```On Thu, 05 Jul 2007 05:58:42 -0000, Neville <digitafilter@gmail.com>
wrote:

>For FM demodulation, on the face of it, it appears that demodulating
>it using a real baseband and is no different from using a complex
>baseband. The end result is the demodulated baseband.
>
>However it would appear that there is probaly an advantage (since most
>implementations using a DSP describe this method) demodulating using a
>complex baseband as opposed to a real baseband signal.
>
>So what are the advantages of demodulating FM using a complex baseband
>over a real baseband signal
>
>Neville
>

Hello Neville,
the advantage of demodulating FM using a complex baseband
is that the process is so simple.  You compute the
instantaneous phase of your complex-valued (centered at
zero Hz) times samples and
then take the derivative of those instantaneous phase samples
to obtain the FM demodulated signal.

One of the problems, though, is how to compute the
instantaneous phase (an arctangent computation) in an
efficient way.  Arctangents are super nonlinear, so computing
accurate (say, to 0.1 degree of accuracy) arctangents usually
requires a painful number of computations.

Actually, thanks to the DSP Pioneers, there's a way to perform
FM demodulation without computing arctangents.  I discuss
this process in Chapter 13 of my DSP book.  Assuming that
you do not have a copy of my book, you can see the process
that I'm referring to in the October 2002 issue at

http://www.globaldsp.com/

Please be aware that the block diagram of the FM
demodulator at that Oct. 2002 website does *NOT* include
the appropriate delays needed to synchronize the signals.
That is, a differentiator has some number of delays (measured
in samples) and the block diagram does not accommodate
those delays.

Good luck,
[-Rick-]

```
```
Jerry Avins wrote:

> Moreover, it needn't be as complex a signal as speech. A single sinusoid
> modulating signal will make symmetric sidebands.

Well. If there are the integer ratios between the frequencies, the FM
spectum may not be symmetrical even for the pure sinusoidal modulation.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```Randy Yates wrote:
> "neville.jarvis@gmail.com" <neville.jarvis@gmail.com> writes:
>
>> Hi Randy,
>
> Hi Neville,
>
>> I was not aware that the spectrum of an FM signal was asymmetric. All
>> the spectrums I have seem show symmetry. However the modulating
>> signals were simple sinusoids.
>
> Note that when I said "symmetric," I meant "symmetric about the carrier"
> and not "symmetric about DC."
>
>> So is it the case then, that an a carreir that has its modulated by an
>> actual speech signal or an audio signal will have asymmetry in its
>> spectrum?
>
> Yes.

Moreover, it needn't be as complex a signal as speech. A single sinusoid
modulating signal will make symmetric sidebands. It is hard to find a
pair of distinct sinusoids that do.

>> On a final note, are they are any naturally occuring signals that have
>> asymmetric spectrum eg speech ?
>
> A non-zero DC level (assuming the transmit signal path responds to
> DC) will generate an asymmetrical output, namely, a tone at one
> frequency corresponding to the magnitude of the DC level and the
> modulation index.

Jerry
--
Engineering is the art of making what you want from things you can get.
&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
```
```"neville.jarvis@gmail.com" <neville.jarvis@gmail.com> writes:

> Hi Randy,

Hi Neville,

> I was not aware that the spectrum of an FM signal was asymmetric. All
> the spectrums I have seem show symmetry. However the modulating
> signals were simple sinusoids.

Note that when I said "symmetric," I meant "symmetric about the carrier"

> So is it the case then, that an a carreir that has its modulated by an
> actual speech signal or an audio signal will have asymmetry in its
> spectrum?

Yes.

> On a final note, are they are any naturally occuring signals that have
> asymmetric spectrum eg speech ?

A non-zero DC level (assuming the transmit signal path responds to
DC) will generate an asymmetrical output, namely, a tone at one
frequency corresponding to the magnitude of the DC level and the
modulation index.
--
%  Randy Yates                  % "So now it's getting late,
%% Fuquay-Varina, NC            %    and those who hesitate
%%% 919-577-9882                %    got no one..."
%%%% <yates@ieee.org>           % 'Waterfall', *Face The Music*, ELO
```
```Hi Randy,

I was not aware that the spectrum of an FM signal was asymmetric. All
the spectrums I have seem show symmetry. However the modulating
signals were simple sinusoids.

So is it the case then, that an a carreir that has its modulated by an
actual speech signal or an audio signal will have asymmetry in its
spectrum?

On a final note, are they are any naturally occuring signals that have
asymmetric spectrum eg speech ?

Neville

On Jul 5, 2:25 am, Randy Yates <y...@ieee.org> wrote:
> Neville <digitafil...@gmail.com> writes:
> > For FM demodulation, on the face of it, it appears that demodulating
> > it using a real baseband and is no different from using a complex
> > baseband. The end result is the demodulated baseband.
>
> Hi Neville,
>
> If by "baseband" you mean "signal centered at DC," then there is,
> in general, no such thing as a "real baseband" FM signal. The
> reason is that the FM spectrum is, in general, asymmetrical, so
> when it is translated to baseband the result is necessarily complex.
>
> > So what are the advantages of demodulating FM using a complex baseband
> > over a real baseband signal
>
> One advantage is that the sample rate can be made much lower. For
> example, if you had a real FM signal a 100 kHz bandwidth centered at
> 200 kHz, you'd have to sample at >600 kHz. However, a complex baseband
> form of the same signal only requires a sample rate of >50 kHz (the
> spectrum of the signal is accommodated by the "complex" bandwidth from
> -50 kHz to +50 kHz).
>
> Another advantage, if you call it that, is that you have the
> analytical form of the signal directly, i.e., you can find the phase
> of a sample directly from the complex sample as arctan(im/re).
> --
> %  Randy Yates                  % "Maybe one day I'll feel her cold embrace,
> %% Fuquay-Varina, NC            %                    and kiss her interface,
> %%% 919-577-9882                %            til then, I'll leave her alone."
> %%%% <y...@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO  http://home.earthlink.net/~yate

```
```On Jul 5, 2:25 am, Randy Yates <y...@ieee.org> wrote:
> Neville <digitafil...@gmail.com> writes:
> > For FM demodulation, on the face of it, it appears that demodulating
> > it using a real baseband and is no different from using a complex
> > baseband. The end result is the demodulated baseband.
>
> Hi Neville,
>
> If by "baseband" you mean "signal centered at DC," then there is,
> in general, no such thing as a "real baseband" FM signal. The
> reason is that the FM spectrum is, in general, asymmetrical, so
> when it is translated to baseband the result is necessarily complex.
>
> > So what are the advantages of demodulating FM using a complex baseband
> > over a real baseband signal
>
> One advantage is that the sample rate can be made much lower. For
> example, if you had a real FM signal a 100 kHz bandwidth centered at
> 200 kHz, you'd have to sample at >600 kHz. However, a complex baseband
> form of the same signal only requires a sample rate of >50 kHz (the
> spectrum of the signal is accommodated by the "complex" bandwidth from
> -50 kHz to +50 kHz).
>
> Another advantage, if you call it that, is that you have the
> analytical form of the signal directly, i.e., you can find the phase
> of a sample directly from the complex sample as arctan(im/re).
> --
> %  Randy Yates                  % "Maybe one day I'll feel her cold embrace,
> %% Fuquay-Varina, NC            %                    and kiss her interface,
> %%% 919-577-9882                %            til then, I'll leave her alone."
> %%%% <y...@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO  http://home.earthlink.net/~yatescr

```
```Randy Yates wrote:
> Jerry Avins <jya@ieee.org> writes:
>
>> Randy Yates wrote:
>>
>>   ...
>>
>>> [I]f you had a real FM signal a 100 kHz bandwidth centered at
>>> 200 kHz, you'd have to sample at >600 kHz. However, a complex baseband
>>> form of the same signal only requires a sample rate of >50 kHz (the
>>> spectrum of the signal is accommodated by the "complex" bandwidth from
>>> -50 kHz to +50 kHz).
>> But each complex sample is equivalent to two real samples. In terms of
>> bits/sec, that works out to be the same. (A corollary of the No Free
>> Lunch theorem.) Am I missing something?
>
> Your statement is correct, but there may be more important
> considerations than "bits/sec."
>
> For example, A/D converter cost may be non-linear and two
> low-frequency A/Ds may be cheaper than one fast one.

That makes sense. (At least, I understand it.)

> Along similar lines, a low-performance processor such as a TI MSP430
> series may be usable at the low sample rate while a DSP or higher-cost
> processor would be required at the higher sample rate.

That eludes me. The same number of samples are to be processed in the
same time. Where is the saving?

Jerry
--
Engineering is the art of making what you want from things you can get.
&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
```
```glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:

> Randy Yates wrote:
>> Jerry Avins <jya@ieee.org> writes:
> (snip on complex sampling)
>
>>>But each complex sample is equivalent to two real samples. In terms of
>>>bits/sec, that works out to be the same. (A corollary of the No Free
>>>Lunch theorem.) Am I missing something?
>
>> Your statement is correct, but there may be more important
>> considerations than "bits/sec."
>
>> For example, A/D converter cost may be non-linear and two
>> low-frequency A/Ds may be cheaper than one fast one.
>
> If you are careful, you can use two A/Ds and alternate the
> samples between them.  There are some complications due to
> the possible differences in linearity between them.
> I don't know that complex sampling removes those problems.

That's a good point, but you still have the same input bandwidth
requirement when you stagger-sample, whereas with a complex sampler

Applied Signal Technology was building a flexible demod that admitted
a 130 MHz bandwidth utilizing complex A/Ds running at 130 MSamples/sec
... in 1989! There was no such thing as a 260 MHz converter back then.
--
%  Randy Yates                  % "Ticket to the moon, flight leaves here today
%% Fuquay-Varina, NC            %  from Satellite 2"
%%% 919-577-9882                % 'Ticket To The Moon'
%%%% <yates@ieee.org>           % *Time*, Electric Light Orchestra
```
```glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:
> [...]
> Randy Yates wrote:
>> Along similar lines, a low-performance processor such as a TI MSP430
>> series may be usable at the low sample rate while a DSP or higher-cost
>> processor would be required at the higher sample rate.
>
> It would seem that the total amount of processing would be the same
> or maybe even more for the complex case.

I don't see how. If the intermediate goal is to obtain a complex
sample for subsequent phase determination, then a real signal requires
some operation to obtain the complex signal. That requires extra
cycles. Morever, once that complex signal is obtained, it's running at
a faster sample rate, so more cycles are required to process the
complex sample.

With a complex signal, you're done as soon as you fetch the sample
from the converters, and the samples are coming in more slowly.
--
%  Randy Yates                  % "So now it's getting late,
%% Fuquay-Varina, NC            %    and those who hesitate
%%% 919-577-9882                %    got no one..."
%%%% <yates@ieee.org>           % 'Waterfall', *Face The Music*, ELO
```
```Randy Yates wrote:
> Jerry Avins <jya@ieee.org> writes:
(snip on complex sampling)

>>But each complex sample is equivalent to two real samples. In terms of
>>bits/sec, that works out to be the same. (A corollary of the No Free
>>Lunch theorem.) Am I missing something?

> Your statement is correct, but there may be more important
> considerations than "bits/sec."

> For example, A/D converter cost may be non-linear and two
> low-frequency A/Ds may be cheaper than one fast one.

If you are careful, you can use two A/Ds and alternate the
samples between them.  There are some complications due to
the possible differences in linearity between them.
I don't know that complex sampling removes those problems.

> Along similar lines, a low-performance processor such as a TI MSP430
> series may be usable at the low sample rate while a DSP or higher-cost
> processor would be required at the higher sample rate.

It would seem that the total amount of processing would be the same
or maybe even more for the complex case.

-- glen

```