn’t do the inverse z-transform, it’s OK.

Homework 3 solution

3.11, 3.14 a, b, c, g, 3.15, 3.16 a, b, d, 3.25, 3.26, 3.36, 3.38 a,b, 3.39 and 3.40.

Note:

1. In Problem 3.25(b), the z-transform has complex poles, and the result is very complicated. You may want to use X(z)=1/(1-1/z+0.25/z/z) instead of the original X(z)=1/(1-0.5/z+0.25/z/z) .

2. In problem 3.36. The ROC should be 0.5<|z|<1 instead of "0.5|z|>1".

Homework 4 solution

3.42, 3.43, 3.44, 3.46, 3.49, 3.51, 3.52, 3.55, 3.58 a.

Homework 5 solution

4.9 a, b, c, d, g, 4.10 a, b, 4.11, 4.14, 4.17, 4.19, 4.22, 5.2, 5.5, 5.7 and 5.9

Homework 6 solution

 5.12 a, b, c, 5.17, 5.18, 5.25, 5.27, 5.28, 5.32, 5.49, 5.59 a, b, 5.65, 5.76 and 5.77

Homework 7 solution

6.1, 6.5, 6.9, 6.12, 6.13 and the following problem:

Consider a continuous-time cosine of amplitude 1 and frequency F0(W0=2*pi*F0). This signal is sampled with a sampling frequency Fs=1/T, where T is the sampling period. From the samples we perform reconstruction as we studied in class (i.e., generating a delta train using the samples as weights and filtering the delta train with an ideal low pass filter that is equal to T between -Fs/2 and Fs/2 and 0 otherwise). 
1) What is the relationship between F0 and Fs that guarantees that the reconstructed signal (i.e., the output of the filter) is the initial
continuous-time cosine?
2) Obtain the reconstructed signal for all values of F0 ranging from 0 to 4Fs (i.e., 0<F0<4Fs). Explain your answer by sketching the Fourier transform of the delta train at the input of the filter. 

Problem 6.1(d)(e) involves using methods not mentioned in class. Problem 6.9 has some problems itself that makes this problem to be very complicated. Therefore, as long as you have demonstrated that you understand sampling process, I will not be strict on this homework. Thanks

Homework 8 solution

 7.1, 7.7, 7.8, 7.9, 7.13, 7.21 and 7.30.

Homework 9 solution