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# Digital Transmitter: Frequency Shift Keying Prelab Exercise

Module by: Matthew Berry. E-mail the author

Summary: Students fill in missing lines of code to create a Matlab simulation of a four-symbol frequency shift keying (FSK) transmitter. Students are encouraged to change the symbol period and observe the change in the transmitted signal's spectrum.

## Prelab: Matlab Preparation

We have made considerable use of Matlab in previous labs to design filters and determine frequency responses of systems. Matlab is also very useful as a simulation tool.

Use the following Matlab code skeleton to simulate your system and fill in the incomplete portions. Note that the code is not complete and will not execute properly as written. How does the spectrum of the transmitted signal change with T symb T symb ?



1    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2    % Matlab code skeleton for Digital Transmitter
3
4    close all;clear;
5
6    % Generate random bits
7    bits_per_symbol=2;
8    num_symbols=64;
9    numbits=bits_per_symbol*num_symbols;
10    bits=rand(1,numbits)>0.5;
11
12    Tsymb=32;           % samples per symbol
13
14
15    % These are the 4 frequencies to choose from
16    % Note that 32 samples per symbol does not correspond to
17    % an integer number of periods at these frequencies
18    omega1 =  9*pi/32;
19    omega2 = 13*pi/32;
20    omega3 = 17*pi/32;
21    omega4 = 21*pi/32;
22
23
24    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
25    % Transmitter section
26
27    % Initialize transmit sequence
28    index=1;			% Initialize bit index
29    n=1;				% Initialize sample index
30    phi=0;				% Initialize phase offset
31
32    % Generate 64 32-sample symbols
33    while (n<=num_symbols*Tsymb)
34
35      if (bits(index:index+1) == [0 0])
36         sig(n:n+Tsymb-1) = sin(omega1*[0:Tsymb-1]+phi);
37         phi = omega1*Tsymb+phi;	% Calculate phase offset for next symbol
38         phi = mod(phi, 2*pi);	% Restrict phi to [0,2*pi)
39
40     % -----------> Insert code here <-------------%
41
42      end % end if-else statements
43
44      index=index+2; % increment bit counter so we look at next 2 bits
45
46      n=n+Tsymb;
47    end   % end while
48
49
50    % Show transmitted signal and its spectrum
51    % ---------------> Insert code here <-----------------%



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