Consider a measurement algorithm where the encoder photodetectors are polled to detect W/B transitions. If the encoder is spinning at frequency f Hertz, show that the minimum sampling rate required to guarantee that no W/B transition is missed is 2 NL/H f

Let the sampling frequency be fs

2N=fs

Step-by-step explanation:

If a function f(x) contains no frequencies higher than f hertz, it is completely determined by giving its ordinates at a series of points spaced 1/2f seconds apart.

A sufficient sample-rate is therefore anything larger than 2f samples per second. Equivalently, for a given sample rate fs, perfect reconstruction is guaranteed possible for a bandlimit N<fs/2

2N=fs

y = - 6

step-by-step explanation:

given the point (- 2, y) lies on the graph then it is a solution of it's equation.

substitute x = - 2 into the equation for value of y

y = 3(- 2) = 3 × - 2 = - 6

the point on the graph is (- 2, 6)