> Note that if you are using a graphical method to define the
> desired response, that's like the starting specification
> that those classical mathematical derivations used. They
> had to work it out in terms that could be implemented by
> analog components, hence polynomials with poles and zeros,
> etc.
>
Speaking of graphical method, here is a demo that allows
one to move poles and zeros using the mouse
(also add/remove) and see the effect right away
http://demonstrations.wolfram.com/TransferFunctionAnalysisByManipulationOfPolesAndZeros/
"
This Demonstration shows how the locations of poles and
zeros of the system transfer function affect the system
properties.
Drag a pole or a zero of a discrete system transfer function
to a different location and observe the effect on the system.
H(z)=Y(z)/X(z) represents the transfer function of a
discrete time system, where Y(z) is the z-transform of the output
signal and Z(z) is the z-transform of the input signal. Writing
H(z) as a ratio of two polynomials in z, the poles of H(z)
are the roots of the denominator and the zeros are the roots of
the numerator.
The continuous time transfer function approximation
is generated using all supported H(z) to H(s) mapping methods
in Mathematica 8. The mapping of the z plane to the s plane is
also generated. A total of 12 different plots can be
generated as you move the poles and zeros to different locations."
Need the free Mathematica player to run it.
> You don't need to do any of that (other than for your
> understanding), since you can use digital methods to go
> directly to the FIR weights, without ever seeing a
> polynomial with 1024 terms. (!)
>
> Best regards,
>
>
> Bob Masta
>
> DAQARTA v9.20
> Data AcQuisition And Real-Time Analysis
> www.daqarta.com
> Scope, Spectrum, Spectrogram, Sound Level Meter
> Frequency Counter, Pitch Track, Pitch-to-MIDI
> FREE 8-channel Signal Generator, DaqMusiq generator
> Science with your sound card!
>
--Nasser
Reply by Allan Herriman●July 4, 20162016-07-04
On Sun, 03 Jul 2016 10:50:52 -0500, Tim Wescott wrote:
> On Fri, 01 Jul 2016 12:36:05 +0000, Bob Masta wrote:
>
>> On Thu, 30 Jun 2016 09:18:42 -0700 (PDT), Matti Viljamaa
>> <viljamaadsp@gmail.com> wrote:
>>
>>>On Thursday, June 30, 2016 at 4:28:14 PM UTC+3, Bob Masta wrote:
>>>> On Wed, 29 Jun 2016 02:58:52 -0700 (PDT), Matti Viljamaa
>>>> <viljamaadsp@gmail.com> wrote:
>>>>
>>>> >I've been reading sources that merely give the transfer functions of
>>>> >the filters that are presented, but give no information regarding
>>>> >how have these transfer functions been found.
>>>> >
>>>> >So are there any sources that would explain how the transfer
>>>> >functions of some common filters have been found/derived?
>>>>
>>>> Perhaps you are asking for the rationale behind each design?
>>>> Youl'll find that in most any text on filters, but the basic idea is
>>>> that Butterworth is designed for the flattest passband with no
>>>> ripple.
>>>> Chebychev is designed for the sharpest cutoff given a specified
>>>> amount of ripple. Bessel is designed for the best transient response
>>>> (flattest phase response, least waveform alteration).
>>>
>>>Yes, this is what I'm after. I'm not so keen on using transfer
>>>functions without understanding why are they formulated that way (i.e.
>>>understanding the derivation of that transfer function).
>>
>> Note that if you are using a graphical method to define the desired
>> response, that's like the starting specification that those classical
>> mathematical derivations used. They had to work it out in terms that
>> could be implemented by analog components, hence polynomials with poles
>> and zeros, etc.
>>
>> You don't need to do any of that (other than for your understanding),
>> since you can use digital methods to go directly to the FIR weights,
>> without ever seeing a polynomial with 1024 terms. (!)
>
> It wouldn't have been so much that they were bound to IIR filters as
> that they couldn't do the sort of brute-force computational optimization
> that we do now. So they invented a few filter types that covered their
> most common cases and that could be scaled with minimal math. And even
> then, tables of component values for LC filters were fairly commonly
> used.
On Fri, 01 Jul 2016 12:36:05 +0000, Bob Masta wrote:
> On Thu, 30 Jun 2016 09:18:42 -0700 (PDT), Matti Viljamaa
> <viljamaadsp@gmail.com> wrote:
>
>>On Thursday, June 30, 2016 at 4:28:14 PM UTC+3, Bob Masta wrote:
>>> On Wed, 29 Jun 2016 02:58:52 -0700 (PDT), Matti Viljamaa
>>> <viljamaadsp@gmail.com> wrote:
>>>
>>> >I've been reading sources that merely give the transfer functions of
>>> >the filters that are presented, but give no information regarding how
>>> >have these transfer functions been found.
>>> >
>>> >So are there any sources that would explain how the transfer
>>> >functions of some common filters have been found/derived?
>>>
>>> Perhaps you are asking for the rationale behind each design?
>>> Youl'll find that in most any text on filters, but the basic idea is
>>> that Butterworth is designed for the flattest passband with no ripple.
>>> Chebychev is designed for the sharpest cutoff given a specified
>>> amount of ripple. Bessel is designed for the best transient response
>>> (flattest phase response, least waveform alteration).
>>
>>Yes, this is what I'm after. I'm not so keen on using transfer functions
>>without understanding why are they formulated that way (i.e.
>>understanding the derivation of that transfer function).
>
> Note that if you are using a graphical method to define the desired
> response, that's like the starting specification that those classical
> mathematical derivations used. They had to work it out in terms that
> could be implemented by analog components, hence polynomials with poles
> and zeros, etc.
>
> You don't need to do any of that (other than for your understanding),
> since you can use digital methods to go directly to the FIR weights,
> without ever seeing a polynomial with 1024 terms. (!)
It wouldn't have been so much that they were bound to IIR filters as that
they couldn't do the sort of brute-force computational optimization that
we do now. So they invented a few filter types that covered their most
common cases and that could be scaled with minimal math. And even then,
tables of component values for LC filters were fairly commonly used.
There's still use for IIR filters in DSP, and some of those applications
can still use the old classics, so it's not entirely useless information
to know today.
--
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work! See my website if you're interested
http://www.wescottdesign.com
Reply by ●July 1, 20162016-07-01
On Friday, July 1, 2016 at 5:36:10 AM UTC-7, Bob Masta wrote:
> On Thu, 30 Jun 2016 09:18:42 -0700 (PDT), Matti Viljamaa
(snip)
> >Yes, this is what I'm after. I'm not so keen on using transfer functions
> > without understanding why are they formulated that way
> > (i.e. understanding the derivation of that transfer function).
> Note that if you are using a graphical method to define the
> desired response, that's like the starting specification
> that those classical mathematical derivations used. They
> had to work it out in terms that could be implemented by
> analog components, hence polynomials with poles and zeros,
> etc.
OK, but you might not want exactly the drawn shape, but a smoothed
version, instead.
I do still remember my first try with polynomial fitting (higher than degree 1),
where I fit N points to an N degree polynomial.
In case it takes more than a few seconds to figure out, that is at least
one degree too much.
If you hand draw the function, it is likely to have some wiggles due
to hand jitter that you really don't want, and so a little smoothing is
likely good.
There are many ways to do smoothing, most of which should be on topic
for comp.dsp.
Reply by Bob Masta●July 1, 20162016-07-01
On Thu, 30 Jun 2016 09:18:42 -0700 (PDT), Matti Viljamaa
<viljamaadsp@gmail.com> wrote:
>On Thursday, June 30, 2016 at 4:28:14 PM UTC+3, Bob Masta wrote:
>> On Wed, 29 Jun 2016 02:58:52 -0700 (PDT), Matti Viljamaa
>> <viljamaadsp@gmail.com> wrote:
>>
>> >I've been reading sources that merely give the transfer functions of the filters that are presented, but give no information regarding how have these transfer functions been found.
>> >
>> >So are there any sources that would explain how the transfer functions of some common filters have been found/derived?
>>
>> Perhaps you are asking for the rationale behind each design?
>> Youl'll find that in most any text on filters, but the basic
>> idea is that Butterworth is designed for the flattest
>> passband with no ripple. Chebychev is designed for the
>> sharpest cutoff given a specified amount of ripple. Bessel
>> is designed for the best transient response (flattest phase
>> response, least waveform alteration).
>
>Yes, this is what I'm after. I'm not so keen on using transfer functions without understanding why are they formulated that way (i.e. understanding the derivation of that transfer function).
Note that if you are using a graphical method to define the
desired response, that's like the starting specification
that those classical mathematical derivations used. They
had to work it out in terms that could be implemented by
analog components, hence polynomials with poles and zeros,
etc.
You don't need to do any of that (other than for your
understanding), since you can use digital methods to go
directly to the FIR weights, without ever seeing a
polynomial with 1024 terms. (!)
Best regards,
Bob Masta
DAQARTA v9.20
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
Frequency Counter, Pitch Track, Pitch-to-MIDI
FREE 8-channel Signal Generator, DaqMusiq generator
Science with your sound card!
Reply by ●June 30, 20162016-06-30
On Thursday, June 30, 2016 at 9:18:45 AM UTC-7, Matti Viljamaa wrote:
(snip)
> Yes, this is what I'm after. I'm not so keen on using transfer functions without
> understanding why are they formulated that way (i.e. understanding the
> derivation of that transfer function).
On Thursday, June 30, 2016 at 4:28:14 PM UTC+3, Bob Masta wrote:
> On Wed, 29 Jun 2016 02:58:52 -0700 (PDT), Matti Viljamaa
> <viljamaadsp@gmail.com> wrote:
>
> >I've been reading sources that merely give the transfer functions of the filters that are presented, but give no information regarding how have these transfer functions been found.
> >
> >So are there any sources that would explain how the transfer functions of some common filters have been found/derived?
>
> Perhaps you are asking for the rationale behind each design?
> Youl'll find that in most any text on filters, but the basic
> idea is that Butterworth is designed for the flattest
> passband with no ripple. Chebychev is designed for the
> sharpest cutoff given a specified amount of ripple. Bessel
> is designed for the best transient response (flattest phase
> response, least waveform alteration).
Yes, this is what I'm after. I'm not so keen on using transfer functions without understanding why are they formulated that way (i.e. understanding the derivation of that transfer function).
Reply by ●June 30, 20162016-06-30
On Thursday, June 30, 2016 at 6:28:14 AM UTC-7, Bob Masta wrote:
> On Wed, 29 Jun 2016 02:58:52 -0700 (PDT), Matti Viljamaa
> <viljam...@gmail.com> wrote:
> >I've been reading sources that merely give the transfer functions of the filters
> > that are presented, but give no information regarding how have these transfer
> > functions been found.
(snip)
> Perhaps you are asking for the rationale behind each design?
> Youl'll find that in most any text on filters, but the basic
> idea is that Butterworth is designed for the flattest
> passband with no ripple. Chebychev is designed for the
> sharpest cutoff given a specified amount of ripple. Bessel
> is designed for the best transient response (flattest phase
> response, least waveform alteration).
> There are many others, but the idea is the same: given
> some goal, what transfer function best meets it? If I
> recall correctly, the above 3 types are all based on
> polynomials that were found by "pure" mathematicians long
> before they were latched onto by engineers.
Seems the Butterworth was a physicist and engineer, but yes,
Bessel and Chebychev were more mathematicians.
Butterworth designed his filter around 1930, soon after vacuum tube
amplifiers allowed for cascading to build higher-order filters.
https://en.wikipedia.org/wiki/Butterworth_filter
explains some of what went into the design.
-- glen
Reply by Bob Masta●June 30, 20162016-06-30
On Wed, 29 Jun 2016 02:58:52 -0700 (PDT), Matti Viljamaa
<viljamaadsp@gmail.com> wrote:
>I've been reading sources that merely give the transfer functions of the filters that are presented, but give no information regarding how have these transfer functions been found.
>
>So are there any sources that would explain how the transfer functions of some common filters have been found/derived?
Perhaps you are asking for the rationale behind each design?
Youl'll find that in most any text on filters, but the basic
idea is that Butterworth is designed for the flattest
passband with no ripple. Chebychev is designed for the
sharpest cutoff given a specified amount of ripple. Bessel
is designed for the best transient response (flattest phase
response, least waveform alteration).
There are many others, but the idea is the same: given
some goal, what transfer function best meets it? If I
recall correctly, the above 3 types are all based on
polynomials that were found by "pure" mathematicians long
before they were latched onto by engineers.
Best regards,
Bob Masta
DAQARTA v9.20
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
Frequency Counter, Pitch Track, Pitch-to-MIDI
FREE 8-channel Signal Generator, DaqMusiq generator
Science with your sound card!
Reply by robert bristow-johnson●June 30, 20162016-06-30
On Thursday, June 30, 2016 at 3:00:09 AM UTC-4, Matti Viljamaa wrote:
> On Thursday, June 30, 2016 at 2:09:39 AM UTC+3, herrman...@gmail.com wrote:
> > On Wednesday, June 29, 2016 at 2:58:57 AM UTC-7, Matti Viljamaa wrote:
> > > I've been reading sources that merely give the transfer functions of the filters
> > > that are presented, but give no information regarding how have these transfer
> > > functions been found.
> >
> > As far as I know, it is the other way around. You desire a transfer function, and then
> > design a filter to have that function.
>
> So you mean that finding a transfer function is "guessing" the numerator and the denominator and then doing plots until the shape is something desired?
yeah, Glen. i think you mean "desired frequency response" instead of "transfer function".
r b-j