Consider a function
$y[n]= \cos[w n ]$, where $n$ is an integer.
I have to prove that this signal will have highest rate of oscillation at $w = \pi$. I was thinking I can take the derivatives (of rate of oscillation) and set condition of maxima, but the variable is a discrete variable and not a continuous one.
How do I actually prove this?
This is what I observe:
at $w = 0$ all samples will have value 1 and at $w = \pi$ samples will have positive and negative values in succession- highest rate of oscillation
Please [see this, page number 16], but they have not proved it.
Here is the corresponding page from the book (Digital Signal Processing: Principles, Algorithms and Applications (3rd Edition) ):
As can be seen they have just verified, and not proved. I want to prove this.