I don't think these are discrete functions. The value of n can be any real number -- right? Step functions have always been defined on [-∞,∞].Well, what do you get if you subtract the second one from the first one?
Don't forget that you are working with a discrete function that is not defined, for instance, between N and (N+1), but rather AT N and AT (N+1)
In which part of the definition are you referring to?Even if the functions are discrete the result is still not what they say it should be because they use the ≤ operator in the definition.
I don't see a problem here. Whether it is continuous or discrete, you haveIn the definition of the second function it was a ≥, and not a ≤ operator.
u(n - N - 1) = 1, for n ≥ N + 1; and = 0 , for n < N + 1
Agreed. Which is why I say that their results are consistent with it being a discrete function and not a continuous function.The subtraction of the two functions will not go to zero until you reach n = N + 1
The subtraction of the two functions will be 1, when n = N
As I look at it, if the functions are discrete then they have stated things correctly (at least for N>0).So now it appears that if the functions are discrete then they get the intended result. I don't like problems that leave out crucial information like that and are subject to misinterpretation. Maybe the TS/OP left out some information when he restated the problem. Certainly the use of the term "step function" without additional qualification was misleading.
I think we agree, too. To some degree we did get snookered (though not by the TS), though I was careful not to show the algebraic approach to the solution.I think we agree that the stated result is correct for discrete functions, and wrong for continuous functions. Did we get snookered into hashing this out for his benefit, with minimal effort on his part? I think maybe we did -- oh well.
It matters here because you get a different answer if you use continuous compared to discrete.Hi,
I dont think 'n' has to be discrete, but who cares. As long as they say what it is, we dont have to worry
by Don Wilcher
by Duane Benson
by Jake Hertz
by Jake Hertz