Please complete the following questions from the text:

Problem 1.2 (iii) and (vi)

Problem 1.3 (v) and (vi)

Problem 1.5 (iii) and (vii)

Problem 1.6 (i) and (iv)

Problem 1.7 (i) and (v)

Problem 1.8 (iii) and (iv)

Problem 1.14 (iv) and (v)

Problem 1.15 (iv) and (v)

Problem 1.21 (iii)

Problem 1.22 (v) and (vii)

Problem 1.24

Solution to Assignment 1 is now available.

Student Questions on Assignment 1:

Q1. For the assignment Problem 1.8 # (iv), how did you make exp(j(pi*k/2 + pi/8)) = 1. I don't understand this equality.

A1. Note that exp(j(pi*k/2 + pi/8)) does not equal 1 but the magnitude of exp(j(pi*k/2 + pi/8)) equals 1.

Recall exp(j \theta) = cos \theta + j sin \theta Now, | exp(j \theta) | = sqrt (cos^2 \theta + sin^2 \theta) = sqrt (1) = 1

Q2. How do i Evaluate and find the period of exp(-j*pi*k).

A2. Note that exp(-j*pi*k) = cos(pi*k) - j sin(pi*k). Since sin(pi*k) = 0, therefore, exp(-j*pi*k) = cos(pi*k) which has a period of pi radians/s or 1/2 Hz.

Q3. If (-1^k) = exp(j*pi*k), what does (-5^k) or (5^k) equal to?

A3. You can not express (-5^k) or (5^k) in the form that (-1^k) was expressed.