On Wed, 8 Jan 2014 16:08:52 +0100, Martin Trummer
<m.trummer@nospam.org> wrote:

>Hi DSP-experts,
>
>I'm using a FIR hilbert-transformer (designed with Matlab's fdatool, 
>200 coefficients) for a envlope detection. For eg:
>
>% Signal is x, h contains coefficients of hilbert transforemer
>x_analytical = filter(h,1,x);
>x_delay = filter([zeros([1,99]), 1],1,x);
>envelope = sqrt(x_analytical.^2+x_delay.^2);
>
>My problem is that the envelope doesn't fit very well since there is a 
>lot ringing on the envelope itself as you can see on the following 
>screenshot:
>
>http://s14.directupload.net/images/140108/8cmreir2.png
>
>What's the exact problem for this behavior and how can this be avoided?
>Thank you in advance!
>
>Cheers Martin

Hello Matrin,
  Wow, this is a long thread.  I haven't read 
all the posts but I'll just mention that some 
of the info at the following web page may be 
of some small value to you.

http://www.dsprelated.com/showarticle/153.php

Good Luck,
[-Rick-]

On Sun, 12 Jan 2014 21:40:26 -0500, Randy Yates
<yates@digitalsignallabs.com> wrote:

>radams2000@gmail.com writes:
>
>> On Wednesday, January 8, 2014 10:08:52 AM UTC-5, Martin Trummer wrote:
>>> Hi DSP-experts,
>>> 
>>> 
>>> 
>>> I'm using a FIR hilbert-transformer (designed with Matlab's fdatool, 
>>> 
>>> 200 coefficients) for a envlope detection. For eg:
>>> 
>>> 
>>> 
>>> % Signal is x, h contains coefficients of hilbert transforemer
>>> 
>>> x_analytical = filter(h,1,x);
>>> 
>>> x_delay = filter([zeros([1,99]), 1],1,x);
>>> 
>>> envelope = sqrt(x_analytical.^2+x_delay.^2);
>>> 
>>> 
>>> 
>>> My problem is that the envelope doesn't fit very well since there is a 
>>> 
>>> lot ringing on the envelope itself as you can see on the following 
>>> 
>>> screenshot:
>>> 
>>> 
>>> 
>>> http://s14.directupload.net/images/140108/8cmreir2.png
>>> 
>>> 
>>> 
>>> What's the exact problem for this behavior and how can this be avoided?
>>> 
>>> Thank you in advance!
>>> 
>>> 
>>> 
>>> Cheers Martin
>>
>> Sure. Basically you want to use two parallel allpass chains where the
>> phase difference between their outputs is 90 degrees over some
>> frequency range. You start by choosing 1st-order or 2nd-order sections
>> (if you need to get close to DC then 2nd-order might be better). The
>> phase of each allpass will start from from 0 degrees and go to 360
>> degrees (for 2nd-order) so if you cascade them with frequencies offset
>> by some factor, you get a net phase curve that decreases continuously
>> with wiggles, over frequency. Generally, you want to construct the 2nd
>> chain with the center freqs of the allpass filters in between the
>> center freqs of the 1st chain. By plotting the unwrapped phase
>> difference you can manually wiggle the center freqs and Q's to get the
>> phase diff as close as possible to 90 degrees over the frequency range
>> of interest. You won't be able to do a very good job manually, but you
>> just want to get close enough the the optimizer won't fall into some
>> local minimum trap.
>> Then you write a function for the optimizer that returns an array of
>> phase errors over the desired frequency range, and give it the freedom
>> to adjust the allpass center freqs and Q's. Then hit return and go get
>> a cup of coffee. When you come back you will hopefully find that the
>> phase has equiripple errors around 90 degrees. It's not very hard to
>> get phase error numbers that are very small (hundredths of a degree).
>> It's also nice that you benefit from all the usual benefits of
>> allpass-based filters (coefficient sensitivity, etc).
>
>PS: Bob, from your usenet client, did it appear that you were responding
>to me? My client indicates your response to Martin's original post. I've
>also noticed multiple times in the past that your responses don't line
>up with the person you're responding to. 
>-- 
>Randy Yates
>Digital Signal Labs
>http://www.digitalsignallabs.com

For some reason Bob's posts almost always have the context deleted, so
it does make it challenging to follow sometimes.

Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

On 1/13/14 6:14 AM, radams2000@gmail.com wrote:
> Sorry, I usually respond on my iphone via google groups, can anyone suggest a way to improve this?
>

i think trials where we make these crappy engineers and crappy managers 
and crappy designers account for their crappy software.

complete with public firing squads.  even televized.  that'll improve it 
awful fast.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

Sorry, I usually respond on my iphone via google groups, can anyone suggest a way to improve this?

Bob

On 1/12/14 9:40 PM, Randy Yates wrote:
> radams2000@gmail.com writes:
>
>> On Wednesday, January 8, 2014 10:08:52 AM UTC-5, Martin Trummer wrote:
>>> Hi DSP-experts,
>>>
>>>
>>>
>>> I'm using a FIR hilbert-transformer (designed with Matlab's fdatool,
>>>
>>> 200 coefficients) for a envlope detection. For eg:
>>>
>>>
>>>
>>> % Signal is x, h contains coefficients of hilbert transforemer
>>>
>>> x_analytical = filter(h,1,x);
>>>
>>> x_delay = filter([zeros([1,99]), 1],1,x);
>>>
>>> envelope = sqrt(x_analytical.^2+x_delay.^2);
>>>
>>>
>>>
>>> My problem is that the envelope doesn't fit very well since there is a
>>>
>>> lot ringing on the envelope itself as you can see on the following
>>>
>>> screenshot:
>>>
>>>
>>>
>>> http://s14.directupload.net/images/140108/8cmreir2.png
>>>
>>>
>>>
>>> What's the exact problem for this behavior and how can this be avoided?
>>>
>>> Thank you in advance!
>>>
>>>
>>>
>>> Cheers Martin
>>
>> Sure. Basically you want to use two parallel allpass chains where the
>> phase difference between their outputs is 90 degrees over some
>> frequency range. You start by choosing 1st-order or 2nd-order sections
>> (if you need to get close to DC then 2nd-order might be better). The
>> phase of each allpass will start from from 0 degrees and go to 360
>> degrees (for 2nd-order) so if you cascade them with frequencies offset
>> by some factor, you get a net phase curve that decreases continuously
>> with wiggles, over frequency. Generally, you want to construct the 2nd
>> chain with the center freqs of the allpass filters in between the
>> center freqs of the 1st chain. By plotting the unwrapped phase
>> difference you can manually wiggle the center freqs and Q's to get the
>> phase diff as close as possible to 90 degrees over the frequency range
>> of interest. You won't be able to do a very good job manually, but you
>> just want to get close enough the the optimizer won't fall into some
>> local minimum trap.
>> Then you write a function for the optimizer that returns an array of
>> phase errors over the desired frequency range, and give it the freedom
>> to adjust the allpass center freqs and Q's. Then hit return and go get
>> a cup of coffee. When you come back you will hopefully find that the
>> phase has equiripple errors around 90 degrees. It's not very hard to
>> get phase error numbers that are very small (hundredths of a degree).
>> It's also nice that you benefit from all the usual benefits of
>> allpass-based filters (coefficient sensitivity, etc).
>
> PS: Bob, from your usenet client, did it appear that you were responding
> to me? My client indicates your response to Martin's original post. I've
> also noticed multiple times in the past that your responses don't line
> up with the person you're responding to.

another thing, Bob, your blankity-blank lines are so blankity-blank 
long.  i can't ever figure out why *my* client program doesn't wrap them.

at least it ain't what plagues gyansorova's postings.  each time anyone 
replies to his post, it doubles the number of lines, complete with the 
commenting ">" mark.

what's happened to all these client programs?  have they just gotten 
stupid or something?  like since 2005?  heaven knows that google.groups 
has become totally brain dead now.  i remember when they took over for 
dejanews i thought google was so smart that they could never ever get 
dumb.  maybe not, but like Microshit, they can lose good taste and all 
perspective of utility for their marked "client" (or "target" or krill 
or whatever we are to Google).

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

radams2000@gmail.com writes:

> On Wednesday, January 8, 2014 10:08:52 AM UTC-5, Martin Trummer wrote:
>> Hi DSP-experts,
>> 
>> 
>> 
>> I'm using a FIR hilbert-transformer (designed with Matlab's fdatool, 
>> 
>> 200 coefficients) for a envlope detection. For eg:
>> 
>> 
>> 
>> % Signal is x, h contains coefficients of hilbert transforemer
>> 
>> x_analytical = filter(h,1,x);
>> 
>> x_delay = filter([zeros([1,99]), 1],1,x);
>> 
>> envelope = sqrt(x_analytical.^2+x_delay.^2);
>> 
>> 
>> 
>> My problem is that the envelope doesn't fit very well since there is a 
>> 
>> lot ringing on the envelope itself as you can see on the following 
>> 
>> screenshot:
>> 
>> 
>> 
>> http://s14.directupload.net/images/140108/8cmreir2.png
>> 
>> 
>> 
>> What's the exact problem for this behavior and how can this be avoided?
>> 
>> Thank you in advance!
>> 
>> 
>> 
>> Cheers Martin
>
> Sure. Basically you want to use two parallel allpass chains where the
> phase difference between their outputs is 90 degrees over some
> frequency range. You start by choosing 1st-order or 2nd-order sections
> (if you need to get close to DC then 2nd-order might be better). The
> phase of each allpass will start from from 0 degrees and go to 360
> degrees (for 2nd-order) so if you cascade them with frequencies offset
> by some factor, you get a net phase curve that decreases continuously
> with wiggles, over frequency. Generally, you want to construct the 2nd
> chain with the center freqs of the allpass filters in between the
> center freqs of the 1st chain. By plotting the unwrapped phase
> difference you can manually wiggle the center freqs and Q's to get the
> phase diff as close as possible to 90 degrees over the frequency range
> of interest. You won't be able to do a very good job manually, but you
> just want to get close enough the the optimizer won't fall into some
> local minimum trap.
> Then you write a function for the optimizer that returns an array of
> phase errors over the desired frequency range, and give it the freedom
> to adjust the allpass center freqs and Q's. Then hit return and go get
> a cup of coffee. When you come back you will hopefully find that the
> phase has equiripple errors around 90 degrees. It's not very hard to
> get phase error numbers that are very small (hundredths of a degree).
> It's also nice that you benefit from all the usual benefits of
> allpass-based filters (coefficient sensitivity, etc).

PS: Bob, from your usenet client, did it appear that you were responding
to me? My client indicates your response to Martin's original post. I've
also noticed multiple times in the past that your responses don't line
up with the person you're responding to. 
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

radams2000@gmail.com writes:

> On Wednesday, January 8, 2014 10:08:52 AM UTC-5, Martin Trummer wrote:
>> Hi DSP-experts,
>> 
>> 
>> 
>> I'm using a FIR hilbert-transformer (designed with Matlab's fdatool, 
>> 
>> 200 coefficients) for a envlope detection. For eg:
>> 
>> 
>> 
>> % Signal is x, h contains coefficients of hilbert transforemer
>> 
>> x_analytical = filter(h,1,x);
>> 
>> x_delay = filter([zeros([1,99]), 1],1,x);
>> 
>> envelope = sqrt(x_analytical.^2+x_delay.^2);
>> 
>> 
>> 
>> My problem is that the envelope doesn't fit very well since there is a 
>> 
>> lot ringing on the envelope itself as you can see on the following 
>> 
>> screenshot:
>> 
>> 
>> 
>> http://s14.directupload.net/images/140108/8cmreir2.png
>> 
>> 
>> 
>> What's the exact problem for this behavior and how can this be avoided?
>> 
>> Thank you in advance!
>> 
>> 
>> 
>> Cheers Martin
>
> Sure. Basically you want to use two parallel allpass chains where the
> phase difference between their outputs is 90 degrees over some
> frequency range. You start by choosing 1st-order or 2nd-order sections
> (if you need to get close to DC then 2nd-order might be better). The
> phase of each allpass will start from from 0 degrees and go to 360
> degrees (for 2nd-order) so if you cascade them with frequencies offset
> by some factor, you get a net phase curve that decreases continuously
> with wiggles, over frequency. Generally, you want to construct the 2nd
> chain with the center freqs of the allpass filters in between the
> center freqs of the 1st chain. By plotting the unwrapped phase
> difference you can manually wiggle the center freqs and Q's to get the
> phase diff as close as possible to 90 degrees over the frequency range
> of interest. You won't be able to do a very good job manually, but you
> just want to get close enough the the optimizer won't fall into some
> local minimum trap.
> Then you write a function for the optimizer that returns an array of
> phase errors over the desired frequency range, and give it the freedom
> to adjust the allpass center freqs and Q's. Then hit return and go get
> a cup of coffee. When you come back you will hopefully find that the
> phase has equiripple errors around 90 degrees. It's not very hard to
> get phase error numbers that are very small (hundredths of a degree).
> It's also nice that you benefit from all the usual benefits of
> allpass-based filters (coefficient sensitivity, etc).

Bob, thanks for this. I'm not sure I follow it completely, but I think
there's enough here to guide me if I decide to try it. Thanks for adding
another item to my Hibert transform bag-of-tricks!
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On Wednesday, January 8, 2014 10:08:52 AM UTC-5, Martin Trummer wrote:
> Hi DSP-experts,
> 
> 
> 
> I'm using a FIR hilbert-transformer (designed with Matlab's fdatool, 
> 
> 200 coefficients) for a envlope detection. For eg:
> 
> 
> 
> % Signal is x, h contains coefficients of hilbert transforemer
> 
> x_analytical = filter(h,1,x);
> 
> x_delay = filter([zeros([1,99]), 1],1,x);
> 
> envelope = sqrt(x_analytical.^2+x_delay.^2);
> 
> 
> 
> My problem is that the envelope doesn't fit very well since there is a 
> 
> lot ringing on the envelope itself as you can see on the following 
> 
> screenshot:
> 
> 
> 
> http://s14.directupload.net/images/140108/8cmreir2.png
> 
> 
> 
> What's the exact problem for this behavior and how can this be avoided?
> 
> Thank you in advance!
> 
> 
> 
> Cheers Martin

Sure. Basically you want to use two parallel allpass chains where the phase difference between their outputs is 90 degrees over some frequency range. You start by choosing 1st-order or 2nd-order sections (if you need to get close to DC then 2nd-order might be better). The phase of each allpass will start from from 0 degrees and go to 360 degrees (for 2nd-order) so if you cascade them with frequencies offset by some factor, you get a net phase curve that decreases continuously with wiggles, over frequency. Generally, you want to construct the 2nd chain with the center freqs of the allpass filters in between the center freqs of the 1st chain. By plotting the unwrapped phase difference you can manually wiggle the center freqs and Q's to get the phase diff as close as possible to 90 degrees over the frequency range of interest. You won't be able to do a very good job manually, but you just want to get close enough the the optimizer won't fall into some local minimum trap.
Then you write a function for the optimizer that returns an array of phase errors over the desired frequency range, and give it the freedom to adjust the allpass center freqs and Q's. Then hit return and go get a cup of coffee. When you come back you will hopefully find that the phase has equiripple errors around 90 degrees. It's not very hard to get phase error numbers that are very small (hundredths of a degree). It's also nice that you benefit from all the usual benefits of allpass-based filters (coefficient sensitivity, etc).

radams2000@gmail.com writes:

> Randy
>
> Yes sounds like that should work. If the desired frequency band was
> near DC, and you want unity magnitude in both paths, would that result
> in a very long filter?

Bob, see my response to Clay. The optimization of the filter length I
thought you would get with a smaller passband bandwidth won't happen. :(

Perhaps I'm a little thick, but can you please explain the technique

  I start out by manually tuning a parallel set of allpass filters using
  staggered frequencies and then use Matlab lsqnonlin which is in the
  optimization toolbox.

a little more?
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

clay@claysturner.com writes:

> Randy,
>
> This approach is certainly doable as long as you can design the low
> pass filter. What if you needed 10,000 taps? The following paper shows
> how to do this and the needed constraints to do it cleanly.
>
>
> A. Reilly, G. Frazer, and B. Boashash, “Analytic
> signal generation—Tips and traps,” IEEE Trans.
> Signal Processing, vol. 42, no. 11, Nov. 1994, pp.
> 3241–3245.

Thanks for the reference, Clay. 

I see from that paper (namely, the way the stop-band edges line up in
figure 2) that you really can't increase the transition band like I
thought when reducing the passband bandwidth (otherwise you'd get some
negative frequency leakage). Bummer.
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com