- #1
JFo
- 92
- 0
This is a simple problem which I'm having trouble finding an answer.
What would [tex] \sum_{n = 0}^{-1} 1[/tex] be?
Would this be undefined? 0? 2? or ?
The reason this came up in the first place is that I was trying to prove that the convolution sum is commutative, that is h*x = x*h.
I started with h*x
[tex] \sum_{n = - \infty}^{infty} h(n-m)x(m) [/tex]
making the substitution [itex]k = n-m [/itex], i get
[tex] \sum_{k = \infty}^{- \infty} x(k-m)h(k) [/tex]
The problem I have is witht the upper/lower limits of the sum. Does this mean the sum "decrements" through values of k?
What would [tex] \sum_{n = 0}^{-1} 1[/tex] be?
Would this be undefined? 0? 2? or ?
The reason this came up in the first place is that I was trying to prove that the convolution sum is commutative, that is h*x = x*h.
I started with h*x
[tex] \sum_{n = - \infty}^{infty} h(n-m)x(m) [/tex]
making the substitution [itex]k = n-m [/itex], i get
[tex] \sum_{k = \infty}^{- \infty} x(k-m)h(k) [/tex]
The problem I have is witht the upper/lower limits of the sum. Does this mean the sum "decrements" through values of k?