PARALLEL COMPUTING WITH SPIN WAVES - Bio-Inspired and Nanoscale Integrated Computing - page 230

mesh. We explain two methods for implementing the shifting operation on one
row of the spin-wave reconfigurable mesh. In both methods, first the elements of
the list are mapped to the processing nodes.
In the first method, the shift operation is performed by using the spin-wave
switches. As explained in the previous section, spin waves can be forced in one
direction by using the spin-wave switches. To implement shifting to the right, all
the nodes first turn off their left switch and send out a spin-wave with an
amplitude equal to their data while their right switch is open. This forces the waves
to be directed to the right. As soon as the nodes send their waves, they
immediately open their left switch and close their right switch. This allows each
node to receive the spin wave from its left neighbor, while blocking the channel
and preventing this received wave to go through to the next node on the right hand
side. Similarly, shifting to the left can be implemented by forcing the waves to the
left and not letting the wave pass through the immediate neighboring node. This
method can not be used in a crossbar or fully interconnected cluster, since there
are no switches between two adjacent nodes.
No spin-wave switches are used as the second method for implementing the
shift operation. The nodes are required to dynamically tune their frequency. In
this method a distinct frequency is assigned to each node as its receiving
frequency. In addition, each node's sending frequency is tuned on its right
neighbor's assigned frequency. For instance, the sending frequency of node x i is
tuned on f i 1 . Since these data transmissions between adjacent nodes are done at
different frequencies, all can be performed simultaneously. This method can be
used in implementing the shift operation on the reconfigurable mesh, as well as the
crossbar and fully interconnected cluster.
One of the applications of the shifting operation is in implementing a spin-
wave finite impulse response (FIR) filter module. An FIR filter is one of the
primary types of filters used in digital signal processing [6]. An FIR filter works by
multiplying an array of the most recent n data samples by an array of constants
(called the tap coefficients), and summing up the elements of the resulting array.
The filter then inputs another sample of data, which causes the oldest piece of data
to be discarded, and repeats the process [7].
FIR filters are implemented using a finite number M delay taps on a delay line
and M computation coefficients to compute the algorithm (filter) function.
Figure 8.3 illustrates the block diagram of an FIR filter with M taps [8]. In the
FIR filter, the output at time n, y(n), is computed as the summation of inputs
multiplied by the tap coefficient as illustrated by the following equation:
y ð n Þ¼ b 0 x ð n Þþ b 1 x ð n 1 Þþþ b M x ð n M Þ:
To implement a spin-wave FIR filter, we use the superposition property of the
waves to realize the summation function and we employ spin-wave switches to
implement the shifting operation. First, each coefficient is stored in the nodes with
respect to the node's index. In the next step, each processing node computes the
multiplication of its fixed coefficient and the input mapped to it. All the processing