Weighted Sliding DFT (1 of 3)

Digital Engines has developed a powerful new architecture for sliding signal processing. The filter shown below produces one Hamming-weighted DFT output using only 16 real multiply operations and 17 real addition operations. The process requires no convolution, and it is compatible with just about any amplitude weighting function.

The filter works by splitting the weighted sliding DFT into parts and applying a modified version of the classical sliding DFT filter to each part. Adding the parts together creates one amplitude-weighted DFT output. A cascade of N of these filters generates an N-point sliding DFT, where N is the length of the sliding window that moves along the input data stream.

Computing an N-point weighted DFT requires executing the left half of the filter one time, and the right half of the filter N times. Ignoring the one-off operations on the left side of the filter, the total number of complex multiply operations needed for an N-point DFT is thus on the order of 3N.

The amplitude weighting process occurs within the sliding DFT operation so that each output contains the correct frequency-domain weighting coefficients without the need for convolution. The methodology is by no means limited to the Hamming function. It is compatible with nearly all of the weighting functions implemented in practical signal processing systems.