12,028 research outputs found
Selection of an optimal substructure in the distributed arithmetic FIR digital filter
Nerekurzivna digitalna sita v porazdeljeni aritmetiki in aritmetiki s fiksno decimalno vejico se uporabljajo v hitrih sistemih za digitalno obdelavo podatkov, kjer se zahteva stabilnost odzivov in linearne fazne poteke pri zahtevanem velikem dušenju ali veliki strmini bokov. Med različnimi realizacijskimi oblikami smo primerjali kaskadno, vzporedno in kombinirano realizacijsko obliko. Primerjali smo frekvenčne lastnosti, kvantizacijski šum in aparaturno kompleksnost.For digital signal processing in high-speed systems FIR digital filters are used, especially in applications where linear time-invariant stable response and linear phase are needed. A fixed point arithmetic is applied in such systems. The hardware main problem in the design of high-speed FIR digital filters is the complexity. In practical realizations of FIR digital filters, the circuits containe many adders, inverters, registers and multipliers. Among these basic digital elements, the multiplier has most of the hardware complexity and its time response is the greatest. A distributed arithmetic was developed for this reason by some authors. In the hardware realization the multiplier is substituted with a memory, adder and register. The partial sum of coefficients is written in the memory. The partial sum from memory with the previous result from the adder divided by two in the adder is calculated. The previous result from the adder is written in the register on b-iteration of the summed partial results is needed for the calculation of one entire product in the case of the distributed arithmetic. b is the number of bits in the input word. The complexity of the hardware realization of all FIR digital filters in the distributed arithmetic is determined with the word length in all substructures, with ripple in passband and stopband and with the width of transition band on the frequency response. With an increase in the word length, sharpness of the frequency response in transition band and reduction of ripple in passband and stopband the number of basic elements and the time response are increased. The capacity of the memory is determined with 2N, N is the number of impulse response coefficients. In modern digital filter designs the sampling frequency is limited to 20MHz and the number of impulse response coefficients to 200. With the new technology of digital circuits this limit will be increased. Our paper deals with the possibility of reducing the memory capacity by using a combined realization form. The combined realization form contains a cascade-connected structure built with a parallel subsection. We present two FIR digital filters in the distributed arithmetic realization form. The first one is realized with digital elements such as logic gates, adders, inverters and registers, and the other one with digital elements and read-write memory. Both forms are suitable for realization in custom-design integrated circuits or in PLD. Another advantage of our contribution is an optimal word length in all subsections with consideration of the roundoff noise and expected ripple in passband and stopband. As a result, an optimal lowpass FIR digital filter in the distributed arithmetic with 61 coefficients of the impulse response usefulness of the combined realization form is presented and analysed. For the combined realization form of the FIR digital filter design impulse response coefficients are needed. These coefficients can be calculated with software such as MATLAB. The impulseresponse coefficients h(k) are the coefficients of transfer function H(z). From the zeros of the transfer function of the FIR digital filter the zeros of the cascade structure are selected. This selection requires approximately an equal number of zeros in all cascaded structures, and a similar frequency response in all cascaded structures with the frequency response of the whole FIR digital filter. With this selection, the hardware complexity of the cascaded structure is almost the same and the magnitude of the output signal from all the cascaded structures is suitably high. The output signal as a response to the input white noise signal is calculated with our program package for simulation of an FIR digital filter structure. Depending on quantization errors, an optimal word length in all sections is chosen. The simulated results and the theoretically calculated quantization errors with linear quantization error models are compared. A simplified method for determination of the optimal word length was searched for by using theoretically calculated quan
Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks
A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included
Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks
A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included
Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters
Two perfect-reconstruction structures for the two-channel quadrature mirror filter (QMF) bank, free of aliasing and distortions of any kind, in which the analysis filters have linear phase, are described. The structure in the first case is related to the linear prediction lattice structure. For the second case, new structures are developed by propagating the perfect-reconstruction and linear-phase properties. Design examples, based on optimization of the parameters in the lattice structures, are presented for both cases
Fractional biorthogonal partners in channel equalization and signal interpolation
The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners
Biorthogonal partners and applications
Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications
Efficient algorithm for solving semi-infinite programming problems and their applications to nonuniform filter bank designs
An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorith
- …