Homework 1

ECE4603 Fall'00 Homework Assignment #2 (v.1.0) 


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#1.  A/D Conversion 

[ 16,000 ]   In order to digitize an analog signal with frequency components
from 0 to 8000 Hz, how many time per second would you have to sample the
value of the signal (neglect the extra amount needed because filters have a
finite roll-off).

[ 7 | 8 ]  If you wanted to send a binary value of the signal voltage accurate
to less than 1% of the peak value (40 dB), how many bits per sample would
be required to represent the value.

[ 28,000 | 32,000  ]  How many bits per second would be transmitted (or stored).


#2.  According to Nyquist, if a digital encoder can NRZ encode 16 levels
per time slot of 100 microseconds, what is the:

[      4 ]    Bits per symbol.               log2(16)
[ 10,000 ]    Baud Rate (Baud/s).           1/100E-6
[ 40,000 ]    Capacity (bits per second).    answer 1 * answer 2
[  5,000 ]    Bandwidth required (Hz).        1/2 answer 2

#3.  If a 100,000 Hz baseband digital signal modulates a 1,000,000 Hz
carrier wave, what is the 

[   200,000 ] - bandwidth of the broadband signal (in Hz).
[   900,000 ] - the lower frequency edge of the broadband signal (in Hz).
[ 1,100,000 ] - the upper frequency edge of the broadband signal (in Hz).

#4.   If the receiver input noise level in an 8-level system  is -10 dBm
(dB relative to one milliwatt), what is the theoretical (Shannon Limit)
minimum power needed at the receiver? 

[ 6.3 ]  Power in milliwatts  8 = sqrt(S/N + 1 ) , S/N = 64 - 1 = 63
              63 * 0.1 mW = 6.3 mW
[   8 ]  Power in dBm    S/N in dB:  = 10*log(63) = 18 dB, N = -10 dBm

#5.   What is the bandwidth (in Hz) needed if 200 Baud per second  are
transmitted using the following types of modulation:

[ 100 ]     Two-level NRZ (non-return to zero)    F = 0.5
[ 200 ]     Two-level RTZ (return to zero)        F = 1.0
[ 100 ]     Two-level NRZ-I (NRZ inverted)        F = 0.5
[ 200 ]     Any common type of broadband moduation (ASK, PSK, QPSK, QAM).
[ 200 ]     Manchester Encoding                   F = 1.0

#7.   What bandwidth (Mhz) is needed to send 1 Mbps in a broadband
system using the following modulation techniques:

[ 1    ]  Two-level amplitude modulation (ASK).  F=1.0, 1 bit/Baud
[ 0.5  ]  Four-level phase-shift keying (PSK)    F=1.0  2 bits/Baud           
[ 0.5  ]  Four-level quadrature phase-shift keying (QPSK)      "  
[ 0.25 ]  Sixteen-level quadrature amplitude keying (QAM-16)  4 b/B

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