## 1.2. Solved exercises

EXERCISE 1.6.

Define a 4×3 matrix zero everywhere excepting the first line that is filled with 1.

b = ones (1, 3); m = zeros (4, 3); m(1, :) = b m = 1 1 1 0 0 0 0 0 0 0 0 0

EXERCISE 1.7.

Consider the couples of vectors (*x*_{1} *y*_{1}) and (*x*_{2}, *y*_{2}). Define the vector *x* so that:

*x(j)* = 0 if *y*_{1}(*j*) <*y*_{2}*(j)*;

*x(j)* = *x*_{1}(*i*) if *y*_{1}*(j)* = *y*_{2}(*j*);

*x(j)* = *x*_{2}*(j)* if *y*_{1}(*j*) > *y*_{2}*(j)*

function x = vectors(x1,y1,x2,y2) x = x1.*[y1 == y2] + x2.*[y1 > y2]; vectors ([0 1],[4 3], [-2 4] ,[2 0]) ans = -2 4

EXERCISE 1.8.

Generate and plot the signal: *y(t)* = sin(2π*t*) for 0 ≤ *t* ≤2, with an increment of 0.01, then undersample it (using the function decimate) with the factors 2 and 16.

t = 0:0.01:2; y = sin(2*pi*t); subplot(311) plot(t,y) ; ylabel('sin(2.pi.t)'); title('Original signal'); t2 = decimate(t, 2); t16 = decimate(t2, 8); y2 = decimate(y, 2); y16 = decimate(y2, 8); subplot(312) plot(t2, y2); ylabel('sin(2.pi.t)') title('Undersampled signal with a factor 2'); subplot(313); plot(t16, y16); ylabel('sin(2.pi.t)'); xlabel('Time t'); title('Undersampled signal with a factor 16');

You can save the figures in *eps* (Encapsulated PostScript) format, which is recognized by many software programs. The command print -eps file_name creates the file *file_name.eps*.

EXERCISE 1.9.

Plot the paraboloid defined by the equation: ...

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