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what is monotonic signal?

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A function y=f(x) is
monotonic- if increasing as x increases
monotonic- if decreasing as x increases
non monotonic - if increasing and decreasing
monotonic - if not increasing or not decresing
For more info: check wikipedia
 

A monotonic signal is a function that keeps increasing or decreasing as its domain variable proceeds.
That's for f(x):
f(x+k) > f(x), for all k > 0 : This is a monotonically increasing function, while
f(x+k) < f(x), for all k > 0 : This is a monotonically decreasing function
 

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