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# Discussion Groups | Comp.DSP | Advantages of Envelope detector using Hilbert Transform

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# Advantages of Envelope detector using Hilbert Transform - c1910 - 2008-02-11 21:06:00

```hi!
i make an envelope detector for AM demodulation using Hilbert Transform
and complex envelope...

Transform and complex envelope...

what is the advantages of using Hilbert Transform and complex envelope?

why using Hilbert Transform method is more effective than square-law?

and i think i can make an envelope detector just without hilbert
transform.
i can use the I-phase, then multiply with exp(-jwt), then LPF. and we can
multiply the output by 2, because the output will give me only half
amplitude...

thanks...```

# Re: Advantages of Envelope detector using Hilbert Transform - robert bristow-johnson - 2008-02-11 22:33:00

```On Feb 11, 9:06 pm, "c1910" <c_19...@hotmail.com> wrote:
>
> i make an envelope detector for AM demodulation using Hilbert Transform
> and complex envelope...
>
> but i don't really understand about the advantages of using Hilbert
> Transform and complex envelope...

i also don't see any advantage, for the purpose of regular AM (no
suppressed carrier) detection for computing the complex envelope.
square-law might not be what you want, unless you like applying the
square-root after filtering out the carrier (actually a frequency that
is twice the carrier frequeny).  some non-linearity that leave an
amplitude proportional to (1+mu*x(t)) where x(t) is your message after
unbiasing is what you want.  maybe abs(), maybe 1/2 wave rectifier, i
dunno.

i think that sometimes when the signal is more complex than a
modulated sinusoidal carrier (what AM is), such as a broadbanded
signal, that the complex envelope might be desired because it gives
you an envelope without creating new frequency components.  it *does*
eliminate the negative frequency components but it does not introduce
new frequencies like the square-law does.  i dunno when that is
advantageous, but i know of audio signal practioners (these guys walk
around and fly around to places with expensive analytical test gear
and come up with all sorts of numbers describing a room) think that
the complex envelope (or the magnitude of the complex "analytic
signal") is a super salient measure of stuff.  dunno why, and maybe i
should, since i'm sorta into audio, but i dunno.

r b-j```

# Re: Advantages of Envelope detector using Hilbert Transform - Jerry Avins - 2008-02-11 22:34:00

```c1910 wrote:
> hi!
> i make an envelope detector for AM demodulation using Hilbert Transform
> and complex envelope...
>
> but i don't really understand about the advantages of using Hilbert
> Transform and complex envelope...
>
> what is the advantages of using Hilbert Transform and complex envelope?
>
> why using Hilbert Transform method is more effective than square-law?
>
> and i think i can make an envelope detector just without hilbert
> transform.
> i can use the I-phase, then multiply with exp(-jwt), then LPF. and we can
> multiply the output by 2, because the output will give me only half
> amplitude...
>
>
> thanks...

Square-law detectors suffer from distortion (with the rare exception of
single-sideband with carrier. They have no place in digital designs that
I know of. Peak detectors work with continuous signals, but there is no
reason to think that most samples will be near the carrier peak in a
sampled system unless the oversampling ratio is quite high relative to
the carrier or IF frequency. I-Q demodulation allows you to get the
magnitude at much lower sample rates.

If you didn't know that, what led you to that method?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯```

# Re: Advantages of Envelope detector using Hilbert Transform - robert bristow-johnson - 2008-02-11 22:37:00

```On Feb 11, 10:34 pm, Jerry Avins <j...@ieee.org> wrote:
>
> Peak detectors work with continuous signals, but there is no
> reason to think that most samples will be near the carrier peak in a
> sampled system unless the oversampling ratio is quite high relative to
> the carrier or IF frequency. I-Q demodulation allows you to get the
> magnitude at much lower sample rates.

yer right, Jerry.  that's a good reason and one i didn't think about.

r b-j```

# Re: Advantages of Envelope detector using Hilbert Transform - c1910 - 2008-02-12 02:16:00

```>c1910 wrote:
>> hi!
>> i make an envelope detector for AM demodulation using Hilbert
Transform
>> and complex envelope...
>>
>> but i don't really understand about the advantages of using Hilbert
>> Transform and complex envelope...
>>
>> what is the advantages of using Hilbert Transform and complex
envelope?
>>
>> why using Hilbert Transform method is more effective than square-law?
>>
>> and i think i can make an envelope detector just without hilbert
>> transform.
>> i can use the I-phase, then multiply with exp(-jwt), then LPF. and we
can
>> multiply the output by 2, because the output will give me only half
>> amplitude...
>>
>>
>> thanks...
>
>Square-law detectors suffer from distortion (with the rare exception of
>single-sideband with carrier. They have no place in digital designs that

>I know of. Peak detectors work with continuous signals, but there is no
>reason to think that most samples will be near the carrier peak in a
>sampled system unless the oversampling ratio is quite high relative to
>the carrier or IF frequency. I-Q demodulation allows you to get the
>magnitude at much lower sample rates.
>
>If you didn't know that, what led you to that method?
>
>Jerry
>--
>Engineering is the art of making what you want from things you can get.
>ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½
>

i use that method because i think there is a lot of distorsion in square
law...coz, square law still have the Carrier's Amplitude...```

# Re: Advantages of Envelope detector using Hilbert Transform - Rune Allnor - 2008-02-12 03:55:00

```On 12 Feb, 03:06, "c1910" <c_19...@hotmail.com> wrote:

> what is the advantages of using Hilbert Transform and complex envelope?
> why using Hilbert Transform method is more effective than square-law?

I don't know much about envelope detectors in AM systems,
but generally speaking, when you have more than one way
of implementing the same operation, there are a few trade-
offs involved:

- One method may require fewer components or FLOPS
- One method may be more accurate
- One method may be faster/simpler to design
- One method may be faster/simpler to implement
- One method may be better at suppressing artifacts
- One method may provide more, more useful internal results

and so on. Depending on the constraints on what you try
to do, one method may score better on this sort of overview
and would thus be the preferred one. It seems to me that
processing methods often falls into two groups: Those that
are cheap to implement or runs very fast (but which may give
inaccurate results), and those that give accurate results
but which are expensive to implement and/or cost more time
to run.

If cost and speed is all that matters, then the 'simpler'
(or 'naive' or 'obvious') methods often come out on top
in the evaluation.

If you need high accuracy or error control, or other
processing steps require information that can be squeezed
out of the data by more elaborate algorithms, that would
be deciding factors what methods to choose.

So no methods can be said to be 'best' for any particular
purpose. One needs to know one's own priorities (speed/cost
or accuracy). Then one needs to know what can be obtained
by each method -- and what the cost is.

Rune```

# Re: Advantages of Envelope detector using Hilbert Transform - Jerry Avins - 2008-02-12 11:34:00

```c1910 wrote:
>> c1910 wrote:
>>> hi!
>>> i make an envelope detector for AM demodulation using Hilbert
> Transform
>>> and complex envelope...
>>>
>>> but i don't really understand about the advantages of using Hilbert
>>> Transform and complex envelope...
>>>
>>> what is the advantages of using Hilbert Transform and complex
> envelope?
>>> why using Hilbert Transform method is more effective than square-law?
>>>
>>> and i think i can make an envelope detector just without hilbert
>>> transform.
>>> i can use the I-phase, then multiply with exp(-jwt), then LPF. and we
> can
>>> multiply the output by 2, because the output will give me only half
>>> amplitude...
>>>
>>>
>>> thanks...
>> Square-law detectors suffer from distortion (with the rare exception of
>> single-sideband with carrier. They have no place in digital designs that
>
>> I know of. Peak detectors work with continuous signals, but there is no
>> reason to think that most samples will be near the carrier peak in a
>> sampled system unless the oversampling ratio is quite high relative to
>> the carrier or IF frequency. I-Q demodulation allows you to get the
>> magnitude at much lower sample rates.
>>
>> If you didn't know that, what led you to that method?
>>

> i use that method because i think there is a lot of distorsion in square
> law...coz, square law still have the Carrier's Amplitude...

I don't understand the part the reason for the distortion. Squaring a
signal inevitably distorts it. Forget square-law detectors for
recovering ordinary AM. Most "simple" AM demodulators are peak
detectors. A digital peak detector is not only hard to design, hard even
to define what it is. You can approximately extract the envelope by
ensuring that the RF or IF signal is zero mean, then taking its absolute
value -- not squaring -- and low-pass filtering. That will work fairly
well most of the time, but on occasion it can fail horribly. Those
failures will be brief enough to go unnoticed, except when you're

Jerry
--
Engineering is the art of making what you want from things you can get.
Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯```

# Re: Advantages of Envelope detector using Hilbert Transform - 2008-02-12 12:52:00

```On Feb 11, 9:06 pm, "c1910" <c_19...@hotmail.com> wrote:
> hi!
> i make an envelope detector for AM demodulation using Hilbert Transform
> and complex envelope...
>
> but i don't really understand about the advantages of using Hilbert
> Transform and complex envelope...
>
> what is the advantages of using Hilbert Transform and complex envelope?
>
> why using Hilbert Transform method is more effective than square-law?
>
> and i think i can make an envelope detector just without hilbert
> transform.
> i can use the I-phase, then multiply with exp(-jwt), then LPF. and we can
> multiply the output by 2, because the output will give me only half
> amplitude...
>
>
> thanks...

Basically using a hilbert Xform is a way to find the instantaneous
amplitude. As Jerry et al stated this is not needed in standard AM
radios where the IF is very high compared to the modulation frequency.
In that case a simple diode with lowpass filter does a great job at
demodulating (finding the envelope).

But as often the case with software radios, the signal is mixed to a
very low frequency (to reduced the sampling rate and its attendent
overhead). In this case the observed peaks aren't very likely to occur
at or near the actuall peaks, so the envelope is not represented very
well. So the Hilbert method is a great analytical way to get there. In
practice though, all you really need is a pair of filters (flat or
nearly flat magnitude in the band of interest) that differ by 90
degrees. Call the outpouts A(t) and B(t) and your amplitude is simply
sqrt( A(t)^2 + B(t)^2 ).

IHTH,

Clay```

# Re: Advantages of Envelope detector using Hilbert Transform - Jerry Avins - 2008-02-12 13:12:00

```c...@claysturner.com wrote:
> On Feb 11, 9:06 pm, "c1910" <c_19...@hotmail.com> wrote:
>> hi!
>> i make an envelope detector for AM demodulation using Hilbert Transform
>> and complex envelope...
>>
>> but i don't really understand about the advantages of using Hilbert
>> Transform and complex envelope...
>>
>> what is the advantages of using Hilbert Transform and complex envelope?
>>
>> why using Hilbert Transform method is more effective than square-law?
>>
>> and i think i can make an envelope detector just without hilbert
>> transform.
>> i can use the I-phase, then multiply with exp(-jwt), then LPF. and we can
>> multiply the output by 2, because the output will give me only half
>> amplitude...
>>
>>
>> thanks...
>
>
> Basically using a hilbert Xform is a way to find the instantaneous
> amplitude. As Jerry et al stated this is not needed in standard AM
> radios where the IF is very high compared to the modulation frequency.
> In that case a simple diode with lowpass filter does a great job at
> demodulating (finding the envelope).
>
> But as often the case with software radios, the signal is mixed to a
> very low frequency (to reduced the sampling rate and its attendent
> overhead). In this case the observed peaks aren't very likely to occur
> at or near the actuall peaks, so the envelope is not represented very
> well. So the Hilbert method is a great analytical way to get there. In
> practice though, all you really need is a pair of filters (flat or
> nearly flat magnitude in the band of interest) that differ by 90
> degrees. Call the outpouts A(t) and B(t) and your amplitude is simply
> sqrt( A(t)^2 + B(t)^2 ).

Or just A(t)^2 + B(t)^2 if you're dead set on a square-law detector. :-)

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯```

# Re: Advantages of Envelope detector using Hilbert Transform - Philip Martel - 2008-02-13 21:03:00

```"Jerry Avins" <j...@ieee.org> wrote in message
news:G...@rcn.net...
> c1910 wrote:
>>> c1910 wrote:
>>>> hi!
>>>> i make an envelope detector for AM demodulation using Hilbert
>> Transform
>>>> and complex envelope...
>>>>
>>>> but i don't really understand about the advantages of using Hilbert
>>>> Transform and complex envelope...
>>>>
>>>> what is the advantages of using Hilbert Transform and complex
>> envelope?
>>>> why using Hilbert Transform method is more effective than square-law?
>>>>
>>>> and i think i can make an envelope detector just without hilbert
>>>> transform.
>>>> i can use the I-phase, then multiply with exp(-jwt), then LPF. and we
>> can
>>>> multiply the output by 2, because the output will give me only half
>>>> amplitude...
>>>>
>>>>
>>>> thanks...
>>> Square-law detectors suffer from distortion (with the rare exception of
>>> single-sideband with carrier. They have no place in digital designs that
>>
>>> I know of. Peak detectors work with continuous signals, but there is no
>>> reason to think that most samples will be near the carrier peak in a
>>> sampled system unless the oversampling ratio is quite high relative to
>>> the carrier or IF frequency. I-Q demodulation allows you to get the
>>> magnitude at much lower sample rates.
>>>
>>> If you didn't know that, what led you to that method?
>>>
>
>
>> i use that method because i think there is a lot of distorsion in square
>> law...coz, square law still have the Carrier's Amplitude...
>
> I don't understand the part the reason for the distortion. Squaring a
> signal inevitably distorts it. Forget square-law detectors for recovering
> ordinary AM. Most "simple" AM demodulators are peak detectors. A digital
> peak detector is not only hard to design, hard even to define what it is.
> You can approximately extract the envelope by ensuring that the RF or IF
> signal is zero mean, then taking its absolute value -- not squaring -- and
> low-pass filtering. That will work fairly well most of the time, but on
> occasion it can fail horribly. Those failures will be brief enough to go
> unnoticed, except when you're demonstrating your system.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯¯
Perhaps I'm missing something.  I *think* this is a "digital peak detector"
that behaves like a diode feeding an RC network

y(0) = 0;
y(n+1) = x(n) > y(n) ? x(n) : A * y(n);

A should be a bit smapper than 1...

Best wishes,
--Phil Martel```

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