**4.2 Cortical manifestation of PaSH-FFT**

The next step in accounting for global convolution in cortical circuitry is to explore how PaSH-FFT manifests itself in cortical architecture. The raw data, at the lowest level of PaSH-FFT, are complex numbers that must be multiplied and added. The first issue to address is to justify our assumption that the operations being performed by a neuron could be represented as complex arithmetical operations on complex numbers. Specifically, PaSH-FFT requires that a neuron can be regarded as a mechanism capable of representing and manipulating complex numbers in accordance with the arithmetical operations of addition and multiplication. There are many ways in which to interpret neuronal function in terms of complex addition and multiplication. The model presented by (MacLennan, 1999) is adequate for the purposes of this paper, where it is shown how the representation of complex numbers can be encoded as the rate and relative phase of axonal impulse. From this encoding, complex multiplication is associated with the strength of a synaptic connection as the signal passes through it and complex addition is associated with the summing of the neuronal inputs. Thus at the lowest level of computation in our model, we assume that the operation being performed by a neuron can be represented as complex addition and multiplication.
