How to scale discrete differential equations

[pontotochs]

Hi,
It is easy to do the derivative of sampled data by doing something like
[X - X(n-1)]/Δt, however, what do you do to make sure the answer is scaled correctly?
For example if you take a 10 Hz sine wave (+/- 1) and sample it at 25 Hz, then do the derivative- as above, you will get a cosine, but the amplitude will be off, increase the sample rate and you will get a different answer.

Thanks

 

[LouisSheffield]

Your equation is in the formation of a difference equation, as opposed to a differential.
If you are STUCK with finite sampled data, I can give you a formulation for the derivative of a bandlimited signal, but if not, we need to dig more deeply into the problem.
(by the way - the phenominon you spotted is quite real)

 

[pontotochs]

I am stuck with sampled, band-limited data, therefore I would be interested in your formulation for the derivative.

Thanks for your help