Introduction to MATLAB - Continuous and Discrete Time Signals and Systems - page 834

>>f=[14-23-2*i]; % initialize f

>> g = [-3 5+7*i 6 2]; % initialize g

>>r1=f+g %Calculate the sum of f and g

% The result is displayed due
% to the absence of a
% semicolon at the end of the
% instruction

results in the following value for r1 :

r1 =
-2.0000 9.0000+7.0000i 4.0000 5.0000-2.0000i

which can be confirmed by direct addition of vectors f and g .
(ii) To compute part (ii), we use the M ATLAB function dot as follows:

>> r2 = dot(f,g) % dot returns dot product btw f and g

which returns

r2 =
11.0000+32.0000i

An alternative approach to compute the dot product is to multiply the row vector
f by the conjugate transpose of g . The transpose is needed to make the two
vectors conformable for multiplication. You may verify that the instruction

>> r2 = g*f'; % alternative expression for calculating

% the dot product. Operator ' denotes
% complex-conjugate transpose

returns the same value as above.
(iii) The instruction for part (iii) is as follows:

>> r3 = sum(f)/length(f) % sum(f) adds all row entries

% of vector f length(f)
% returns no. of entries in f

which returns

r3 =
1.5000 − 0.5000i

(iv) The instruction for part (iv) is as follows:

>> r4 = sum(f.*conj(f))/length(f)
% Operation f.*g does an element by
% element multiplication of vectors f
% and g. Operation conj(f) takes complex
% conjugate of each entry in f