Deutsche Welle: Radio Training Centre

In stereophony, correlation means the interrelationship between the signals of the left and right channels. The size of this relation is the correlation degree.
If we compare two sine oscillations of the same frequency and phase relation with each other, we see that both have the same tendency (fig.37):

During the period t = 0....1 both oscillations rise from 0 to their maximal positive value; during t = 1....2 both fall from their maximal positive value to 0; during t = 2....3 both fall from 0 to their maximal negative value, etc..
Mathematically seen, both oscillations in fig. 37 show the same positive behavior:

In our example, this relation lasts for as long as we examine it. In mathematical terms this means the value 1. If the same tendency exists only during a part of the examination time, the value will also be only a part of 1.

If two oscillations are identical in frequency and phase, they have the correlation degree +1.

The two oscillations in fig. 38 have the same frequency, but a phase difference of 180°. These two signals are also correlated, but they show an opposite, mathematically negative, behavior.

During t = 0...1 the left oscillation rises to the positive peak value and the right one falls to the negative peak value; during t = 1...2 the left one falls to 0 and the right one rises from the negative peak value to 0, etc.. Since this opposite behavior continues permanently, the two oscillations have the correlation degree -1.

During t = 0....1, which means during the first period of signal I, signal II has the same tendency, except the small part at the end of it's period. Consequently, the correlation degree for this short time is almost +1.

By period 10 both oscillations have diverged so much that the phase difference already reaches 180°, meaning that the following period (11) of signal I has the opposite tendency as signal II; thus the correlation degree for this moment is about -1.

Since this phase shift happens continuously, the correlation degree also changes continuously from +1 to -1.

If we determine the mean value of the correlation degree over a longer time, the result will be a value of 0.

For almost all, in sound recording techniques interesting signals we can state that:

According to this, a correlation degree meter has to indicate 0 for different frequencies in the left and right channels. For identical frequencies with the same phase in both channels it has to indicate +1; and for identical frequencies with opposite phases it has to indicate -1. The indication has to be independent of the corresponding levels; it should not vary over the whole dynamic range.

Example	L	R	r
flute middle			+1
flute half-left			+1
flute middle + piccolo left (weak)			+0,8
flute half-right + piccolo left (loud)			+0,2
flute left			0
flute middle wrong polarity			-1
flute half-left wrong polarity			-1

In the preceding chapter we pointed out the demands on a correlation degree meter. The basic function of a correlation degree meter, that is to measure the phase difference between two signals, is fulfilled by a synchronous rectifier. But there are additional functional groups in the complete correlation degree meter.
So a precise reading is only possible if sufficiently big and constant signals are available at the inputs of the synchronous rectifier. That's why the signals of both stereo channels have to first be amplified and then rectified.
The amplified and rectified L-signal is used as an indicator signal, whereas the amplified and rectified R-signal is used as a switch signal.
The synchronous rectifier delivers a pulsating dc-voltage that is first integrated and then lead to the indicating instrument.

What happens if a correlation degree meter is mistakenly connected to the MS-channels?

1) Sound source from the right: R = +1 and L = 0	M = L + R = +1
	S = L - R = -1
Antiphase signals have a correlation degree of -1

2) Sound source from middle: R = +0,5 and L = +0,5	M = L + R = +1
	S = L - R = 0
If one of both signals is zero, also the correlation degree is zero.

3) Sound source from the left: R = 0 and L = +1	M = L + R = +1
	S = L - R = +1
In phase signals have the correlation degree +1

This shows that the correlation degree can be measured only between the L and R channels.

The stereoscope has become more common for display and control of stereo signals in recent years. It displays phase, direction and intensity of stereo signals on an oscilloscope tube. The basic circuit diagram is shown in fig. 40.

In this example the input of the stereoscope is connected to an LR-signal of +6 dBm. For a higher accuracy of reading at smaller input levels, or for the head alignment of tape recorders with the help of an alignment tape, the input sensitivity can be increased by 10 dB. If the input level falls short of a level of -30 dB, the electron beam of the tube is blanked to avoid a burning-in of an ion spot on the screen during modulation pauses. The blanking threshold is variable. Also, focus and intensity of the beam can be adjusted externally.
Compared to a normal oscilloscope, the tube of the stereoscope is turned by 45°.

	Signals in one channel:
Fig. 41-1
	L=1 (=left)	L=1/2 (=left)	R=1 (=right)

	Coherent signals:
Fig. 41-2
	L=1 R=1 (=middle)	L=1 R=1/2 (=half left)	L=1/2 R=1 (=half right)

	Incoherent signals:
Fig. 41-3
	(mainly left)	(full basis)	(mainly right)

	Incompatible signals:
Fig. 41-4
	L=1 R=-0,5	L=1 R=1	L=1 R=-1	+ Incoherent signal
	L=1 R=-0,5	L=1 R=1
Stereo:	outside basis	diffuse	outside basis	mainly left
Mono:	low level	no signal	no signal	audible

Correlation degree meter	Stereoscope

Fig. 42-1 Signal in one channel only - left or right


Fig. 42-2 Identical signals in both channels


Fig. 42-3 Correct stereo signal (compatible)


Fig. 42-4 Phase shifted parts in the stereo signal (not compatible)

1.	Different displays with a 1 kHz test signal: M-Signal (mono) only left channel modulated only right channel modulated M-Signal, one channel antiphase	fig. 43.1	fig. 43.2
2.	Full stereo signal with big basis width.
3.	Stereo signal with soloist group half-left. The small soloist signal shows a recording with mono mike.	fig. 43.3	fig. 43.4
4.	Stereo signal with stereo soloist signal of wrong polarity (antiphase). Soloist signal is cancelled at mono replay.
5.	Pseudo-stereo signal. (Mono signal is converted into pseudo-stereo signal with help of different filters).	fig. 43.5	fig. 43.6
6.	Limiters in the stereo- or soloist channel do not have the same working characteristics. Left channel is limited earlier than right channel.

Relation between left and right channels		corr. degree
different frequencies		0
identical frequencies	in phase	+1
	in anti-phase	-1