# Design a Discrete-Time System

Could you help me with this theoretical question.

The purpose is to design a discrete-time system. What it does is, it finds the maximum value in a one-dimensional sequence whose elements consist only of "non-negative" real numbers and contains only a single global maximum with no local maxima.

• so you have a set of positive numbers and you need to write an algorithm to find the max in that set. – spet Oct 25 '18 at 17:52

Since you have defined your signal $$x[n]$$ to be a set of non-negative numbers with a single global maxima, the algorithm to find the maximum is quite simple.
compute the first (causal , backward) difference $$y[n] = x[n] - x[n-1]$$
Then look for the sign change of $$y[n]$$; i.e., at the extreme point you will have the sign of $$y[n]$$ changing from positive to negative, assuming you had a single global maxima.
$$z[n] = \text{sign_change_detector} \{ y[n] \}$$