Ljiljana Milic

Design of multiplierless elliptic IIR filters with a small quantization error

We present a new technique for the design of multiplierless IIR elliptic filters. The multiplierless filter has all multiplication constants implemented with a small number of shifters and adders. The proposed technique is based on sensitivity analysis. An analytical expression for amplitude response sensitivity is derived for the filter structures consisting of two allpass subfilters in parallel. It is shown that the amplitude response sensitivity to some constant x can be expressed as a product of the filter reflectance function and the phase sensitivity of the allpass section that implements the constant. The closed-form expressions for the phase sensitivities of the first- and second-order allpass sections are also developed. It is shown in the paper that the (n+1)/2 most sensitive constants can be directly controlled by the transfer function parameters if the transfer function is derived by the bilinear transformation from an elliptic minimal Q-factors (EMQF) analog prototype. This way, (n+1)/2 multiplication constants can be implemented without quantization, leaving the filter characteristic strictly elliptic. This is achieved for a class of low-noise allpass sections and for the wave lattice digital filter as well. The quantization of the remaining (n-1)/2 less-sensitive constants is performed using the phase-tolerance scheme and phase-sensitivity functions. The proposed design technique is straight-forward and, consequently, very fast. The application is demonstrated on the examples of narrowband, wideband, and halfband filters.

Multirate Filters: An Overview

Multirate filtering techniques are widely used in both sampling rate conversion systems and in constructing filters with equal input and output rates in the case where the use of a conventional method becomes extremely costly. The purpose of this paper is twofold. First, this paper gives a short review on designing proper digital filters that are useful in providing the desired sampling-rate conversion between the output and input signals. Second, this paper shortly reviews on how to apply multirate technolgies as well as complementary filters for constructing digital filters in cases where the implementation of a conventional filter becomes, due to a too huge arithmetic complexity and the effects of finite word length effect, so large that this filter is not possible to construct in practice. In the second case, when using both multirate filtering and complementary filters enable one to share the overall filtering task between several simplified low-order sub-filters that operate at the lowest possible sampling rates and have significantly relaxed design constraints. Due to these facts, the resulting filter has significant reductions in the overall complexity as well in finite word-length effects

Reducing the number of multipliers in the parallel realization of half-band elliptic IIR filters

It is shown in this correspondence that a halfband IIR filter with the poles on the imaginary axis can be derived by the bilinear transformation of an elliptic minimal Q-factors analog prototype. For an odd degree transfer function, the residues at the poles are real or imaginary. Consequently, in the parallel realization, the number of multipliers can be reduced by half.

High speed IIR filters for QMF banks

In this paper, we show that using allpass IIR subfilters and half-band FIR optimal filters from the minimal phase solution it is possible to design a filter which exhibits simultaneously very low passband attenuation, large stopband attenuation, narrow transition region and low arithmetic complexity, and thus high maximal sample frequency. We introduce the closed form relations for the design of fast IIR filters for interpolation, decimation, and QMF banks with perfect magnitude reconstruction. The design is based on the third-order half-band IIR filters and the fifth-order non minimum-phase optimal FIR filters.

Approximate linear phase Hilbert transformer

The IIR realization of the Hilbert transformer require less computations than FIR realizations, but the main disadvantage of the minimum phase IIR realization is the nonlinearity of the phase characteristic. In this paper, we show that using all-pass IIR subfilters from the minimal phase solution it is possible to design an IIR Hilbert transformer which exhibits simultaneously approximate constant amplitude response and approximate linear phase.

A class of FRM-based all-pass digital filters with applications in half-band filters and Hilbert transformers

In this paper, we consider the application of the frequency-response masking (FRM) technique in constructing the IIR approximately linear-phase half-band filters and Hilbert transformers. An efficient implementation structure, consisting of a FRM-based nearly all-pass filter and a pure delay term, has been derived. The FRM-based branch being composed of the recursive all-pass filter and the two polyphase components of FIR masking filters, exhibits nearly all-pass magnitude response and approximately linear phase. We are focused on the low-complexity implementation of the recursive all-pass filter. We propose a new simple approximation method, which we apply to design the approximately linear phase IIR filter with simple powers-of-two coefficients. The example half-band filters and Hilbert transformers show sharp magnitude responses and approximately linear phase.

Frequency Transformations of IIR Filters with Filter Bank Applications

Low-complexity half-band IIR filters implemented as two-path polyphase structures use all-pass sub-filters as polyphase components. With a simple first-order frequency transformation applied in the half-band filter all-pass sections, the new filter is obtained with the cut-off frequency at the desired position. In this paper, the authors apply the frequency transformations to construct minimum phase filters and filter pairs of desired regularity order, and with the cut-off frequency at an arbitrary location. In this way, an IIR filter design problem simplifies to the half-band filter design problem. Several solutions based on half-band filters and frequency transformations are shown: (i) multilevel IIR filter bank composed of IIR filter pairs with desirable regularity order and with changeable crossover frequency in sub-bands, (ii) IIR implementation of 2/3, 1/3 two-channel resempler, (iii) simple and effective approach to designing band-pass/band-stop filter pairs

Efficient multirate filtering using EMQF subfilters

In this paper, we present the application of the elliptic minimal Q-factors (EMQF) subfilters in constructing IIR multirate filters. We show that using EMQF subfilters, efficient implementations are reached for the sampling rate conversion systems, multistage filtering, and tree structured IIR filter banks. It is demonstrated through examples that the proper use of EMQF subfilters provides efficient filtering with a small number of multiplications per output sample.

Recursive digital filters and two-channel filter banks: Frequency-response masking approach

In this paper, we present the application of frequency-response masking (FRM) technique in constructing digital filters and two-channel filter banks. With the FRM approach, digital filters with sharp transition bands and two-channel filter banks with narrow transition bands between the channels can be achieved. The FRM structure considered in this paper is composed of IIR model filters and linear-phase FIR masking filters. The efficient structures for analysis and synthesis banks consisting of all-pass sub-filters and polyphase components of masking filters are obtained. We particularly consider the frequency responses of filters and filter banks when the IIR model filters are of approximately linear phase. It is shown that by using an FRM-based two-channel filter bank and an additional set of masking filters, the two-stage very selective filters and two-channel filter banks can be developed. It is shown by means of examples that the usage of IIR model filters reduces the computational complexity and decreases the overall group delay as compared with an equivalent FRM structure based on FIR filters only.

Recursive two-channel filter banks based on FRM approach

In this paper, we consider the application of a recursive half-band filter pair in the structure of two-channel filter bank, which is based on the frequency response masking (FRM) technique. The recursive filter pair is used as a complementary model filter pair, whereas the masking filters are linear-phase FIR filters. Efficient realization structures for the analysis and synthesis filter banks consisting of all-pass sub-filters and polyphase components of masking filters are derived. The resulting analysis/synthesis filter bank satisfies the all-pass and the nearly perfect magnitude reconstruction properties. It is shown in the paper that by making use of the two-channel filter bank and the two-stage FRM-approach, very sharp filters with nearly linear phase can be achieved. The performances of the analysis/synthesis bank are demonstrated by means of example. An example is also used to illustrate the application of the two-stage FRM-based filter design.