Re: OT. FM stereo noise cancellation.
- From: Robert Orban <donotreply@xxxxxxxxxxxxx>
- Date: Wed, 07 May 2008 17:54:31 -0800
In article <DuCTlnMp1DGIFw4v@xxxxxxxxxxxx>, tony@xxxxxxxxxxxx says...
In article <EHMRj.241$b4.53@xxxxxxxxxxxxxxxxxxxx>, Richard Evans
<R.P.Evans.NoSpam@xxxxxxxxxxxx> scribeth thus
davidrobinson@xxxxxxxxxxxxxxxx wrote:
Richard,
I haven't looked at the thread, but the theory is dead simple. FM uses
M/S (mid/side) encoding - where mid is "mono", and side is the
difference between the two stereo channels.
Broadcast:
M=L+R
S=L-R
Decoding:
L=M+S
R=M-S
What you are doing:
mono=L+R = (M+S) + (M-S) = 2M
So what you get out of a stereo receiver by summing the two channels
is exactly the same as what you would get out of a mono receiver (all
other things being equal, inter-channel component tolerances not
withstanding, 15kHz+ content may be different due to filtering / lack
of it).
Cheers,
David.
Yes, exactly.
I'm not actually sure whether I'm supposed to answer this message, as
what you have said is exactly what I already knew. I posted the samples
because people were repeatedly telling me that I was wrong about it, so
naturally in the end I had to prove that I was right.
Richard E.
Come on Bob O if your on channel.. I reckon no one else on this ng has
more experience than U with FM modulation;)....
I believe I posted on this already.
David's quoted post above is correct.
The reason that stereo reproduction is noisier than mono is that the L-R
is coded as a DSB suppressed carrier subcarrier at 38 kHz and the FM
modulation index of the subcarrier region (23 to 53 kHz) of the FM
baseband signal is sibstantially lower than that of the main carrier.
The receiver uses the 19 kHz pilot tone to reconstruct the 38 kHz carrier.
Some radios use a switching demodulator instead of directly decoding the
L-R subcarrier. It is fairly easy to show mathematically that this
produces an identical result to direct decoding and matrixing. I know that
I posted the entire proof of this a few years back, IIRC on
rec.audio.tech. (I couldn't find it in a quick Google search.)
I found a similar post I made (for the encoding equations of a switching
stereo coder), which is as follows:
====
Here is the derivation of the encoding equation for the switching
generator. 'ws' is the sampling frequency. We multiply the left channel by
a squarewave whose frequency is ws and which has maximum value is 2 and a
minimum value of zero. We multiply the right channel by the same
squarewave, but delayed by 180 degrees with reference to ws.
From the Fourier transform of a square wave, we use only the DC term and
the fundamental frequency, COS(ws), in the equation. To justify this, we
know from AM modulation theory that the multiplication will produce
symmetrical sidebands above and below the sampling frequency. Because the
second harmonic of ws is at 76 kHz, the lowest sideband of this harmonic
(assuming 15 kHz audio bandwidth) is 76 - 15 kHz = 61 kHz, so we can
filter this out. Hence, we can ignore the higher harmonics of the square
wave because the baseband lowpass filter will remove the spectrum around
the harmonics. This is why I will only include the DC and fundamental
terms in the equation.
The DC term of our squarewave is 1 and the peak magnitude of the
fundamental is 4/pi. Because the peak magnitude of the fundamental is not
the same as the DC term, we need to add a bit of extra L+R into the output
of the switches to get the ideal FM matrix stereo waveform. Here is the
equation, including the L+R correction term:
L[1+(4/pi)COS(ws)]+R[1-(4/pi)COS(ws)] + [(4-pi)/pi](L+R)
A little algebra shows that this equals
(4/pi)[(L-R)COS(ws)+L+R]
One can now clearly see the matrix representation, with L+R at baseband
and L-R as a double sideband suppressed carrier AM signal generated by
multiplying L-R by COS(ws).
(The 4/pi is a trivial gain factor).
Please note that these equations do not assume a sample-and-hold
operation. Such an operation is unnecessary.
.
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