[NEWBIE question] How do I filter a digitized signal

Rick Lyons wrote:
> On Fri, 13 Aug 2004 16:43:51 -0500, Richard Owlett
> <rowlett@atlascomm.net> wrote:
> 
>   (snipped)
> 
-- snip --
> I don't know about Scilab, but MATLAB has a 
> "filter" command that's used to filter some 
> time-domain "x" variable (a list of input sample values) 
> using a filter that's defined by its feedforward and 
> feedback coefficients.  For nonrecursive FIR filters,
> the feedforward coefficients needed by MATLAB are the 
> FIR filter's coefficients (h), and the feedback 
> coefficients needed by MATLAB turn out to be a simple 
> single value of one.  In MATLAB language, filtering 
> an input sequence, x, with an FIR filter looks like:
> 
>   Output = filter([h0,h1,h2,h3],1,x);
> 
> Maybe Scilab is similar to the above,  I don't know.
> 
> That above MATLAB command implements my Eq. (6-1) on 
> page 213.  [Please note that there is a "typo" in Eq. 
> (6-1) that I'm desperately trying to get the 
> publisher to correct.  In Eq. (6-1) the term 
> "h(4)x(n-4)" should NOT be there.  Please cross out 
> that h(4)x(n-4) term.]
> 
> For an IIR filter, my Eq. (6-2), on page 214, gives the 
> necessary computations to implement the IIR filter in 
> Figure 6-3. In MATLAB language, filtering 
> an input sequence, x, with the Figure 6-3 IIR filter 
> looks like:
> 
> Output = filter([b(0),b(1),b(2),b(3)],[1,-a(1),-a(2),-a(3)],x);
> 
> No, the minus signs for the above a(k) feedback coefficients 
> are not a mistake.  The minus signs are necessary because 
> of the way MATLAB expects the feedback coefficients to 
> be defined.
> 
-- snip --

> [-Rick-]
> 
> Where am I?
>   In the Village.
> What do you want?
>   Information.
> Whose side are you on?
>   That would be telling ... We want Information.
> You won't get it.
>   By hook or by crook ... we will.
> Who are you?
>   The new Number Two.
> Who is Number One?
>   You are Number Six.
> I am not a number ... I am a free man!
>   (Mocking laughter)
> 

To do this in SciLab you first define a linear system (syslin), then you 
get its response with 'flts'.  Type 'apropos syslin' and 'apropos flts' 
for help; for the FIR case (here a raised-cosine):

H_fir=syslin(0.0001, 0.01*poly(1 - cos(2*%pi*(0.01:0.01:0.99)), 'z', 
'coeff'), poly([zeros(1,98) 1], 'z', 'coeff'));

For the IIR case, a 2nd-order whomped-up lowpass:

d=0.95; th=0.05; H_iir=syslin(0.0001, abs(1-d*exp(%i*th))^2*poly([0 0], 
'z'), poly(d*[exp(%i*th) exp(-%i*th)], 'z'));

Then you can plot their responses:

clf; plot2d(flts(ones(1,200), H_iir)); plot2d(flts(ones(1, 200), H_fir))

Its more formalized than Matlab so it's harder to do something little 
like this, but it should take longer to get ungainly as your application 
grows.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com