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Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Signal representation and orthogonality

Choose difficulty:

Beginner

Intermediate

Advanced

Let

v_1=\left[\begin{array}{lll}1 & 0 & 0\end{array}\right]^T, v_2=\left[\begin{array}{lll}1 & 2 & 0\end{array}\right]^T

and

v_3=\left[\begin{array}{ll}0 & 3 & 2\end{array}\right]^T

. Which pairs of vectors are orthogonal to each other?

a:

v_1

and

v_2

Explanation

Explanation

b:

v_2

and

v_3

Explanation

Explanation

c:

v_1

and

v_3

Explanation

Explanation

d: all above Explanation

Explanation

What is

a_0

for the periodic signal

x(t)=\frac{\sqrt{(1-\sin (x))}}{2}

?

a:

\frac{1}{2}

Explanation

Explanation

b:

\pi

Explanation

Explanation

c: 0 Explanation

Explanation

d:

\frac{3}{2} \pi

Explanation

Explanation

What is

\exp (j \theta)

equal to, where

j

is the square root of unity?

a:

\sin (\theta)+\cos (\theta)

Explanation

Explanation

b:

\cos (\theta)+j \sin (\theta)

Explanation

Explanation

c:

\sin (\theta)+j \cos (\theta)

Explanation

Explanation

d:

j \cos (\theta)+j \sin (\theta)

Explanation

Explanation

If the signals

x_1(t)

and

x_2(t)

are orthogonal in

[0 , T]

, then the signals

a:

-x_1(t)

and

-x_2(t)

are orthogonal in

[0 , T]

Explanation

Explanation

b:

x_1(-t)

and

x_2(-t)

are orthogonal in

[-T , 0]

Explanation

Explanation

c:

y(t)=x_1(t) x_2(t)

and

z(t)=1

are orthogonal in

[0 , T]

Explanation

Explanation

d: all 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 (

v_1+v_3

) Explanation

Explanation

d:

v_1

is always orthogonal to

\left(v_2+v_3\right)

Explanation

Explanation

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