For All Problems Involving Math, Show Your Work

TDC 460

Autumn 2010

Homework #6

Not Accepted After November 8th

For all problems involving math, show your work.

1. Given a periodic composite signal composed of 4 individual frequencies – 1000Hz at 5v, 5000Hz at 15v, 10000Hz at 3v, and 12000Hz at 8v, draw the frequency domain representation for this composite.

2. Redraw the frequency domain representation from the previous problem but add a DC component of 6v.

3. A signal is composed of frequencies from 500Hz up to 5000Hz. What is the spectrum of the frequencies? The absolute bandwidth? What might a drawing of the effective bandwidth look like?

4. A signal starts with 50 watts of power and ends with 10 watts of power. What is the dB loss?

5. If a signal starts with 100 watts and experiences a 10 dB loss, what was its ending power level?

6. If the signal at the beginning of a cable with -0.5dB/km has a power level of 10mW, what is the power of the signal at 6km?

7. We need to send 320 kbps over a noiseless channel with a bandwidth of 40 kHz. How many signal levels do we need?

8. We have a channel with a 1.2 MHz bandwidth. The SNR for this channel is 463. What are the appropriate bit rate and signal level?

9. We have a channel with a 500 kHz bandwidth. The SNRdb for this channel is 78db. What are the appropriate bit rate and signal level?

10. An analog signal has a baud rate of 3000 baud and a bit rate of 33000 bps. How many data elements are carried by each signal element? How many signal elements do we need?

11. What is the required bandwidth for the following cases if we need to send 4000 bps?

a. ASK (d=1)

b. FSK with 2Df = 4kHz (d=1)

c. QPSK (d=0)

d. 16-QAM (d=0)

12. What is the number of bits per baud for the following techniques?

a. ASK with 4 different amplitudes

b. FSK with 8 different frequencies

c. PSK with 16 different phases

d. QAM with a constellation of 128 points

13. Draw the constellation diagram for the following:

a. ASK with peak amplitude values of 1 and 3

b. BPSK, with a peak amplitude value of 2

c. QPSK, with a peak amplitude value of 3

14. Draw the signal constellation for a modem that used the QAM defined by the following:

Bit Values Amplitude of Signal Phase Shift of Signal

000 1 0

001 3 0

010 1 90 degrees

011 3 90 degrees

100 1 180 degrees

101 3 180 degrees

110 1 270 degrees

111 3 270 degrees