Four Samples
Fall 2018
Signal and Noise
Sampling a cosine function
Learn It!
Pre-Requisite Knowledge
Goal
What are the first four sample values?
What are the first four values sampled from the function?
\(x(t)=3 cos(6 \pi t) \)
If \(x(t)=3 cos(6 \pi t) \) 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.