On the design of inphase and quadrature filters for delay compensation

This correspondence addresses the problem of simultaneous separation and delay compensation of the inphase and quadrature components of a signal. The proposed approach is based on the notions of combined filter and common filter. The combined filter for a given delay has twice as many coefficients as the inphase filter or the quadrature filter. The coefficients of the combined filter for an arbitrary delay are computed as a linear combination of two members of a set of discrete delay filters. Finally, to further simplify the design, all the discrete delay filters in the above mentioned set are polyphase components of a long filter called the common filter. The length of the common filter is determined by the requirement that all possible linear combinations of adjacent coefficients result in a filter that meets the desired passband and stopband ripple specifications. This method, which requires the design of one single filter, has much less computational complexity than extant approaches which require the design of a filter for every specified delay. The design of a product detector for an agile beamformer motivates the proposed method