  This paper consists of two parts. First, the (undirected) Hamiltonian path
problem is reduced to a signal filtering problem - number of Hamiltonian paths
becomes amplitude at zero frequency for (a combination of) sinusoidal signal
f(t) that encodes a graph. Then a 'divide and conquer' strategy to filtering
out wide bandwidth components of a signal is suggested - one filters out
angular frequency 1/2 to 1, then 1/4 to 1/2, then 1/8 to 1/4 and so on. An
actual implementation of this strategy involves careful local polynomial
extrapolation using numerical differentiation filters. When conjectures
regarding required number of samples for specified filter designs and time
complexity of obtaining filter coefficients hold, P=NP conditionally.
