  The integrate and fire converter transforms an analog signal into 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 signal processing operations of
addition, multiplication, and convolution of analog signals using their pulses
train representations is explored. Theoretical framework to perform signal
processing with pulse trains imposing minimal restrictions is derived, and
algorithms for online implementation of the operators are developed.
Performance of the algorithms in processing simulated data is studied. An
application of noise subtraction and representation of relevant features of
interest in electrocardiogram signal is demonstrated with mean pulse rate less
than 20 pulses per second.
