ETC-M2
Digital Communication
Homework 2
1- A telephone signal with cut-off frequency of 4 khz is digitzed into bit PCM,
sampled at nyquist rate. Calculate baseband transmission bandwidth and
quantization S/N ratio
2- A telephone signal band limited to 4 kHz is to be transmitted by PCM. The
signal to quantization noise is to be at least 40 db. Find the number of levels
into which the signal has to be encoded. Also find the bandwidth of
transmission.
3- An audio signal has its spectral components limited to the frequency band of
0.3 to 3.3 kHz. A PCM signal is generated with sampling rate of 8000
samples/sec. the required output signal to quantizing noise is 30 dB.
i)
Calculate the minimum number of uniform quantization levels required.
ii)
How many minimum number of bits per sample needed.
iii)
Calculate the minimum system bandwidth required.
4- Find the output of the matched filter and determine the maximum value of
(S/N)0 if the input S(t) is a rectangular pulse of amplitude A and duration T.
5- A discrete signal S(t) is transmitted through an AWGN channel where the white
noise n(t) has a two sided noise spectral density equal N 0/2. Given that the
signal is:
𝐴 𝑐𝑜𝑠(𝜔0 𝑡)
𝑆(𝑡) = {
0
0≤𝑡≤𝑇
𝑜𝑡ℎ𝑒𝑤𝑖𝑠𝑒
1) Find the matched filter impulse response of S(t)
2) The SNR at the output matched filter
3) For high frequency signal pulse within T (i.e. 𝜔0 𝑇 ≫ 1) what does SNR reduces
to?
2018-2019
ETC-M2
6- Consider the signal s(t) shown in below Figure.
1- Determine the impulse response of a filter matched to this signal and
sketch it as function of time.
2- Plot the matched filter output as a function of time
3- What is the peak value of the output?
7- Consider the two digital modulation schemes shown in the figure below. For
each scheme, determine the minimum distance between two symbols dmin , the
average energy per symbol Eav, and the average energy per transmitted bit Eb.
Which scheme is more efficient in terms of transmission energy usage?
8- Consider a channel with bandwidth 1MHz.
1- Suppose the channel is noiseless, what is the maximum number of bits that
can be transmitted reliably if you use 2-ASK for modulation? What if you use
8-ASK?
2- Suppose the channel suffers from noise with a signal to noise ratio of 10
dB. What is the maximum number of bits that can be transmitted reliably?
What if the channel SNR is 30 dB?
2018-2019
ETC-M2
9- In a additive white Gaussian noise channel with noise power spectral density of
N0/2, two equi-probable message are transmitted by
1- Determine the structure of the optimal receiver.
2- Determine the probability of error.
10- Consider the binary sequence 0101101. Draw the waveforms for the following
signaling formats.
a) Unipolar NRZ signaling format
b) Bipolar RZ signaling format
11- In a binary PCM system, the output signal to quantization noise ratio is to be
held to a minimum of 40 dB. Determine the number of required levels, and find
the corresponding output signal to quantizing noise ratio.
12- A binary baseband communication system uses the signal set consisting of
s0(t)=s(t) and s1(t)=-s(t) with equal probability, where
The channel is AWGN channel with double sided noise power spectral desnity
N0/2.
a) What is the minimum error probability of this system? Express your answer
in terms of A, T and N0.
b) Find the impulse response of the receiving filter that achieves the minimum
error probability.
c) Find the optimum sampling time and the optimum threshold for the receiver
that uses the filter in b).
13- A multi-level digital communication system sends one of 32 possible levels
over a channel every 0.8 milliseconds.
a) What is number of bits corresponding to each level?
b) What is the Baud rate?
c) What is the bit rate?
2018-2019
ETC-M2
14- An analog signal has time variation f(t) = 3 + 0.2 cos (8000π t) - 0.3 sin (4000π t) .
a) Minimum how many samples should be taken to satisfy Nyquist requirement?
b) 256 levels is used to represent one sample. How many bits are required to transmit
one sample value.
c) What is the minimum transmission rate of this signal?
d) Would you allocate a 256 kbps channel to transmit this signal? Why?
e) Would you allocate a 32 kbps channel to transmit this signal? Why?
15- The following is a BPSK transmission:
a) Determine the transmitted bits
b) Determine the bit rate
c) QAM is a combination of which two types of modulations.
2018-2019