Spring 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?
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
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