ELEC ENG – 3TR4 COMMUNICATION SYSTEMS

INSTRUCTOR NAME

                                             S. Kumar

 

DURATION OF EXAMINATION: 3 hours                                                  April 17, 2008

McMASTER UNIVERSITY FINAL EXAMINATION

 

THIS EXAMINATION PAPER INCLUDES 4 PAGES AND 8 QUESTIONS. YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING ANY DISCREPANCY TO THE ATTENTION OF YOUR INVIGILATOR.

 

Special Instructions:

                     Use of any calculator is allowed.

                     Answer all the questions.

Good luck and have a great summer!

 

1.     Find the inverse Fourier transform of the following spectrum                          7 marks

Continued on Page 2

2.     Consider the message signal given by        

,

carrier frequency =50 Hz and carrier amplitude Ac=1 V. Assume 75% modulation.

(a)   Sketch (to the scale) the resulting standard AM signal in time domain.

(b)  Find the Fourier transform of the AM signal and sketch the magnitude spectrum of the message and AM signals.                                                                                    6 marks

 

3. In a modified DSB-SC scheme, two messages  and were transmitted on carriers and , respectively to obtain the transmitted signal

Suppose the receiver is as shown in Figure 2.  Find the output . Is it possible to separate the messages  and  using this receiver  (i.e. the output  should not contain the term proportional to ) ?                  

 
6 marks

 

 

LPF = Low pass filter.                                 

Fig. 2

 

 

 

Continued on Page 3

 

 

 

4. The standard form of single-tone FM is given by

           .

When the modulation index  (narrow band FM),

(a) Show that the FM signal can be approximated as

(b) Find the Fourier transform of the narrow band FM signal and sketch the magnitude spectrum.                                                                                                             

 7 marks                                                                               

5. A random process X(t) is multiplied by a sinusoidal wave  where  is a random variable uniformly distributed over (0,). The autocorrelation and power spectral density of X(t) are RX(t) and SX(f), respectively. Find the autocorrelation and power spectral density of the random process defined by

 Assume that X(t) and are independent.

7 marks

6.     The transfer function of the filter shown in Fig. 3 is given by

,

where = 1 KHz. The signal  is applied to this filter, along with white noise as shown in Fig. 3.  The power spectral density of the white noise is

 = 1Watt/Hz.

(a)Find the output signal-to-noise ratio when

(b)   as in part (a) above when

output
 

 

7 marks

7. Draw the block diagram of a digital receiver and provide the description of each block.

5 marks 

8. In the case of standard AM receiver using envelope detection, is it possible to recover the message signal without distortion when modulation exceeds 100%? Provide explanation. 

5 marks

 

                                                                                                       Continued on Page 4

 

 

Useful information

 

1. Fourier transform pairs:

 

2.  Trigonometric relations:

 

 

    

                                                                                         

THE END