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Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Signal representation and orthogonality

Choose difficulty:

Beginner

Intermediate

Advanced

Two signals

x_1(t)

and

x_2(t)

are orthogonal if

a: their product is always zero Explanation

Explanation

b: their dot product is zero Explanation

Explanation

c: their sum is always zero Explanation

Explanation

d: their dot product is positive Explanation

Explanation

The signals

\sin (t)

and

\sin (\alpha t)

are orthogonal in the interval

[0, 2\pi]

if

a:

\alpha

is any integer Explanation

Explanation

b:

\alpha

is any integer other than 1 Explanation

Explanation

c:

\alpha

is any integer other than 1 or -1 Explanation

Explanation

d: none of the above Explanation

Explanation

Which of the signals are orthogonal to each other,

x_1(t)=\psi(t), x_2(t)=\cos (2 \pi t), x_3(t)=\psi(2 t)

in the period

[0,1]

?

a:

x_1(t)

and

x_2(t)

Explanation

Explanation

b:

x_1(t)

and

x_3(t)

Explanation

Explanation

c:

x_3(t)

and

x_2(t)

Explanation

Explanation

d: (a) and (b) Explanation

Explanation

Which pairs of signals are orthogonal among

x_1(t)=\cos (t), x_2(t)=5 \sin (5 t), x_3(t)=\sin (t)

in the period

[0, 2\pi]

?

a:

x_1(t)

and

x_2(t)

Explanation

Explanation

b:

x_1(t)

and

x_3(t)

Explanation

Explanation

c:

x_3(t)

and

x_2(t)

Explanation

Explanation

d: all the above Explanation

Explanation

If vectors

v_1

and

v_2

are orthogonal and vectors

v_2

and

v_3

are orthogonal, then which of the following statement is true

a:

v_1

and

v_3

are always orthogonal Explanation

Explanation

b:

v_1

and

v_3

may not be orthogonal Explanation

Explanation

c:

v_2

may not be orthogonal to

\left(v_1+v_3\right)

Explanation

Explanation

d:

v_1

may not be orthogonal to

\left(v_2+v_3\right)

Explanation

Explanation

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