Software Correction of Measured Pulse Data

Abstract

Generally, the fundamental concern in the software correction of measured pulse waveform data is the solution of an illposed deconvolution problem which arises when one (or both) of the known waveforms is (are) corrupted by errors due to interference, noise, instrumentation drift, etc. The convolution equation for a measurement system is $$ y(t) = \int\limits_o^t {x(\lambda )h(t - \lambda )d\lambda } $$ (1) , where the casual waveforms h(t), x(t), and y(t) are the measurement system impulse response, input, and output waveforms, respectively [1], Fig. 1. When one of the integrand functions is unknown, while the other two functions are known, the equation becomes the deconvolution integral equation for the unknown waveform. Solution of an ill-posed deconvolution problem is obtained by signal processing or filtering and at most yields an estimate for the unknown waveform. The filtering is necessary to yield a stable and physically consistent result.