View Single Post
  #2   Report Post  
Posted to sci.electronics.design,alt.binaries.schematics.electronic,sci.electronics.cad,sci.electronics.basics
Phil Hobbs Phil Hobbs is offline
external usenet poster
 
Posts: 635
Default Difference Equations

On 2/5/2013 11:05 AM, Jim Thompson wrote:
It's been too long ago, I can't remember how to reduce difference
equations.

Suppose I have...

f(N+1) = 0.97*f(N)

Now I know, off the seat of my pants (I think :-), that...

f(N) = Const*(0.97^N)

But I can't remember how to rigorously get to that conclusion.

...Jim Thompson


Mathematical induction. It's true for N=0, by construction, and if it's
true for N, it's true for N+1 by the use of your recurrence relation.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510 USA
+1 845 480 2058

hobbs at electrooptical dot net
http://electrooptical.net