On-line Approach for Fast Convolution over Sensor Networks
On-line Approach for Fast Convolution over Sensor Networks

Summary/Abstract: It is assumed that at some time moment, in wireless sensor networks the new set of current samples of input and system impulse response enter a digital memory replacing the previous samples. It is urgent for each new sample or for a small part of new samples to update a convolution as well. Therefore, a recursive fast convolution algorithm is proposed here to solve a linear filtering problem for a nonstationary system. The calculation operations are reduced because most columns of Fourier code matrices and respective rows of the right-hand side vectors were deleted for equal previous and current samples. An example with the ordinary and modified 8-point Fourier code matrices is presented for a nonstationary linear system. The amounts of operations, necessary for recursive and fast Fourier transform algorithms, are calculated. Results are discussed, and the conclusion is given.

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