soft clipping of waveform

Hi,

I am looking for ways to do soft-clipping of waveform, so as to reduce the
crest factor of the signal. Can anybody point me to the right direction, or
advise the rough overall idea behind it.

The implementation will most likely be in FPGA, but anything will do.

Thanks



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paulwu wrote:
> Hi,
> 
> I am looking for ways to do soft-clipping of waveform, so as to reduce the
> crest factor of the signal. Can anybody point me to the right direction, or
> advise the rough overall idea behind it.
> 
> The implementation will most likely be in FPGA, but anything will do.
> 
> Thanks
> 
Paul,

The basic idea behind soft clipping is to map your samples to a curve 
which is linear in the "unclipped" region and rolls gently towards full 
scale in the "clipped" region. For example, if you have a system with 
samples in the range [-1, 1], but some data which needs to be clipped 
going up to [-5, 5] and want to soft clip to the domain [-1, 1], then 
you will use a curve which gives results along these lines:

In	Soft Clip	Hard Clip	Compressed
0.1	0.1		0.1		0.02
0.5	0.5		0.5		0.1
0.9	0.9		0.9		0.18
1	0.95		1		0.20
2	0.975		1		0.4
4	0.99		1		0.8
5	1		1		1

Exactly how that mapping looks, and which curve you use depends on the 
application. What application do you have in mind?

Cheers

Marc


> 
> 
> _____________________________________
> Do you know a company who employs DSP engineers?  
> Is it already listed at http://dsprelated.com/employers.php ?

paulwu wrote:
> Hi,
> 
> I am looking for ways to do soft-clipping of waveform, so as to reduce the
> crest factor of the signal. Can anybody point me to the right direction, or
> advise the rough overall idea behind it.

The total amount of distortion produced by clipping equals to the 
difference between the straight line and the clipped line. You can trade 
the high order nonlinear products vs low order products by making a 
softer knee, but this is generally not going to do much of improvement.

> 
> The implementation will most likely be in FPGA, but anything will do.
> 

You can try log() or sqrt() type of curve, however I don't think it will 
buy you anything compared to just hard clipping of the signal.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

On Apr 4, 9:43 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> paulwu wrote:
> > Hi,
>
> > I am looking for ways to do soft-clipping of waveform, so as to reduce the
> > crest factor of the signal. Can anybody point me to the right direction, or
> > advise the rough overall idea behind it.
>
> The total amount of distortion produced by clipping equals to the
> difference between the straight line and the clipped line. You can trade
> the high order nonlinear products vs low order products by making a
> softer knee, but this is generally not going to do much of improvement.
>
>
>
> > The implementation will most likely be in FPGA, but anything will do.
>
> You can try log() or sqrt() type of curve, however I don't think it will
> buy you anything compared to just hard clipping of the signal.
>
> Vladimir Vassilevsky
>
> DSP and Mixed Signal Design Consultant
>
> http://www.abvolt.com

I worked on a digital system that required clipping like this and
there is an interesting issue to be aware of.

Any kind of clipping will produce harmonics and your sampling rate
must be high enough to accommodate ALL the harmonics that the clipping
generates  or you will get ugly aliasing.

I'm not sure if there is an elegant  solution to this is.
If I recall ,  the solution we considered was to use a clipping
function that produced harmonics only to a limited order say  up to
only 4th order harmonics and NO harmonics above that.    Then we set
the sample rate accordingly.  Its a tough problem because you can't
filter these harmonics until after they are created, so the section
that creates the clipping and generates the harmonics has to run at
the higher sampling rate.  AFTER you low pass filter to remove the
harmonics, then you can reduce the sample rate.

Maybe someone knows a more elegant solution?  Is there a way to
combine the clipping and filtering so  that no section  needs to run
at the higher sampling rate?

thanks
Mark

Mark wrote:


> Any kind of clipping will produce harmonics and your sampling rate
> must be high enough to accommodate ALL the harmonics that the clipping
> generates  or you will get ugly aliasing.

The clipping produces the intermodulation products, which is much worse 
then just harmonics. The intermods of the odd orders are falling into 
the bandwidth of the signal, so it is impossible to filter them out. 
Since the signal is clipped symmetrically, the odd order distortion has 
always to be there.

> 
> I'm not sure if there is an elegant  solution to this is.
> If I recall ,  the solution we considered was to use a clipping
> function that produced harmonics only to a limited order say  up to
> only 4th order harmonics and NO harmonics above that.    Then we set
> the sample rate accordingly.  Its a tough problem because you can't
> filter these harmonics until after they are created, so the section
> that creates the clipping and generates the harmonics has to run at
> the higher sampling rate.  AFTER you low pass filter to remove the
> harmonics, then you can reduce the sample rate.
> 
> Maybe someone knows a more elegant solution?  Is there a way to
> combine the clipping and filtering so  that no section  needs to run
> at the higher sampling rate?

The elegant solution is the complex limiter:

1. The signal is converted to X and X* representation by the Hilbert 
transformer.
2. The complex amplitude A = sqrt(X^2 + X* ^2) is clipped.
3. The signal is converted back to real.


Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

On Apr 4, 10:19 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> Mark wrote:
> > Any kind of clipping will produce harmonics and your sampling rate
> > must be high enough to accommodate ALL the harmonics that the clipping
> > generates  or you will get ugly aliasing.
>
> The clipping produces the intermodulation products, which is much worse
> then just harmonics. The intermods of the odd orders are falling into
> the bandwidth of the signal, so it is impossible to filter them out.
> Since the signal is clipped symmetrically, the odd order distortion has
> always to be there.
>
>
>
> > I'm not sure if there is an elegant  solution to this is.
> > If I recall ,  the solution we considered was to use a clipping
> > function that produced harmonics only to a limited order say  up to
> > only 4th order harmonics and NO harmonics above that.    Then we set
> > the sample rate accordingly.  Its a tough problem because you can't
> > filter these harmonics until after they are created, so the section
> > that creates the clipping and generates the harmonics has to run at
> > the higher sampling rate.  AFTER you low pass filter to remove the
> > harmonics, then you can reduce the sample rate.
>
> > Maybe someone knows a more elegant solution?  Is there a way to
> > combine the clipping and filtering so  that no section  needs to run
> > at the higher sampling rate?
>
> The elegant solution is the complex limiter:
>
> 1. The signal is converted to X and X* representation by the Hilbert
> transformer.
> 2. The complex amplitude A = sqrt(X^2 + X* ^2) is clipped.
> 3. The signal is converted back to real.
>
> Vladimir Vassilevsky
>
> DSP and Mixed Signal Design Consultant
>
> http://www.abvolt.com

The usual goal is to emulate an analog system that has a clipper
followed by a low pass filter.  So, yes the intermodulation products
are produced but they are also present in an analog system and that is
just the nature of clipping.

However, in a analog system, the harmonics are produced and those that
fall above the upper band limit (say 20 kHz) are filtered and cause no
issues.    However, in a digitized system,  the harmonics  above 20
kHz will also produce aliasing if the sampling rate is not high
enough.  This aliasing is an additional distortion  that does not
exist in an analog system.  The usual objective is to create a digital
version of an anlog system so whatever distortions an anlog clipper/
filter would have created are acceptable, but no new additional
distortions (or aliasing) due to the digital implementation are
acceptable.

Does the complex method you described resolve this alisaing problem?


Mark

Mark wrote:


>>The elegant solution is the complex limiter:
>>
>>1. The signal is converted to X and X* representation by the Hilbert
>>transformer.
>>2. The complex amplitude A = sqrt(X^2 + X* ^2) is clipped.
>>3. The signal is converted back to real.

> 
> The usual goal is to emulate an analog system that has a clipper
> followed by a low pass filter.

The complex limiter action is different from that. It is similar to 
so-called analog RF limiter. It performs much better then the 
straightforward limiting of the signal.

> The usual objective is to create a digital
> version of an anlog system so whatever distortions an anlog clipper/
> filter would have created are acceptable, but no new additional
> distortions (or aliasing) due to the digital implementation are
> acceptable.
> 
> Does the complex method you described resolve this alisaing problem?
> 

Yes and No.
There will be none of the harmonics or aliased harmonics.
However there will be the intermods and the aliased intermods.


Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

> The complex limiter action is different from that. It is similar to
> so-called analog RF limiter. It performs much better then the
> straightforward limiting of the signal.



OK, is it correct to say that this complex method works the same as
using the original signal to create (modulate) an SSB RF signal, apply
limiting to the RF SSB signal, then demodulate the SSB RF signal back
to baseband?

Mark

Mark wrote:

>>The complex limiter action is different from that. It is similar to
>>so-called analog RF limiter. It performs much better then the
>>straightforward limiting of the signal.
> 
> 
> OK, is it correct to say that this complex method works the same as
> using the original signal to create (modulate) an SSB RF signal, apply
> limiting to the RF SSB signal, then demodulate the SSB RF signal back
> to baseband?


1. The analog complex limiter - yes, this is correct.
2. The digital complex limiter - not quite correct. There is no aliased 
harmonics, but there are aliased intermods.

VLV

On Apr 4, 1:40 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> Mark wrote:
> >>The complex limiter action is different from that. It is similar to
> >>so-called analog RF limiter. It performs much better then the
> >>straightforward limiting of the signal.
>
> > OK, is it correct to say that this complex method works the same as
> > using the original signal to create (modulate) an SSB RF signal, apply
> > limiting to the RF SSB signal, then demodulate the SSB RF signal back
> > to baseband?
>
> 1. The analog complex limiter - yes, this is correct.
> 2. The digital complex limiter - not quite correct. There is no aliased
> harmonics, but there are aliased intermods.
>
> VLV

thanks
Mark