Using a delicate temperature sensor$,$ two students are continuously measuring temperature

which fluctuates with a frequency of $50$ Hz$.$

$4-1)$ What sampling frequency is required so that the $50$ Hz temperature signal will not be

aliased?

Fs $100$ Hz

$4-2)$ Student A decided to sample the temperature signal at $200$ Hz$.$ What is the time between

samples? If the sampling continues for $20$ seconds, how many samples will be taken?

N $=4000$ samples

$$t $=0\mathrm{.}005$ s

$4-3)$ Student B sampled the temperature signal at $1000$ Hz$,$ with $1024$ samples, and then

performed an FFT routine to create a spectrum of the signal. What is the increment between

frequencies in the FFT and what is the maximum useful frequency returned by the FFT$?$