Please complete the following questions from the text:

Problem 1.2 (iv) and (v)

Problem 1.3 (iii) and (iv)

Problem 1.5 (v) and (vi)

Problem 1.6 (ii) and (iii)

Problem 1.7 (iii) and (vi)

Problem 1.8 (i) and (v)

Problem 1.14 (i) and (iii)

Problem 1.15 (i) and (iii)

Hints for Problem 1.5 part (v)

Note that:

1. All CT complex exponentials are periodic.
2. A real valued exponential signal is not periodic.
3. Sum of a periodic signal and an aperiodic signal is not periodic.

Hints for Problem 1.5 part (vi)

Note that:

1. Sum of a periodic signal and an aperiodic signal is not periodic.
2. Product of two periodic signals is not necessarily periodic.
3. If we have y(t) = x_1(t)+x_2(t)+x_3(t) where all three are periodic with periods T_1, T_2, and T_3 respectively, then y(t) is periodic if all combinations of T_1/T_2, T_1/T_3, and T_2/T_3 are rational numbers.
4. Use the following identities to simplify the function:

• sin^2(t) = 1/2(1 − cos(2t))
• cos(a)cos(b) = 1/2[cos(a+b) + cos(a−b)]

Problem 1.15

There is a typo and the correct one is as follows:

x1[k] = sin(4k)+cos(2*pi*k/3).