Exercises 1-7
Exercise 8.
Exercise 9.

A tube system is linear, i.e., an input and the corresponding output satisfy a linear equation A = . Consider the following tube system:

Use the following measurements to find the transition matrix A:

Input x1 = 1 (units), x2 = 0 => output y1 = 1/7 (units), y2 = 3/7, y3 = 3/7
Input x1 = 0, x2 = 1 => output y1 = 2/5, y2 = 1/5, y3 = 2/5

What is the output corresponding to the input x1 = 2, x2 = 1?

Answer

Exercise 10. (Fourier transform)


Let

A = 1/4 1111
1-j-1j
1-11-1
1j-1-j
and

B = 1/2 11,
1-1
where j is the imaginary unit ( j2 = -1).
a) Show that the inverse matrix A-1 of A is 4, where is the conjugate matrix of A, and find B-1.
b) The Fourier transform F = F(f) = AfB of a 4 x 2 matrix is

F = 1/8 3-1.
-3j-2+3j
11
3j-2-3j

Find the original f.

An example
Answer

Exercises 11-15
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