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Topic: Difference in cumsum/filter
Replies: 1   Last Post: Feb 23, 2013 12:38 AM

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Peter Mairhofer

Posts: 29
Registered: 8/18/10
Re: Difference in cumsum/filter
Posted: Feb 23, 2013 12:38 AM
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On 2013-02-22 20:42, Peter Mairhofer wrote:
> Hi,

Sorry, found the problem for myself.

> I want to create an ideal, analog integrator for function x(t). Given
> that x(t) is BL to 500Hz, the integration of a signal x=randn(1000,1)
> can be replaced by a cumulative sum:
>
> y1 = cumsum(x)


This assumes that x(t) is /not/ a piecewise constant function but rather
a sinc interpolation (x(t) is BL to 500).

Therefore it is not an exact result but rather an approximation with the
finite Riemann sum

> On the other hand, I can transfer the ideal integrator 1/s to z-domain
> and filter the signal with that:
>
> [numd, dend] = bilinear([1], [1 0], 1000);
> y2 = filter(numd, dend, x) * 1000;


And this does the "real" integration based on the same assumptions on x(t).


Peter




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