[PD] derivative function

[Federico]

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Piotr Majdak wrote:

> Federico wrote:
>> don't know if derivative is the right term..
>> i mean:
>> f(x)=x      => f'(x)=1
>> f(x)=ln(x)  => f'(x)=1/x
>> f(x)=sin(x) => f'(x)=cos(x)
> 
> 
> I don't know such as object, but maybe this will help you a little bit:
> Because you're dealing with finite discrete signals, the derivative of a
> signal becomes a difference between two consecutive samples. You can
> easily implement it using [z~] (from zexy, I think) and then subtract
> the delayed and original sequence:
> 
> y[n]= x[n]-x[n-1]

hmm... I tried this with [z~] and [fexpr~], achieving the same result....

I wonder if there are errors in this way of computing derivative...

I am looking at my math notebook, where I read that derivatives are the
"limit for the incremental ratio of a function", where h is the
increment, and f(x) is the function, and I have this formula:


y' = lim {h >> 0}  ( f(x+h) - f(x) ) / h

translating this into a fexpr~ I do:

[osc~]                    [float (h)]
|                         |
[fexpr~ ($x1-$x1[-$f2])/$f2]

recalling the rules above, for f(x)=sin(x),
I should have f'(x)=cos(x), however its amplitude lower as frequency
lowers... and phase offset of [osc~]' is 180° not 90°....
what's the problem? h isn't enough close to zero?

is there an "ideal" derivator? or I am say something totally wrong?

- --
Federico
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