Digital Communication Assignment -

Assignment Outcomes

1. Differentiate the types of pulse modulation techniques implemented in communication systems;

2. Critically evaluate the baseband demodulation and detection techniques;

3. Critically evaluate digital modulation techniques including multi-level digital modulation.

Rules & Regulations -

• If any coursework assessment is found to be copied from other candidates using unacceptable means, then it shall be cancelled and the total marks awarded will be zero. No chance of resubmission or appeal will be given.
• Your source of information should be mentioned in the reference page clearly. (For example: If it's from book, you have to mention the full details of the book with title, author name, edition and publisher's name. If it is from the internet you have to mention the correct URL). Otherwise the assignment will be considered as plagiarized.
• The students may be asked to appear for a viva voce to validate the assignment solutions submitted. The viva voce does not carry any marks.
• Title Page must have Assignment Name, Module name, your name, ID, Section and the name of the faculty.
• For late submission, 5%of the awarded marks will be deducted for each working day.
• For plagiarism, please refer to student guide and clarification uploaded on Moodle.
• Refer MIG for feedback dates on assignment.

Questions -       

1. a. i. A waveform that is band limited to 50 k Hz is sampled every 10μs. Show graphically that these samples uniquely characterize the waveform. (Use a sinusoidal example. Avoid sampling at points where the waveform equals zero.)

ii. If the samples are taken 30µs apart instead of 10 µs, show graphically that the waveforms other than the original can be characterized by the samples.

b. A Sinusoidal voice signal s(t) = cos (6000πt) is to be transmitted using either PCM or DM. The sampling rate for PCM is 8 kHz and for the transmission with DM, the step size ? is decided to be of 31.25mV. The slope overload distortion is to be avoided. Assume that the number of quantization levels for a PCM system is 64. Determine the signaling rates of the both the systems and also comment on the result.

2. A compact disc (CD) records audio signals digitally by using PCM. Assume that the audio signal bandwidth equals 15 kHz.

i. If the Nyquist sample are uniformly quantized into L = 65,536 levels and then binary-coded, determine the number of binary digits required to encode a sample.

ii. If the audio signal has average power of 0.1 W and peak voltage of 1 V. Find the resulting ratio of signal to quantization noise (SQNR) of the uniform quantizer output in part (i).

iii. Determine the number of binary digits per second (bit/s) required to encode the audio signal and minimum bandwidth required to transmit the encoded signal.

Practically signals are sample well above the Nyquist rate. Practical CDs use 44100 samples per second. If L=65536, determine the number of bits per second required to encode the signal, and the minimum bandwidth required to transmit the encoded signal.

b. Given an analog waveform that has been sampled at its Nyquist rate, fs using natural sampling, prove that a waveform (proportional to the original waveform) can be recovered from the samples, using recovery technique shown in figure 2. The parameter mfs, is the frequency of local oscillator, where m is an integer.

(Hint:  (x)_p(t) = _n=-∞∑^∞C_n e^j2πnfst   x_s(t) = x(t).x_p(t))

3. a. Consider the signals shown below Figure.

i. Each of the signals shown in Figure can be written using the form Asin(2π ft + φ). For each signal, determine the values of A, f and φ.

ii. Consider a composite signal which contains each of the four signals shown in Figure added together. Show the combined signals amplitude versus frequency-domain plot. What is the equation for this combined signal? What is the bandwidth of this signal?

iii. If the composite signal from part (ii) was passed through a special filter that removes its DC component, what would be the bandwidth of the filtered signal?

b. Coherent detectors are used to detect FSK signal with a rate of 2Mbps. Assuming AWGN channel with the noise power spectral density No/2 = 10^-20W/Hz. Determine the probability error. Assume the amplitude of the received signal is 1μV.

4. a. Imagine you wish to transmit the last four digits of your ID no (12f9612). First you will need to convert your student ID from its decimal (base 10) representation into a 28-bit binary (base 2) representation. Using clearly labeled diagrams, show an encoding of your ID using:

i. NRZ-L signal,

ii. NRZ-AMI

iii. Bi - ∅ - L

iv. Delay Modulation

(Note that ASCII Conversion sheet provided to you)

b. A binary communication system transmits signals s_i(t) (i = 1, 2). The receiver test statistic z(T) = a_i + n₀, where the signal component a_i is either a₁ = +1 or a₂ = -1 and the noise component n₀ is uniformly distributed, yielding the conditional density functions p(z/s_i)  given by

Find the probability of a bit error, P_B for the case of equally likely signaling and the use of an optimum decision threshold.

5. Show that for a bit stream b(t) = 011011100001, the  MSK  waveform has phase continuity with the help of suitable mathematical analysis and waveforms.

Assume that m = 5 for  f_H = (m+1) f_b/4  

                                   f_L = (m-1) f_b/4.