Hello, I have a question concerning the conversion of a stereo recording to ambisonics. In the Wireless World of 1977 articles there are equations for the conversion of stereo to W,X,Y equivalent signals. The use of j*Diff term doesn't seem to make sense. As I found no background info on them, maybe someone in the group has.
The WW1977 article states: W=0.71*Sum-0.291*j*Diff X=0.71*Sum+0.291*j*Diff Y=0.583*Diff where Sum=L+R and Diff=L-R. I was puzzled with the addition of the j*Diff, so I tried to find some mathematical support for it. The reasoning I did is as follows: 1. As W,X,Y are a representation of a supposed plane wave with amplitude S coming from a certain angle phi (phi=0 if straight ahead), we need to suppose a analoguous encoding for stereo. I supposed a the sin-like law of encoding f.e.: (L-R)/(L+R)=sin(phi)/sin(30) if loudspeakers are placed at -30 and 30 degrees. 2. As a starting point a naive conversion of the L,R signals (projection of L,R on X,Y) to ambisonic-like format gives: W=Sum X=Sum*cos(30) Y=Diff*sin(30) If we write Sum and Diff in relation to the supposed direction encoding in (1) as function of S and phi, then W=S X= S*cos(30) Y= S*sin(phi) X is independent of the direction, Y correctly encodes the direction neatly. X is only correct for the center direction (phi=0) but for all other directions the magnitude of the encoded vector is to large (sqrt(X²+Y²)>W). 3. The adding of the j*Diff terms makes af first sight everything even worse, it makes the magnitude of X and W higher and it also introduces a phase differences between X,Y and W which is in theory not possible if one encodes a plane wave directly. The only reason I could think of is that by introducing phase differences once you construct the loudspeaker signals by adding weighted versions of the W, X and Y signal together these phase differences introduce lower amplitudes (than adding signals in phase). I did not go through with this calculation yet. So if someone have some idea's on it, Johan -- -------------- next part -------------- An HTML attachment was scrubbed... URL: <https://mail.music.vt.edu/mailman/private/sursound/attachments/20120720/47cd95a9/attachment.html> _______________________________________________ Sursound mailing list [email protected] https://mail.music.vt.edu/mailman/listinfo/sursound
