# FM Demodulation - Complex baseband versus Real baseband

Started by July 5, 2007
```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

```
```Neville <digitafilter@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."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO
```
```Randy Yates <yates@ieee.org> writes:

> you'd have to sample at >600 kHz.

Wups! I made an arithmetic error: that should be ">500 kHz."
--
%  Randy Yates                  % "Bird, on the wing,
%% Fuquay-Varina, NC            %   goes floating by
%%% 919-577-9882                %   but there's a teardrop in his eye..."
%%%% <yates@ieee.org>           % 'One Summer Dream', *Face The Music*, ELO
```
```Randy Yates <yates@ieee.org> writes:
> [...]
> 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).

I've got to stop posting first thing in the morning before my first
cup of coffee...

SORRY! The baseband sample rate would have to be >100 kHz.

So the real FM signal example I gave required a sample rate of >500 kHz
and the complex baseband signal requires >100 kHz.

To be more fair, we could move the real baseband signal center
frequency down to 50 kHz, so that the highest frequency in the signal
spectrum is at 100 kHz (the FM spectrum runs from 0 to 100 kHz), and
therefore the real sample rate would have to be 200 kHz.
--
%% Fuquay-Varina, NC            %       'cause no one knows which side
%%% 919-577-9882                %                   the coin will fall."
%%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
```
```Neville 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.

Assuming you work out a way to demodulate, indeed.

> 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

Demodulating involves computing phase or phase difference. a complex
representation is clearly called for.

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;
```
```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?

...

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;
```
```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.

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.
--
%  Randy Yates                  % "She tells me that she likes me very much,
%% Fuquay-Varina, NC            %     but when I try to touch, she makes it
%%% 919-577-9882                %                            all too clear."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO
```
```
Neville 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

The complex baseband allows for the lower sample rate, hence it takes
less of computation.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```
Jerry Avins wrote:

>
> But each complex sample is equivalent to two real samples. In terms of
> bits/sec, that works out to be the same.

In the ideal case, yes. In the case of FM demodulation, the real
sampling has to be faster and there are the other inconveniences, too.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```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

```