Quantization Error for Vectocardiogram Spherical Coordinates

The vectocardiography (VCG) is the methodological extension of electrocardiography (ECG) that allows three-dimensional imaging of the cardiac electrical field. For the lack of the sufficient technological support it was underestimated for years, and currently comes back to the clinical practice thanks to the use of numerically performed spatial transforms. The VCG signal is usually acquired with use of the pseudoorthogonal Frank leads and stored as three simultaneous signals corresponding to three Cartesian coordinates XYZ. This paper addresses the issue of the alternative format for the VCG storage: the Spherical Coordinates. The Spherical Transform is fully reversible in theory, but due to the use of floating-point functions the subsequent quantization affects the perfect reconstruction property. The most important question investigated by the author is the signal distortion level as a function of the wordlength used. With use of a numerical experiment, the reconstruction error was estimated globally for the whole heartbeat and locally in P, QRS and T waves. As it were expected beforehand, the spherical transform features the data compression because, in general, the angular variables do not need to be represented as precisely as the magnitude.