Al Clark wrote:
> I have an old addition of Antoniou. It
> also has some of the IIR details you mention although maybe not the same
> as the later addition.

I haven't seen the older versions, but the new one is the only DSP book

I have seen (I have browsed DSP books regularly since around 1990)
where the IIR design techniques are treated systematically. I don't
know
if those techniques are so "common" that everybody who was trained
before 1990 take them for granted, but I searched for a long time
to find all those details. The best I could come up with was the
Van Valkenburg book from 1982 on analog filter design.

It is so much easier to do these kinds of things when all the
necessary material can be found in one place.

Rune

Hi,

Thanks for the tips about the books. It looks like what I need as I'm
wanting to delve deeper into filter design and as I think you picked up
I'm currently not doing this as a job, and perhaps never will, but I 'do'
enjoy coding filters and do it really as a hobby just now. I really use it
to design real-time audio effects and like to use Matlab to design the
algorithms and plot the responses etc...

I'm aware I can use packages to design the coefficients directly, such as
Matlab. However, i need to have a filter which I can tweak the parameters
\ specifications in real-time. So for this reason alone I need to 'design
the whole filter from scratch'. Its definetly a good thing to learn about
books such as the one you mentioned! I have a text which i view as being
good by Sophociles Orfanidis but it doesnt concnetrate on just filter
design... so maybe I need a book which concentrates on just filter design
like the one mentioned. Hopefully my library will have a copy, luckily
they tend to be pretty good with there DSP books.

Its funny you mention designing your own filter design package. I recently
also made a Filter Design Web Service Application using C#. Probably not
all that useful but it was fun to make. Currently it supports 1st Order
IIR High and Low Pass, and 2nd Order IIR Peaking and Notch filters. Quite
rudimentary but its a start. Most of these filters I ported over from
Matlab, then to C++ where I use them for audio effects. I like the object
oriented approach where I can have a dedicated 'filter class'. Makes using
the filter a lot easier. However, I need to concentrate more now on the
actual filter design still so I can make the end filters better. Time to
get that book now!

Best Regards,
David

"Rune Allnor" <allnor@tele.ntnu.no> wrote in
news:1143795767.709380.327030@t31g2000cwb.googlegroups.com: 

> 
> Al Clark wrote:
>> "Rune Allnor" <allnor@tele.ntnu.no> wrote in
>> news:1143618776.758556.80540@z34g2000cwc.googlegroups.com:
>>
>> >
>> > davidross wrote:
>> > ...
>> >> I found even designing a second order butterworth filter from
>> >> scratch quite tricky, but maybe I'm looking at the wrong
>> >> references. Probably I shoudl start digging amongst the journals
>> >> now. 
>>
>> I'm the last guy to say that you shouldn't read books or journals. I
>> have 40-50 DSP books.
> 
> Don't misunderstand me wrong...
> 
> My response was based on my impression that the OP has a casual
> interest in DSP. Reading books and journals is necessary if you take
> classes or need in for your job, it may be a bit overwhelming if you
> start
> too early. As for IIR filter design, the Antoniou book seems to be the
> only reasonably recent book that actually deals with this in a
> systematical way.
> 
>> However....
>>
>> Most DSP guys use computer programs to generate coefficents and
>> analyze filter responses. It's been a very long time since I
>> calculated a filter by hand.
> 
> Sure. A few months a go I implemented my own rudimentary filter design
> program. While it is by no means as elaborate as some of the
> professional
> tools, it lets me do stuff I can't do with Matlab's Signal Processing
> Toolbox.
> As wellas let me explore some techniques of computer programming
> I hadn't really tested before.
> 
> I used the IIR filter design as a case study. While the main benefit
> was
> that I learned how to "really" do object oriented programming in C++,
> I also discovered a few bells and whistles to fine-tune the filter
> responses. 
> Assuming "perfect" maths, but still.
> 
> Rune
> 
> 

There is really nothing better than a real project to learn something 
new. 

I got the same impression that OP has a casual interest. I think he 
really wants/needs a basic book. I have an old addition of Antoniou. It 
also has some of the IIR details you mention although maybe not the same 
as the later addition. I think what OP really wants/needs is a recipe.

1. Buy this or that filter program.
2. Implement the filter structure appropriate for his situation and 
target.
3. Move on to the next thing.


-- 
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com

Al Clark wrote:
> "Rune Allnor" <allnor@tele.ntnu.no> wrote in
> news:1143618776.758556.80540@z34g2000cwc.googlegroups.com:
>
> >
> > davidross wrote:
> > ...
> >> I found even designing a second order butterworth filter from scratch
> >> quite tricky, but maybe I'm looking at the wrong references. Probably
> >> I shoudl start digging amongst the journals now.
>
> I'm the last guy to say that you shouldn't read books or journals. I have
> 40-50 DSP books.

Don't misunderstand me wrong...

My response was based on my impression that the OP has a casual
interest in DSP. Reading books and journals is necessary if you take
classes or need in for your job, it may be a bit overwhelming if you
start
too early. As for IIR filter design, the Antoniou book seems to be the
only reasonably recent book that actually deals with this in a
systematical way.

> However....
>
> Most DSP guys use computer programs to generate coefficents and analyze
> filter responses. It's been a very long time since I calculated a filter
> by hand.

Sure. A few months a go I implemented my own rudimentary filter design
program. While it is by no means as elaborate as some of the
professional
tools, it lets me do stuff I can't do with Matlab's Signal Processing
Toolbox.
As wellas let me explore some techniques of computer programming
I hadn't really tested before.

I used the IIR filter design as a case study. While the main benefit
was
that I learned how to "really" do object oriented programming in C++,
I also discovered a few bells and whistles to fine-tune the filter
responses. 
Assuming "perfect" maths, but still.

Rune

"Rune Allnor" <allnor@tele.ntnu.no> wrote in
news:1143618776.758556.80540@z34g2000cwc.googlegroups.com: 

> 
> davidross wrote:
> ...
>> I found even designing a second order butterworth filter from scratch
>> quite tricky, but maybe I'm looking at the wrong references. Probably
>> I shoudl start digging amongst the journals now.

I'm the last guy to say that you shouldn't read books or journals. I have 
40-50 DSP books.

However....

Most DSP guys use computer programs to generate coefficents and analyze 
filter responses. It's been a very long time since I calculated a filter 
by hand.

One of the features that many filter programs can do is set the precision 
of the coefficents and whether they are in floating or fixed point. This 
can be very useful when you are trying to look at performance of real 
filters with finite precision. Poles that might be close to the unit 
circle with perfect math, might even be outside the unit with finite 
precision math. 

I'm sure everyone has their favorite filter program. I like QEDesign 1000 
(www.mds.com). I have used versions of QED since its original fortran 
implementation. One of the hidden benefits of QED design is that the 
programmer is an excellent DSP guy (Jerry Purcell). Jerry understands a 
lot of the subtleties to good filter design. I think they have a free 
demo program. 


Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com





> 
> No, don't.
> 
> Filter design by analog prototypes is a "classical" design technique
> by now.
> The heyday was during the 60s, when lots of people knew how to design
> analog IIR filters, but before discrete-time techniques had been
> developed
> (it seems Ken Steiglitz was the central person around 1970). The
> relevant
> journal literature dates from the mid-late 60s, and is all but
> incomprehensable
> for the casual reader.
> 
> Nowadays these techniques are so "well known" that only rudimentary
> accounts are included in textbooks on DSP. A few months ago, a book
> appeared
> 
> http://www.amazon.com/gp/product/0071454241/qid=1143618441/sr=1-1/ref=s
> r_1_1/103-2220054-5955052?s=books&v=glance&n=283155 
> 
> that apparently is an extension of a "classical" filter design. This
> book is
> the only book I know of, that reviews IIR filter design in a decent
> way.
> If you are interested in these kinds of things, get a copy. This type
> of
> material is not likely to be available in one book until this book is
> in its
> next edition, or in a Dover reprint.
> 
>> My original thinking about my post was - if i have a nice easy 1st
>> order filter design algorithm - use it, square it, and then cascade
>> it if need be, instead of delving into advanced elliptic design.
>> Maybe its time too though.
> 
> I suppose you can do things that way. The price to pay is that it
> takes 
> 
> a lot of fiddling around to get to a desired response, and the filter
> order
> becomes unnecessary high.
> 
> It is very cumbersome to derive the design formulas for eliptic
> filters,
> but those filters are close to optimum what filter order is concerned.
> The elliptic filter gets the job done with a minimum of FLOPs.
> 
> So it's a trade-off between who is to get the hard job: You, deriving
> the 
> filter, or the computer crunching the numbers.
> 
> Rune
> 



-- 

davidross wrote:

>>> To go to 2nd Order multiply the numerator and denominator  - 
>>> 
>>> %             1 + z^-1      (1 + z^-1)(1 + z^-1)
>>> %   H(z) = b ---------- = b --------------------
>>> %             1 - az^-1     (1 - az^-1)(1 - az^-1)
>>
>>> With this method, once I compute my coefficients I have to
>>> scale them for the frequency response to be correct i.e. 0dB
>>> at frequency 0. 
>>
>>In case you chose b so that the first-order filter has unit DC
>>gain, you need to square the whole thing instead of just the
>>ratio of monic polynomials to keep that feature.

> Sounds like a good idea. I will include b this time and see what
> happens. Maybe if I include b I wont have to scale? Is that what
> you mean? 

Exactly.


Martin

-- 
Quidquid latine scriptum sit, altum viditur.

davidross wrote:
...
> I found even designing a second order butterworth filter from scratch
> quite tricky, but maybe I'm looking at the wrong references. Probably I
> shoudl start digging amongst the journals now.

No, don't.

Filter design by analog prototypes is a "classical" design technique by
now.
The heyday was during the 60s, when lots of people knew how to design
analog IIR filters, but before discrete-time techniques had been
developed
(it seems Ken Steiglitz was the central person around 1970). The
relevant
journal literature dates from the mid-late 60s, and is all but
incomprehensable
for the casual reader.

Nowadays these techniques are so "well known" that only rudimentary
accounts are included in textbooks on DSP. A few months ago, a book
appeared

http://www.amazon.com/gp/product/0071454241/qid=1143618441/sr=1-1/ref=sr_1_1/103-2220054-5955052?s=books&v=glance&n=283155

that apparently is an extension of a "classical" filter design. This
book is
the only book I know of, that reviews IIR filter design in a decent
way.
If you are interested in these kinds of things, get a copy. This type
of
material is not likely to be available in one book until this book is
in its
next edition, or in a Dover reprint.

> My original thinking about my post was - if i have a nice easy 1st order
> filter design algorithm - use it, square it, and then cascade it if need
> be, instead of delving into advanced elliptic design. Maybe its time too
> though.

I suppose you can do things that way. The price to pay is that it takes

a lot of fiddling around to get to a desired response, and the filter
order
becomes unnecessary high.

It is very cumbersome to derive the design formulas for eliptic
filters,
but those filters are close to optimum what filter order is concerned.
The elliptic filter gets the job done with a minimum of FLOPs.

So it's a trade-off between who is to get the hard job: You, deriving
the 
filter, or the computer crunching the numbers.

Rune

"davidross" <david_ross@hotmail.co.uk> wrote in
news:1e2dnWT0m_Pu57TZRVn-pg@giganews.com: 

>>[snip]
>>
>>> So is this design method valid, or is it more of a 'hack' to get a
>>> 2nd Order IIR from a 1st Order IIR transfer function?
>>
>>I don't understand the context of the question.
> 
> 
> Hi Rune,
> 
> The question was probably 'out of context'. By squaring a 1st Order
> transfer function we can arrive at a 2nd order Transfer function,
> which goes from being 1st Order to 2nd Order due to the extra delay
> being added. However, the design method used to create the initial
> coefficients were arrived at via a 1st Order design. So I guess all
> this really does is (like a poster mentioned) 'square the magnitude
> response'. Maybe this would give the same magnitude response as
> cascading two 1st order sections?

Yes.

This will give a you relatively lousy filter however.

Generally, you decide the overall order of the filter based on your 
requirements. You then determine the transfer function. The coefficients 
will probably be different for each section. The filter program will  break 
the poles and zeros out so you can determine the coefficients for each 
individual section. 

This is no different than designing a filter in the s plane. Two cascaded 
real poles are probably not as useful as a second order something else 
(butterworth, bessel, etc).

If you are comparing IIR filters to typical analog filters you will find 
many similarities, however digital filters do not map exactly to an analog 
filter. 



-- 
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com



> 
> 
>>One usually have some sort of reason for choosing a particular order
>>for
>>the filter. I am not aware of any application where one starts out
>>with 
>>
>>a 1st order filter and then designs a 2nd order filter from that[*]
>>
>>The way one usually designs a filter, is that one starts out with a
>>filter specification. The spec for a low-pass filter usually consists
>>of such parameters as
>>
>>- Egde frequency of pass band, f_p
>>- Edge frequency of stop band, f_s
>>- Maximum ripple in pass band, d_p
>>- Minimum attenuation of stop band, d_s
>>
>>Then the designer chooses what type of filter to implement, e.g.
>>Butterworth,
>>Chebuchev, Elliptic, or something else. Once the type of filter has
>>been
>>chosen, one can use the corresponding design formulas to determine
>>the minimum order of the filter. Typically, the filter order is given
>>in terms of the ratio
>>
>>  N ~ (d_s-d_p)/(f_s-f_p)
>>
>>which is a fancy way to say that the filter order increases with
>>increasing
>>roll-off of the transfer function.
>>
>>Once the order of the filter is known, one can use the appropriate
>>formulas to compute the 1st and 2nd order sections needed.
>>
>>Rune
>>
>>* This is what happens in some frequency tranforms, but there one
>>  uses the LP prototype to design a BP or BS filter that necessarily
>>  have twice the number of poles.
>>
>>
> 
> Nice overview of filter design there! I've made butterworth. From
> scratch and in real-time there quite tricky I found. Havent dared to
> look at Elliptic yet. I've heard there quite 'challenging' to design
> from scratch and the maths is quite involved so there on hold just
> now. 
> 
> I found even designing a second order butterworth filter from scratch
> quite tricky, but maybe I'm looking at the wrong references. Probably
> I shoudl start digging amongst the journals now.
> 
> My original thinking about my post was - if i have a nice easy 1st
> order filter design algorithm - use it, square it, and then cascade it
> if need be, instead of delving into advanced elliptic design. Maybe
> its time too though.
> 
> Best regards,
> David
> 
> 

>davidross wrote:
>
>> I was wondering if this is a truly valid method of going from a
>> 1st Order IIR lowpass transfer fucntion to a 2nd Order IIR
>> lowpass transfer function - 
>> 
>> 
>> 1st Order Transfer Function :-
>> 
>> %             1 + z^-1
>> %   H(z) = b ----------
>> %             1 - az^-1
>> 
>> 
>> To go to 2nd Order multiply the numerator and denominator  - 
>> 
>> %             1 + z^-1      (1 + z^-1)(1 + z^-1)
>> %   H(z) = b ---------- = b --------------------
>> %             1 - az^-1     (1 - az^-1)(1 - az^-1)
>
>> With this method, once I compute my coefficients I have to scale
>> them for the frequency response to be correct i.e. 0dB at
>> frequency 0. 
>
>In case you chose b so that the first-order filter has unit DC gain, 
>you need to square the whole thing instead of just the ratio of monic 
>polynomials to keep that feature.
>
>
>Martin
>
>-- 
>Quidquid latine scriptum sit, altum viditur.
>


Hi Martin,

Sounds like a good idea. I will include b this time and see what happens.
Maybe if I include b I wont have to scale? Is that what you mean?

Best Regards,
David

>> I was wondering if this is a truly valid method of going from a 1st
Order
>> IIR lowpass transfer fucntion to a 2nd Order IIR lowpass transfer
function
>
>If you want to square the magniutde response of your filter, then: yes,
>this is a truly valid method to do so.
>...

Good to hear. Basically by squaring it I was intending to improve the
filter performance. A bit like cascading except done a different way.

>> But using this method of scaling seems strange, and the coefficients
look
>> like unusually high values for coefficients.
>
>Why are you worried about how your coefficients look like? If your
>original filter was scaled to have a magnitude of 1 at some frequency,
>then the squared version also has magnitude of 1 at this frequency. If
>you want the new filter to have a magnitude of 1 at some other
>frequency, then you have to normalize.


True, it shouldnt matter 'what they look like'. They just 'looked odd'
some were always 0.25 exactly and some were as big as 50.blabla. I'm used
to seeing coefficients like 0.098766865321. But I guess its nothing to
worry about.

Best Regards and thanks for the feedback,

David