Week 2 - Signals

Question 1

A sine wave has a frequency of 60Hz, what is its period in milliseconds?

Answer 1

60Hz = 1/60s = 1000 / 60 ms

NOTE: flipping from period to frequency must be done in seconds and Hz

Question 2

What is the frequency in kHz if the period is 200 microseconds?

Answer 2

200microseconds = 0.0002s

f = 1/0.0002 = 5000Hz = 5kHz

Question 3

A positive phase shift shifts the sine wave to the ____

Answer 3

Left

Question 4

A negative phase shift, shifts the sine wave to the ____.

Answer 4

Right

Question 5

Describe the phase shift of a sine wave that is offset by 1/9 cycles.

Answer 5

We assume a positive phase shift (sine wave starting point moved to the left).

The phase shift is 360/9 degrees or 2pi/9 radians.

Question 6

What do you get when you decompose a composite periodic signal?

Answer 6

Multiple simple sine waves or discrete frequencies.

Question 7

What do you get when you decompose a composite non-periodic signal?

Answer 7

An infinite number of frequencies or a range of frequencies.

Question 8

A digitized voice channel is made by digitizing a 4-kHz bandwidth
analog voice signal. We need to sample the signal at twice the
highest frequency (i.e., two samples are acquired per cycle). We
assume that each sample requires 8 bits. What is the required bit
rate?

Answer 8

4 kHz = 4000Hz = 4000 cycles per second.

We need to sample at double that which is 8000 cycles per second.

If each sample is 8-bits, 8 x 8000 = 64 000 bits per second

Question 9

Decomposition of a non-periodic digital signal gives us a(n) _____

Answer 9

analog signal with infinite bandwidth (fourier transformation) and continuous frequencies.

Question 10

A decomposition of a periodic digital signal gives us a(n) ____

Answer 10

analog signal with infinite bandwidth and discrete frequencies