Naslov
Design of multiplierless decimation filters based on amplitude sharpening and compensation

Autori
Dudarin, Aljoša ; Molnar, Goran ; Vučić, Mladen

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, prošireni sažetak, znanstveni

Izvornik
Abstract Book of Third International Workshop on Data Science / - Zagreb, 2018, 15-16

Skup
3rd International Workshop on Data Science (IWDS 2018)

Mjesto i datum
Zagreb, Hrvatska, 16.10.2018

Vrsta sudjelovanja
Poster

Vrsta recenzije
Domaća recenzija

Ključne riječi
multirate systems ; FIR filter design ; computational efficiency ; digital down conversion ; software radio receivers

Sažetak
Cascaded-integrator-comb (CIC) decimation filters are the simplest multiplierless filters supporting high sample-rate conversion factors. They find their applications in digital down converters. However, a high-order CIC filter introduces a high passband droop, which is intolerable in multi-standard receivers. The droop can be reduced by connecting a linear-phase finite-impulse-response (FIR) filter called CIC compensator in cascade with the CIC filter. Since the CIC filters are multiplierless, compensators with multiplierless structures are preferable. In the processing of wideband signals, the CIC filter is often incapable of meeting the requirement for high alias rejection. To improve the CIC filter response, various techniques are developed. Most efficient one is polynomial sharpening developed by Kaiser and Hamming. They proposed the polynomial amplitude-change function that is obtained by imposing flatness at the points (0, 0) and (1, 1). Such a polynomial has integer coefficients which are obtained by using analytic expressions. Initially, this technique was used for the sharpening of symmetric FIR filters in a non-recursive form. Later, a well-established structure arose from the polynomial sharpening of the CIC response implementing so-called sharpened CIC (SCIC) filter. Recently, Colman proposed sharpening with the Chebyshev polynomials of the first kind in order to separate each multiple zero of the higher-order CIC in an equiripple stopband. Such a separation of the zeros results in an amplitude response with a very high alias rejection. However, the obtained Chebyshev SCIC filters are multiplierless only for particular passband edge frequencies. Here, we present our work in the design of multiplierless decimation filters based on sharpening and compensation. To obtain multiplierless SCIC filters exhibiting very high alias rejection, the optimization-based design using the minimax sharpening of the folding bands over the sums of signed-power-of-two (SPT) polynomial coefficient space is used. In the optimization, the number of SPT terms for each coefficient is specified. To find the optimum polynomial coefficients, a global optimization technique based on the interval analysis is employed. Such an approach brings significant reduction in filter complexity compared to the Chebyshev sharpening. Presented minimax SCIC filters have a very high alias rejection. However, such rejection is paid by monotonically decreasing passband response with a rather high droop, leaving open the possibility of its improvement. Similar to the CIC compensation, the SCIC passband can be improved by connecting an FIR compensator called SCIC compensator to the output of the SCIC decimation filter. Since the SCIC passband response is monotonically decreasing, the maximally flat compensation using a linear-phase compensator is appropriate for the compensation. A straightforward method for the design of SCIC compensators with an odd number of coefficients which is based on the maximally flat error criterion is developed. In the design, the maximally flat approximation is performed at zero frequency. To obtain compensator coefficients, the system of linear equations is formed. The coefficients generally take real values. However, for the SCIC filters incorporating integer or SPT polynomial coefficients, and whose decimation factors are expressed as powers of two, the coefficients of corresponding maximally flat compensators are integers or SPT representable. To obtain higher compensation capability in wider passband than in the case of maximally flat compensation, the design of SCIC compensators based on the minimization of the maximum passband deviation over the SPT coefficient space is developed. In such minimax design, all compensator coefficients are set as free variables. The complexity of the minimax compensators is regulated by specifying the total number of adders in the structure. For a low number of coefficients, the optimization problem is simple. Therefore, the optimum coefficients are obtained by the exhaustive search.

Izvorni jezik
Engleski

Znanstvena područja
Elektrotehnika, Računarstvo

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