Modified Principal Component Analysis Based Extrapolated Impulse Response

Extrapolated impulse response (EIR) filter design technique can be used to design finite impulse response (FIR) filter with low hardware implementation complexity. The principal component analysis (PCA) based EIR (PCA-EIR) filter design technique is an efficient EIR technique in view of its simple algorithm implementation and good performance. The basic idea of PCA-EIR technique utilizes the PCA technique to lower the dimension of the coefficient matrix, which is formed from the prototype FIR filter coefficient. A simple yet useful modified PCA-EIR technique is proposed in this paper. The modified PCA-EIR technique keeps the first few column vectors of the coefficient matrix unchanged and uses the PCA technique to reduce the dimension of the matrix that is formed by the rest column vectors. The algorithm implementation complexity of the modified PCA-EIR technique and that of the PCA-EIR technique are almost the same. Provided the frequency response performances are almost the same, the modified PCA-EIR technique can save 3.5%-17.5% multipliers and 25.6%-51.6% adders. Thus, by using our proposed modified PCA-EIR technique, the hardware implementation complexity of the FIR filter can be further reduced.