Mono vs Stereo FM Noise

I've seen various figures quoted for the signal-to-noise ratio difference between monophonic and stereophonic FM reception. I decided to write a short computer program to calculate the exact number.

	CONST pi = 3.141593, fc = 1 / (2 * pi * 75E-6)
	DECLARE FUNCTION db (p)

	FOR f = 20 TO 15000             ' Integrate L+R and L-R noise components
	  d = f / fc                    ' Deemphasis corner factor
	  d = 1 + d * d                 ' Deemphasis power factor
	  b = b + f * f / d             ' Accumulate deemphasized baseband noise power
	  u = 38000 + f                 ' USB freq
	  l = 38000 - f                 ' LSB freq
	  s = s + (u * u + l * l) / d   ' Accumulate deemphasized subband noise power
	NEXT f

	PRINT db((b + s / 2) / b / .91 / .91)  ' 2 for no quadrature noise and .91 for 9% pilot

	FUNCTION db(p)
	db = 10 * LOG(p) / LOG(10)
	END FUNCTION

The result is 20.0 dB for a frequency range of 20 to 15000 Hz and a 9% stereo pilot. The figure varies about a tenth of a dB depending on the lower frequency limit and pilot level. If you set the high-frequency limit to 10000 Hz, the S/N difference is 22.0 dB. At 5000 Hz, it is 25.8 dB. The following curves reveal why.

Above its 2122-Hz corner frequency, the 75-µS deemphasis network with its 6 dB per octave rolloff flattens the 6 dB per octave rise of monophonic noise. But stereo noise comes mostly from the L-R subcarrier region where changes in LSB and USB noise levels are roughly complementary, with little rise for the sum. This exposes the deemphasis curve and explains why stereo noise sounds lowpassy.

The calculations assume only that detected composite noise rises 6 dB per octave. This will be true unless the signal is extremely weak and below the FM detector threshold, or extremely strong, where internal noise sources with different spectra may override detector noise.

More is here.

Updated March 7, 2008