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From: rammya.tv on 15 Mar 2010 08:04
hi everybody..

i have some queries regarding the coefficient calculation of filter in
SIGMA STUDIO software..

in the software they had provided equation to calculate the coefficient
but there is some mistakes please help me to get correct equations

ie:in 2nd order band pass filter design in the calculation of alpha
they didn't provide the closing braces of SINH part
equation is like this

alpha = sin(w0) * sinh( ln(2)/2 * bandwidth * w0/sin(w0)

also the bandwidth provide is bandwidth octaves or bandwidth in hertz
ie bandwidth=f0/Q

where f0-> center frequency
Q= (sq rt(2^N))/((2^N) -1)

N-> bandwidth octaves

with regards
rammya
From: Rune Allnor on 15 Mar 2010 08:42
On 15 Mar, 13:04, "rammya.tv" <rammya_tv(a)n_o_s_p_a_m.ymail.com> wrote:
> hi everybody..
>
> i have some queries regarding the coefficient calculation of filter in
> SIGMA STUDIO software..
>
> in the software they had provided equation to calculate the coefficient
> but there is some mistakes please help me to get correct equations
>
> ie:in 2nd order band pass filter design in the calculation of alpha
> they didn't provide the closing braces of SINH part
> equation is like this
>
> alpha = sin(w0) * sinh( ln(2)/2 * bandwidth * w0/sin(w0)

I can't say I recognize the equation off the top of my head.
What kind of filter is this? Where in the algorithm does this
equation occur?

Rune
From: Vladimir Vassilevsky on 15 Mar 2010 10:19


rammya.tv wrote:

> hi everybody..
>
> i have some queries regarding the coefficient calculation of filter in
> SIGMA STUDIO software..
>
> in the software they had provided equation to calculate the coefficient
> but there is some mistakes please help me to get correct equations

That's always that way with canned solutions. Help yourself: take analog
prototypes and do the BLT.

> ie:in 2nd order band pass filter design in the calculation of alpha
> they didn't provide the closing braces of SINH part
> equation is like this
>
> alpha = sin(w0) * sinh( ln(2)/2 * bandwidth * w0/sin(w0)

That's RBJ cookbook heritage. He likes trigonometry with sin/cos/sinh
instead of simply expressing a filter as a function of tg(w).

> also the bandwidth provide is bandwidth octaves or bandwidth in hertz
> ie bandwidth=f0/Q

No slightest clue, huh?

VLV


From: dvsarwate on 15 Mar 2010 11:10
On Mar 15, 7:04 am, "rammya.tv" <rammya_tv(a)n_o_s_p_a_m.ymail.com>
wrote:

> .......
> in 2nd order band pass filter design in the calculation of alpha
> they didn't provide the closing braces of SINH part
> equation is like this
>
> alpha = sin(w0) * sinh( ln(2)/2 * bandwidth * w0/sin(w0)
>

What value of alpha does the design software give when you
plug in *specific numbers*, (e.g. 10^6) for w0 and bandwidth
(or f0 and N)?

There are 5 places where the closing parenthesis for SINH
could go (and 4 of them lead to a cancellation of the leading
sin(w0) term with the trailing sin(w0) term). Put the parenthesis
in each of the five possible places to create 5 new formulas with
with equal numbers of ( and ) properly paired up, **Calculate**
what alpha is according to the 5 different formulas that you have
just created. Does exactly one of these calculations give the
same value for alpha as the software? Good! You have found
the location of the missing parenthesis. If none of the answers
match up, or more than one matches up, contact the software
maker because the software is likely to have a bug.

--Dilip Sarwate
From: robert bristow-johnson on 15 Mar 2010 15:16
On Mar 15, 10:19 am, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote:
> rammya.tv wrote:
> > hi everybody..
>
> > i have some queries regarding the coefficient calculation of filter in
> > SIGMA STUDIO software..
>
> > in the software they had provided equation to calculate the coefficient
> > but there is some mistakes please help me to get correct equations
>
> That's always that way with canned solutions. Help yourself: take analog
> prototypes and do the BLT.
>
> > ie:in 2nd order band pass filter design in the calculation of alpha
> > they didn't provide the closing braces of SINH part
> > equation is like this
>
> > alpha = sin(w0) * sinh( ln(2)/2 * bandwidth * w0/sin(w0)

attach a closing parenth at the end.

> That's RBJ cookbook heritage. He likes trigonometry with sin/cos/sinh
> instead of simply expressing a filter as a function of tg(w).

that's all the cookbook is: "take analog prototypes and do the BLT".

what's "tg"? Vlad, dunno how you deal with the prewarping of the
resonant frequency necessary when using the BLT, but it's going to be
tan(w0/2) or some trig identity to that. can't avoid it. the sinh()
and the ln(2) comes from the way "bandwidth" is defined.

> > also the bandwidth provide is bandwidth octaves or bandwidth in hertz
> > ie bandwidth=f0/Q

rammya should think a little about "dimensional analysis". the
argument to the sinh() function (thus "bandwidth" factor) needs to be
a dimensionless number. in the cookbook, w0 is dimensionless, but f0
is not.

i was told that the ADI sigma lit makes use of the cookbook, but i
have never seen it. maybe they left something out. i have tried to
make the cookbook pretty much self-contained.

r b-j
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