Four Samples

Signal and Noise

Sampling a cosine function

Learn It!

Pre-Requisite Knowledge

To understand this section, you need to know the following concepts:

Goal

What are the first four sample values?

What are the first four values sampled from the function?

$x(t)=3 cos(6 \pi t)$

$x(t)=3 cos(6 \pi t)$ is sampled every

$0.5$ seconds starting at

$t=0$ . What are the first 4 sampled values?

Method 1

Plug and Chug

t=0.0
t=0.5
t=1.0
t=1.5

We know that the sample points are each equally spaced, so we know which values of

$t$ we are sampling at

$x(0.0)=3 cos(6 \pi \cdot 0.0) =3 cos(0)=3$

$x(0.5)=3 cos(6 \pi \cdot 0.5) =3 cos(3 \pi)=-3$

$x(1.0)=3 cos(6 \pi \cdot 1.0) =3 cos(6 \pi)=3$

$x(1.5)=3 cos(6 \pi \cdot 1.5) =3 cos(9 \pi)=-3$

Just plug in the four time points into the function we are sampling. That's all there is to it!
The cosine of an even multiple of

$\pi$ ( such as 0,

$2\pi$ ,

$4\pi$ )is +1, the cosine of an odd multiple of

$\pi$ ( such as

$\pi$ ,

$3\pi$ ) is -1

Put your calculator in radian mode!

★

(3,-3,3,-3)

The correct answer.