# Finding the sampling period to avoid loss of signal

We have: $$s(t) = 4u(t)−u(t−1)−2u(t−2)−2u(t−3.5)+2u(t−4)$$ where $u$ is the Heaviside function.

I had to draw the graph and find the minimum sampling period so we wont have loss of signal. I have drawn the graph.

$t=kT$ where $T$ is the sampling period.So $T=t/k$ so how do I find T?

• What is k? what is t? – willpower2727 Feb 17 '16 at 13:05
• @willpower2727, k is just a constant, the t is time. – Mahendra Gunawardena Feb 17 '16 at 13:11
• Pass from the time domain to frequency. You will see several impulses, and then you can see their frequencies and evaluate the needed from Nyquist statement. – leCrazyEngineer Jul 17 '16 at 5:01

The smallest feature that you need to capture is the dip between 3.5 and 4. If you use a sampling period which is greater than 0.5, then you may end up not capturing this feature. The sampling period must therefore be $T\leq 0.5$ in order not to lose any features of the signal.