High-resolution alignment of action potential waveforms using cubic spline interpolation

A cubic spline interpolation technique is applied to the problem of aligning action potential waveforms. Interpolation is an attractive alternative to sampling at many times the Nyquist rate in order to reduce errors caused by asynchronous sampling of rapidly changing waveforms. Alignment is achieved by locating the peak of the interpolated waveform, which can be found by solving a quadratic equation. The waveform is then reconstructed for comparison with existing templates. The technique was tested using simulated noisy, randomly arriving waveforms, the interpolated signal and alignment time errors being computed as functions of the signal/noise ratio. The spline technique is superior in accuracy to sampling at eight-times the Nyquist rate and is comparable to a Fourier-transform-based interpolation algorithm. It is computationally efficient, requiring approximately five multiplications per sample point. The interpolation concept is extended to the principal component technique for separation of action potential waveforms. The energy function is interpolated and used to align the waveforms, after which the interpolated coefficients can be used for high speed classification. The technique shows an improvement in both alignment error and effective signal/noise ratio in comparison with sampling or interpolation to a voltage peak.