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FM Demodulation - Complex baseband versus Real baseband

Started by Neville 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 http://home.earthlink.net/~yatescr
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 http://home.earthlink.net/~yatescr
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. -- % Randy Yates % "...the answer lies within your soul %% 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 http://home.earthlink.net/~yatescr
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 http://home.earthlink.net/~yatescr

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. Vladimir Vassilevsky 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. Vladimir Vassilevsky 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