Abstract
A novel realization of IIR decimation filters is proposed which is based on merged delay transformation. The transformation is derived analytically and can be applied directly to first- and second-order IIR filters. Computational efficiency is enhanced because the current output can be directly computed fromMth old output. The output data rate is decreased byMby mergingMnumber of delay elements in the recursive path. The proposed transformation is applied to higher-order IIR filter by decomposing it into parallel first-order and second-order sections. This transformation not only gives better stability for coefficient quantization but also reduces the requirement on processing clock, for sample, rate reduction. Filtering and down sampling are performed in the same stage. Number of multiplications is reduced by 45% as compared to the conventional IIR filters where all output samples are computed.
Highlights
Large number of decimation filter realizations exist, that are mainly a combination of identical all-pass subfilters [1], polyphase-FIR filters [2, 3], and comb-FIR-IIR filters [4, 5], and so forth
An Nth order IIR filter can be decomposed into N parallel first-order sections with complex coefficients
The output y[n] calculated from original difference equation is compared with the transformed output computed from (2)
Summary
Large number of decimation filter realizations exist, that are mainly a combination of identical all-pass subfilters [1], polyphase-FIR filters [2, 3], and comb-FIR-IIR filters [4, 5], and so forth. This letter proposes a novel technique to realize IIR decimation filter that computes directly the current value of the output without calculating the intermediate outputs. This is possible because with the help of proposed merged delay transformation (MDT), the current output sample becomes dependent only on Mth old output sample and M input samples. An Nth order IIR filter can be decomposed into N parallel first-order sections with complex coefficients. This is not a problem as two first-order sections having complex conjugate coefficients produce real output for a real input sample. The computational efficiency is enhanced due to reduction in number of multiplications and parallel realization
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