Zoom H2
Zoom H2 Recorder
The Zoom H2 is a pocket-sized recorder with four microphone capsules on top. These are arranged as two pointing forwards at 90 degrees apart, and two facing backwards separated by 120 degrees. Recordings are saved onto an SD card, for which 4GB capacity is easy to come by, and 8GB is now available. The device can record a stereo file from either the front or the rear capsule pair, or their combination, or it can record both pairs into two stereo files simultaneously for quad surround. It also has a range of sample rates available. An intriguing aspect is that it only has three spot settings for the sensitivity (a continuous level control that appears to be available is only a digital gain after the ADC, and so has no influence on clipping). The device will only write 2GB files; longer recordings can be made, and the device will swap to a new file - but there will be a substantial gap of several seconds while it organises this.Quad to B-format
It is a rather obvious question whether we can make use of this device to record horizontal B-format, or rather, whether we can extract horizontal B-format from its quad output. I have decided to try, but my approach is thoroughly simplistic: I just assume that the capsules are perfectly coincident, and that they are ideal cardioids. Given these assumptions, it is quite easy to work out a combinations of sums and differences at varying levels that will cancel out the unwanted signals and leave each of the required components. It would be even easier if all the capsules were at right angles; it might even be worth trying to modify the device to make this so, for greater symmetry in particular - but I haven't.A bit of Maths
Consider each cardioid Lf, Rf, Lb, and Rb, to be a perfect combination of an omni signal and a figure of 8 signal of the same level; assume they are coincident (fine up to about 5kHz). Simple trigonometry and the B-format definition show us that these correspond to B-format signals as follows:
Lf = W * sqrt(2) + X * cos(45) + Y * cos(45) = 1.414W + 0.707X + 0.707Y
Rf = W * sqrt(2) + X * cos(45) - Y * cos(45) = 1.414W + 0.707X - 0.707Y
Lb = W * sqrt(2) - X * cos(60) + Y * cos(30) = 1.414W - 0.5X + 0.866Y
Rb = W * sqrt(2) - X * cos(60) - Y * cos(30) = 1.414W - 0.5X - 0.866Y
We can cancel Y by summing left and right to give Front and Back:
F = Lf + Rf = 2*1.414W + 1.414X
B = Lb + Rb = 2*1.414W - X
So cancelling out the X and W terms in turn, we get:
W = (F / 1.414 + B) / (2 + 2*1.414)
X = (F - B) / (1.414 + 1)
To get Y, we can take the differences of the two microphone pairs, thus cancelling both W and X components, to give two sideways figure of eights consisting only of Y:
Yf = Lf - Rf = 1.414Y
Yb = Lb - Rb = 1.732Y
It is a matter of taste how one combines these to get a final consensus of the Y value; I give them equal weight, which means that the capsules pointing more to the sides contribute more - this seems fair:
Y = (Yf + Yb) / (1.414 + 1.732)
You can see these values (taken to a completely unjustified 6 decimal places) in the Plogue Bidule setup shown below (AudioMulch is not suitable for this, as it doesn't have the maths functions).
Samples & Comparisons
Coming sometime, I expect. It's just occurred to me that before I publish them I need to check which way round the rear signals are in the file...
