# Complex FIR coefficients

Started by March 28, 2010
```What is the physical significance of having an impulse response with
complex coefficients ie

{h0,h1,h2...hn}  where the h values are complex.

Hardy
```
```On 29 Mar, 00:14, HardySpicer <gyansor...@gmail.com> wrote:
> What is the physical significance of having an impulse response with
> complex coefficients

Does there have to be one?

Rune
```
```HardySpicer <gyansorova@gmail.com> writes:

> What is the physical significance of having an impulse response with
> complex coefficients ie
>
> {h0,h1,h2...hn}  where the h values are complex.

Hi,

You know that the the frequency response of an FIR filter is the
Discrete Fourier Transform (DFT) of its impulse response, right? What
are the properties of the DFT when the inputs are real versus complex?
--
Randy Yates                      % "Maybe one day I'll feel her cold embrace,
Digital Signal Labs              %                    and kiss her interface,
mailto://yates@ieee.org          %            til then, I'll leave her alone."
http://www.digitalsignallabs.com %        'Yours Truly, 2095', *Time*, ELO
```
```HardySpicer wrote:
> What is the physical significance of having an impulse response with
> complex coefficients ie
>
> {h0,h1,h2...hn}  where the h values are complex.

That your system, as described, is impossible to implement physically.

You've asked a question with an absurd answer, and you're not dim.  So
what are you _really_ doing?

The two biggest reasons I could think that you may see this happen are:

(1) you've calculated an impulse response from a frequency response
using an FFT and you've either not paid proper attention to phase, or
you have the inevitable numerical inaccuracies and you haven't noticed
that the imaginary parts are minuscule

(2) you're modeling a system that's operating on I/Q data, and you've

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```
```On Mar 29, 1:38&#4294967295;pm, Tim Wescott <t...@seemywebsite.now> wrote:
> HardySpicer wrote:
> > What is the physical significance of having an impulse response with
> > complex coefficients ie
>
> > {h0,h1,h2...hn} &#4294967295;where the h values are complex.
>
> That your system, as described, is impossible to implement physically.
>
> You've asked a question with an absurd answer, and you're not dim. &#4294967295;So
> what are you _really_ doing?
>
> The two biggest reasons I could think that you may see this happen are:
>
> (1) you've calculated an impulse response from a frequency response
> using an FFT and you've either not paid proper attention to phase, or
> you have the inevitable numerical inaccuracies and you haven't noticed
> that the imaginary parts are minuscule
>
> (2) you're modeling a system that's operating on I/Q data, and you've
>
> --
> Tim Wescott
> Control system and signal processing consultingwww.wescottdesign.com

Oh I saw a paper with an example in it that has complex data points,
actually it is matrices but the same principle holds.
It was for Quarternary-Quam. So I suppose it is complex because the
imaginary part also has frequency-selective properties as well as
real.

Hardy
```
```HardySpicer <gyansorova@gmail.com> writes:

> So I suppose it is complex because the imaginary part also has
> frequency-selective properties as well as real.

Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency
response isn't Hermitian symmetric. Note I use "*" here to denote
conjugation.
--
Randy Yates                      % "She's sweet on Wagner-I think she'd die for Beethoven.
Digital Signal Labs              %  She love the way Puccini lays down a tune, and
mailto://yates@ieee.org          %  Verdi's always creepin' from her room."
http://www.digitalsignallabs.com % "Rockaria", *A New World Record*, ELO
```
```Randy Yates wrote:
> HardySpicer <gyansorova@gmail.com> writes:
>
>> So I suppose it is complex because the imaginary part also has
>> frequency-selective properties as well as real.
>
> Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency
> response isn't Hermitian symmetric. Note I use "*" here to denote
> conjugation.

That's not a _physical_ interpretation, because no physical system has a
frequency response that isn't Hermitian symmetric.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```
```HardySpicer wrote:
> On Mar 29, 1:38 pm, Tim Wescott <t...@seemywebsite.now> wrote:
>> HardySpicer wrote:
>>> What is the physical significance of having an impulse response with
>>> complex coefficients ie
>>> {h0,h1,h2...hn}  where the h values are complex.
>> That your system, as described, is impossible to implement physically.
>>
>> You've asked a question with an absurd answer, and you're not dim.  So
>> what are you _really_ doing?
>>
>> The two biggest reasons I could think that you may see this happen are:
>>
>> (1) you've calculated an impulse response from a frequency response
>> using an FFT and you've either not paid proper attention to phase, or
>> you have the inevitable numerical inaccuracies and you haven't noticed
>> that the imaginary parts are minuscule
>>
>> (2) you're modeling a system that's operating on I/Q data, and you've
>
> Oh I saw a paper with an example in it that has complex data points,
> actually it is matrices but the same principle holds.
> It was for Quarternary-Quam. So I suppose it is complex because the
> imaginary part also has frequency-selective properties as well as
> real.

Well, you were asking for physical significance.  The physical
significance is what I outlined in (2) above: the system being modeled
is doing I/Q demodulation down to baseband, and the quadrature channel
is modeled as imaginary.  The spectrum of the _physical_ signal is a
pair of identical, Hermitian-symmetrical spectra reflected around f = 0;
in choosing to treat the quadrature channel as imaginary you're
essentially just doing the math on the frequency-positive half of the
spectrum.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```
```Tim Wescott <tim@seemywebsite.now> writes:

> Randy Yates wrote:
>> HardySpicer <gyansorova@gmail.com> writes:
>>
>>> So I suppose it is complex because the imaginary part also has
>>> frequency-selective properties as well as real.
>>
>> Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency
>> response isn't Hermitian symmetric. Note I use "*" here to denote
>> conjugation.
>
> That's not a _physical_ interpretation, because no physical system has
> a frequency response that isn't Hermitian symmetric.

You are correct by strict interpretation.  I was trying to answer what I
thought his real question was.

It takes two to communicate.
--
Randy Yates                      % "Though you ride on the wheels of tomorrow,
Digital Signal Labs              %  you still wander the fields of your
mailto://yates@ieee.org          %  sorrow."
http://www.digitalsignallabs.com % '21st Century Man', *Time*, ELO
```
```Randy Yates wrote:
> Tim Wescott <tim@seemywebsite.now> writes:
>
>> Randy Yates wrote:
>>> HardySpicer <gyansorova@gmail.com> writes:
>>>
>>>> So I suppose it is complex because the imaginary part also has
>>>> frequency-selective properties as well as real.
>>> Not exactly. It is complex because F(w) != F*(-w), i.e., the frequency
>>> response isn't Hermitian symmetric. Note I use "*" here to denote
>>> conjugation.
>> That's not a _physical_ interpretation, because no physical system has
>> a frequency response that isn't Hermitian symmetric.
>
> You are correct by strict interpretation.  I was trying to answer what I
> thought his real question was.
>
> It takes two to communicate.

I shall find my swagger stick, and polish my monocle and my German accent.

Tee hee!  Schnort!

Hopefully between the two of us we've managed to satisfy Hardy.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```