Signal Transformations, Properties and Models

Question 1

Define a continuous time signal (CT)

Answer 1

A signal that is defined as a continous function of time
x(t)

Question 2

Define a discrete signal (DT)

Answer 2

A discrete function of time has samples taken at a number of intervals
x[n]

Question 3

Define a DT sinusoid signal

Answer 3

x[n] = Acos(wn +ø)
ø is the phase difference
where w = 2πq/r

Question 4

Define a DT unit impulse

Answer 4

∂[0] = 1
otherwise ∂[n] = 0

Question 5

Define a DT unit step

Answer 5

u[n] = ∑∂[n-k]

Question 6

Give an example of a CT unit step in real life

Answer 6

A DC power supply being switched on to a fixed value.

Question 7

Explain the CT unit impulse in terms of the dirac delta function

Answer 7

The width of the signal is infinitely small
-The area of the pulse is 1 ( ∫d(t) = 1)
-d(t) = ∂u(t)/ ∂t

Question 8

How can a CT unit pulse be written in terms of unit steps?

Answer 8

u(t+n) - u(t-n)

Question 9

When is Fourier transform used instead of fourier series?

Answer 9

When the signal is non-periodic

Question 10

For Fourier Transform, what does X(w) mean?

Answer 10

X(w) is the fourier transform of x(t)
-X(w) provides an alternative view of x(t) in the frequency domain ƒ

Question 11

what is the process for finding the fourier series coefficient?

Answer 11

• Sketch the signal and find the fundamental period/ w
  -use the formula for the fourier series coefficient
  ak = 1/T0 ∫ x(t) e^(-jk(wk)t)
• find values for ak when k =0 and when k≠0

Question 12

What is the formula for fourier transform?

Answer 12

X(w) = ∫x(t) e^ - (jwt) dt