Not a member?

# Discussion Groups | Comp.DSP | Clipped sum of sinusoids

There are 22 messages in this thread.

You are currently looking at messages 1 to .

Is this discussion worth a thumbs up?

+1

# Clipped sum of sinusoids - Vladimir Vassilevsky - 2012-10-02 11:26:00

```Let's say there is a sine wave signal, and an amplifier with limited output
amplitude. To produce maximum output power at fundamental frequency, the
sinusoid could be clipped into square wave. So far so good.

What if the input is a short burst of a sum of several unrelated sine waves
with different amplitudes and the goal is to match given amplitude spectrum
and generate maximum power? How hard would be optimal clipping? What should
be the relationship of phases and amplitudes at the input of the amplifier?

The result indeed depends on the phases, amplitudes and clipping level. I am
trying to bruteforce the problem by genetic optimization as I don't see any
systematic approach. The general problem could be restated as generation of
the most constant envelope signal with given spectrum. Could you suggest any
approach or related work?

DSP and Mixed Signal Consultant
www.abvolt.com

```
______________________________

# Re: Clipped sum of sinusoids - Tim Wescott - 2012-10-02 11:43:00

```On Tue, 02 Oct 2012 10:26:10 -0500, Vladimir Vassilevsky wrote:

> Let's say there is a sine wave signal, and an amplifier with limited
> output amplitude. To produce maximum output power at fundamental
> frequency, the sinusoid could be clipped into square wave. So far so
> good.
>
> What if the input is a short burst of a sum of several unrelated sine
> waves with different amplitudes and the goal is to match given amplitude
> spectrum and generate maximum power? How hard would be optimal clipping?
> What should be the relationship of phases and amplitudes at the input of
> the amplifier?
>
> The result indeed depends on the phases, amplitudes and clipping level.
> I am trying to bruteforce the problem by genetic optimization as I don't
> see any systematic approach. The general problem could be restated as
> generation of the most constant envelope signal with given spectrum.
> Could you suggest any approach or related work?
>
> Vladimir Vassilevsky DSP and Mixed Signal Consultant www.abvolt.com

There may be something related in the OFDM literature, since shape factor
is a big deal there.

Probably not, but it may be worth a glance.

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

# Re: Clipped sum of sinusoids - Vladimir Vassilevsky - 2012-10-02 12:01:00

```"Tim Wescott" <t...@seemywebsite.please> wrote in message
news:n...@web-ster.com...
> On Tue, 02 Oct 2012 10:26:10 -0500, Vladimir Vassilevsky wrote:
>
>> Let's say there is a sine wave signal, and an amplifier with limited
>> output amplitude. To produce maximum output power at fundamental
>> frequency, the sinusoid could be clipped into square wave. So far so
>> good.
>>
>> What if the input is a short burst of a sum of several unrelated sine
>> waves with different amplitudes and the goal is to match given amplitude
>> spectrum and generate maximum power? How hard would be optimal clipping?
>> What should be the relationship of phases and amplitudes at the input of
>> the amplifier?
>>
>> The result indeed depends on the phases, amplitudes and clipping level.
>> I am trying to bruteforce the problem by genetic optimization as I don't
>> see any systematic approach. The general problem could be restated as
>> generation of the most constant envelope signal with given spectrum.
>> Could you suggest any approach or related work?
>>

> There may be something related in the OFDM literature, since shape factor
> is a big deal there.
> Probably not, but it may be worth a glance.

I looked through that. The OFDM peak problem is quite different, and they
don't seem to have many ideas to offer either.

VLV

```
______________________________

# Re: Clipped sum of sinusoids - Fred Marshall - 2012-10-02 13:48:00

```On 10/2/2012 8:26 AM, Vladimir Vassilevsky wrote:
> Let's say there is a sine wave signal, and an amplifier with limited output
> amplitude. To produce maximum output power at fundamental frequency, the
> sinusoid could be clipped into square wave. So far so good.
>
> What if the input is a short burst of a sum of several unrelated sine waves
> with different amplitudes and the goal is to match given amplitude spectrum
> and generate maximum power? How hard would be optimal clipping? What should
> be the relationship of phases and amplitudes at the input of the amplifier?
>
> The result indeed depends on the phases, amplitudes and clipping level. I am
> trying to bruteforce the problem by genetic optimization as I don't see any
> systematic approach. The general problem could be restated as generation of
> the most constant envelope signal with given spectrum. Could you suggest any
> approach or related work?
>
> DSP and Mixed Signal Consultant
> www.abvolt.com
>
>

Well it seems that the problem as stated is underconstrained .. so I'm

As I recall, there is a beamformer due to Vic Anderson which clips the
signals at the outset.  Yet, the spectrum is preserved after having done
that .. as a general statement.  Probably has something to do with the
bandwidth one looks at thereafter.  Yet, the notion as I recall was for
fairly wideband beamformers.  Might this suggest "hard clipping" is the

Fred

```
______________________________

# Re: Clipped sum of sinusoids - kaz - 2012-10-02 14:05:00

```>Let's say there is a sine wave signal, and an amplifier with limited
output
>amplitude. To produce maximum output power at fundamental frequency, the
>sinusoid could be clipped into square wave. So far so good.
>
>What if the input is a short burst of a sum of several unrelated sine
waves
>with different amplitudes and the goal is to match given amplitude
spectrum
>and generate maximum power? How hard would be optimal clipping? What
should
>be the relationship of phases and amplitudes at the input of the
amplifier?
>
>The result indeed depends on the phases, amplitudes and clipping level. I
am
>trying to bruteforce the problem by genetic optimization as I don't see
any
>systematic approach. The general problem could be restated as generation
of
>the most constant envelope signal with given spectrum. Could you suggest
any
>approach or related work?
>
>DSP and Mixed Signal Consultant
>www.abvolt.com
>
>
>

Peak limiting algorithm rather than brute clipping. Peak limiting sets a
threshold for instantaneous peak power in time domain as ratio to mean
power of composite signal. Then it subtracts a percentage of excess value
above threshold from peak itself and all adjacent signal samples on either
side of peak. Thus you shrink the signal gently whenever peaks occur. You
are only limited by the degree of noise floor rise acceptable to you.

```
______________________________

# Re: Clipped sum of sinusoids - glen herrmannsfeldt - 2012-10-02 15:27:00

```Vladimir Vassilevsky <n...@nowhere.com> wrote:
> Let's say there is a sine wave signal, and an amplifier with limited output
> amplitude. To produce maximum output power at fundamental frequency, the
> sinusoid could be clipped into square wave. So far so good.

OK, so a square wave of a given frequency maximizes the component
sine with that frequency and amplitude limit, I agree.

> What if the input is a short burst of a sum of several unrelated sine waves
> with different amplitudes and the goal is to match given amplitude spectrum
> and generate maximum power? How hard would be optimal clipping? What should
> be the relationship of phases and amplitudes at the input of the amplifier?

My first thought was to separately compute the square waves and add
them. Each has to be scaled by the amplitude of the appropriate sine,
and then the sum rescaled to match the clipping level.

I believe that works as long as no harmonic component of one adds
to the fundamental of another. It can add to any other harmonic,
which doesn't affect the result.

> The result indeed depends on the phases, amplitudes and clipping level. I am
> trying to bruteforce the problem by genetic optimization as I don't see any
> systematic approach. The general problem could be restated as generation of
> the most constant envelope signal with given spectrum. Could you suggest any
> approach or related work?

My other thought is to do the problem backwards. You know what the
result has to be, at least some constraints on the result.
Then do the inverse transform.

Otherwise, it might be easier to figure out if we knew the
application of the result.

-- glen
```
______________________________

# Re: Clipped sum of sinusoids - Greg Berchin - 2012-10-02 16:39:00

```On Tue, 02 Oct 2012 10:49:01 -0700, Fred Marshall
<f...@acm.org> wrote:

>As I recall, there is a beamformer due to Vic Anderson which clips the
>signals at the outset.

DIMUS beamformer.

>Yet, the spectrum is preserved after having done
>that .. as a general statement.  Probably has something to do with the
>bandwidth one looks at thereafter.

Also has to do with the fact that many separate versions of the same signals are
uncorrelated signals still add incoherently (more or less), despite the
hard-clipping -- which is what a beamformer is for.

Vladimir appears to be adding many clipped "unrelated" signals, which may tend

Greg
```
______________________________

# Re: Clipped sum of sinusoids - 2012-10-03 07:14:00

```On Tuesday, October 2, 2012 5:26:10 PM UTC+2, Vladimir Vassilevsky wrote:
> Let's say there is a sine wave signal, and an amplifier with limited output
>
> amplitude. To produce maximum output power at fundamental frequency, the
>
> sinusoid could be clipped into square wave. So far so good.
>
>
>
> What if the input is a short burst of a sum of several unrelated sine waves
>
> with different amplitudes and the goal is to match given amplitude spectrum
>
> and generate maximum power? How hard would be optimal clipping? What should
>
> be the relationship of phases and amplitudes at the input of the amplifier?
>
>
>
> The result indeed depends on the phases, amplitudes and clipping level. I am
>
> trying to bruteforce the problem by genetic optimization as I don't see any
>
> systematic approach. The general problem could be restated as generation of
>
> the most constant envelope signal with given spectrum. Could you suggest any
>
> approach or related work?
>
>
>
>
> DSP and Mixed Signal Consultant
>
> www.abvolt.com

GRUMPIDENT!

take a look at voltera kernels.

```
______________________________

# Re: Clipped sum of sinusoids - mnentwig - 2012-10-03 09:28:00

```>> take a look at voltera kernels.

Volterra kernels for weakly nonlinear systems, business as usual.
But, hard clipping, I don't see how the pieces fit together.
```
______________________________
```Somewhere in the distant past I recall a paper about maximizing the range of AM broadcast