Theory and Algorithms for Pulse Signal Processing

The integrate and fire converter (IFC) transforms an analog signal into a train of biphasic pulses. The pulse train has information encoded in the timing and polarity of pulses. While it has been shown that any finite bandwidth analog signal can be reconstructed from these pulse trains with an error as small as desired, there is a need for fundamental signal processing techniques to operate directly on pulse trains without signal reconstruction. In this paper, the feasibility of performing online the operations of addition, multiplication, and convolution of analog signals using their pulses train representations is presented. The theoretical framework to perform signal processing with IFC pulse trains imposing minimal restrictions is derived, and algorithms for online implementation of the operators is developed. The performance of the proposed algorithms is studied by quantifying the variations in instantaneous occurrence of pulses. Comparisons are performed with digital processing of reconstructed pulse trains. Moreover, an application of noise subtraction and representation of relevant features of interest in electrocardiogram signal is demonstrated with a sparse data rate of less than 20 IFC pulses per second, and an absolute error in heart rate of 0.16 +/- 0.18 bpm.