Frequency domain analysis of wraparound error in fast convolution algorithms

Fast algorithms exist for computing cyclic convolutions. To obtain the linear convolution required for an FIR filter, the data records must be overlapped by at least L - 1 points, where L is the length of the filter impulse response. If the overlap is too small, wraparound error occurs. This error transforms a linear time-invariant filter into a periodic time-varying filter, whose output is periodically nonstationary for a wide-sense stationary input. The first part of this paper contains a review of the frequency domain theory of periodic filters and processes, in the second part of the paper the theory is applied to the specific periodic filter that results from wraparound error in fast convolution algorithms.