1. Sketch the signals:

(a)
2.(a) Find the even and odd components of e^jt.

(b) Show that the product of two even signals or of two odd signals is an even signal.

3.(a) Determine whether the following signals are energy signals, power signals, or neither: 0
For the signal shown in Figure sketch and label each of the following signals f(t 6)
<img src='./qimages/10959-3b.jpg'>

4.(a) Show that:
<img src='./qimages/10959-4a.jpg'>

4.(b) Show that:
<img src='./qimages/10959-4b.jpg'>

4.(c) Show that:
<img src='./qimages/10959-4c.jpg'>

4.(d) Show that:
<img src='./qimages/10959-4d.jpg'>

5. Evaluate where and are shown in Figure 2,
by an analytical technique, by a graphical method. <img src='./qimages/10959-5.jpg'>

6. Consider the discrete time system in Figure 3. Write a difference equation that relates the output and the input <img src='./qimages/10959-6.jpg'>

7.(a) Find the. trigonometric Fourier series for shown in Figure 4.
<img src='./qimages/10959-7a.jpg'>

7.(b) Find the Fourier transform of the rectangular pulse defined by

x(t) a

8.(a) Find the Fourier transform of the signum. function, which is defined as

sgn(t) t>0 t 0

8.(b) Find the Fourier transform of the periodic impulse train·defined as <img src='./qimages/10959-8b.jpg'>

9. Find the Z-transform and sketch the pole-zero plot with the ROC for each of the following sequences:

(a)

10.(a) Find the inverse Z-transform of 2

10.(b) Write down the properties of ROC in Z-transform.