Sinusoidal Signals

Question 1

Why sinusoidal signals?

Answer 1

• they’re abundant in nature

- bases: sums of sinusoids can describe any signal

Question 2

CT and DT sinusoids are described by…

Answer 2

amplitude, frequency, and phase

Question 3

formula for CT sinusoid

Answer 3

x(t) = Acos(capitalOmega*t + theta)

A: amplitude
captialOmega: frequency
theta: phase shift

Question 4

what is the period of a CT sinusoid?

Answer 4

• T = 2*pi / captialOmega
• measured by time for one cycle of sinusoid
• 1 cycle = angle of CT sinusoid changing by 2*pi radians

Question 5

formula for DT sinusoid

Answer 5

x[n] = Acos(lowerOmega*n + theta)

A: amplitude
lowerOmega: frequency
theta: phase shift

Question 6

what is the period of a DT sinusoid?

Answer 6

• N: the number of samples in one cycle
• measured by number of samples for one cycle of sinusoid
• 1 cycle = angle of DT sinusoid changing by 2pim radians where m = integer

Question 7

is the relationship b/w period and frequency of a DT sinusoid the same as that of a CT sinusoid?

Answer 7

no because b/c w/DT sinusoids, the period, N, and the time index, n, are both integers

For this to be true, the frequency (lowerOmega), has to be related to the period, N

Question 8

what is the relationship b/w frequency (lowerOmega) and period (N) for DT sinusoids?

Answer 8

frequency (lowerOmega) = 2pim / N for some integer value of m

N = period

Question 9

frequency of a CT sinusoid?

Answer 9

• capitalOmega

- measured in radians/time (Hz) or cycles/time

Question 10

frequency of a DT sinusoid?

Answer 10

• lowerOmega

- measured in radians/sample or rads

Question 11

frequency is the inverse of…

Answer 11

the period