[pt] Este trabalho apresenta uma formulação geral da teoria de sensibilidade de filtros digitais lineares e invariantes no tempo, representados por variáveis de estado nas formas canônicas Diagonal e Jordan, com relação aos seus coeficientes quantizados devido ao tamanho finito da palavra. É estabelecida uma estrutura única que permite a análise de sensibilidade com respeito aos vários parâmetros do modelo de estado. São estudados sistemas compostos por cascatas de blocos e feita a análise de sensibilidade, considerando que há presença de elementos quantizados de blocos. É feita a análise de complexidade computacional das formulações estudadas. / [en] This work presents a general formulation on sensitivity analysis of digital linear filters modeled by state variables in canonical forms (Diagonal and Jordan), with respect to its coeficients which are aproximated due to the finite size of the word. We studied systems of cascated blocks which present quantization in its coefficients. It is established one block structure that permits the sensitivity analysis with respect to all the parameters of the state model. At last, the expressions complexity computational is calculated.

This thesis presents a study on the design of two-dimensional (2-D) digital filters by using the singular-value decomposition (SVD). A new method for the design of 2-D quadrantally symmetric FIR filters with linear phase response is proposed. It is shown that three realizations are possible, namely, a direct realization, a modified version of the direct realization, and a realization based on the combined application of the SV and LU decompositions. Each of the three realizations consists of a parallel arrangement of cascaded pairs of 1-D filters; hence extensive parallel processing and pipelining can be applied. The three realizations are compared and it is shown that the realization based on the SV and LU decomposition leads to the lowest approximation error and involves the smallest number of multiplications. It is shown that the SVD of the sampled amplitude response of a 2-D digital filter with real coefficients possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD method can be applied along with 1-D FIR techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (ω1, ω2) plane. A method for the design of 2-D IIR digital filters based on the combined application of the SVD and the balanced approximation (BA) is proposed. It is shown that the approximation error in the phase angle is bounded by the sum of the neglected Hankel singular values of the filter. Consequently, the phase response of the resulting filter is approximately linear over the passband region provided that only small Hankel singular values are neglected. It is also shown that the resulting 2-D filter is nearly balanced, which implies that the filter has low roundoff noise as well as low parameter sensitivity. Furthermore, the 2-D filter obtained is more economical and computationally more efficient than the original 2-D FIR filter, and in the case where an IIR filter is obtained the stability of the filter is guaranteed. Efficient general algorithms for the evaluation of the 1-D and 2-D gramians for 1-D and 2-D, causal, stable, recursive digital filters are proposed, which facilitate the application of the BA method in the design of digital filters. The algorithms obtained are based on a two-stage extension of the Astrom-Jury-Agniel (AJA) algorithm. It is shown that the AJA algorithm can be modified to solve a 1-D Lyapunov equation in a recursive manner. The recursive algorithm is then extended to the case where the rational function vector involved depends on two complex variables. It is shown that the two algorithms obtained can be combined to evaluate the 2-D gramians. The proposed algorithms are also useful in obtaining optimal digital filter structures that minimize the output-noise power due to the roundoff of products. / Graduate

[pt] Nos dias de hoje, são cada vez maiores as implicações de filtragem digital de sinais. Diversos tipos de algoritmos e de estruturas de filtros digitais, além de implementações por hardware tem sido desenvolvidos. A implementação de filtros tem sido bastante simplificada através do uso de microprocessadores; no entanto, as implementações atuais por hardware são limitados em estruturas ou ordem ou ambos. Este trabalho propõe uma arquitetura de um microcomputador que permite a implementação de filtros digitais programáveis (em estrutura, coeficientes e ordem). Também é mostrado que apenas um pequeno set de instruções é necessário e que não há limitações quanto à estrutura do filtro. / [en] Work on digital filtering of signals has been continuously increasing and the literature presents several algorithms and structures, besides hardware implementations. Filter implementation has been greathy simplified by using microprocessors; nevertheless present filter hardware is limited in structure or order or both. This work proposes a microcomputer architecture which allows the implementation of programmable (in structure coeficients and order) digital filters. It is also shown that only a small set of instructions is needed and that there is no limitation on the filter structure.

No description available.

No description available.

[pt] É feito um estudo da análise da sensibilidade das respostas impulsional e genérica de filtros IIR digitais, lineares, causais, monovariáveis e variantes no tempo modelados por equações de estado, supondo que as matrizes do sistema não se encontram em forma canônica e que, primeiro, não existe relação de dependência entre os parâmetros do sistema e, segundo, existe uma certa relação entre eles (dependência de tempo). Também é feito um estudo da análise de sensibilidade das respostas impulsional e genérica de uma estrutura em cascatas de filtros. / [en] This work presents results on the study of the sensitivity of the impulse response and generic response of linear, time-varying, causal, monovariable IIR digital filters modeled by dynamic equations in noncanonical form. First, all coefficients are considered to be independent of each other. Second, there is relationship among the coefficients (time dependence). It is studied systems of cascated blocks which present quantization in its coefficients.

[pt] Este trabalho apresenta e resolve o problema da determinação das sensibilidades de filtros digitais modelados por equações de estado em forma genérica (não canônica), com relação aos seus coeficientes que são aproximados devido ao tamanho finito da palavra. São consideradas as respostas impulsional e devida a uma excitação qualquer, nos domínios do tempo e da freqüência. / [en] This work presents and solves the problem of determining the sensitivities of digital filters modeled by state variables in generic form (noncanonical), with respect to its coefficients which are approximated due to the finite size of the word. The impulse response, as well as the response due to a generic excitation are considered. Both the time and the frequency domains are studied.

In this thesis we discuss design and implementation of low-complexity digital filters. Digital filters are key components in most digital signal processing (DSP) systems and are, for example, used for interpolation and decimation. A typical application for the filters considered in this work is mobile communication systems, where high throughput and low power consumption are required. In the first part of the thesis we discuss implementation of high throughput lattice wave digital filters (LWDFs). Here arithmetic transformation of first- and second-order Richards’ allpass sections are proposed. The transformations reduces the iteration period bound of the filter realization, which can be used to increase the throughput or reduce the power consumption through power supply voltage scaling. Implementation of LWDFs using redundant, carry-save arithmetic is considered and the proposed arithmetic transformations are evaluated with respect to throughput and area requirements. In the second part of the thesis we discuss three case studies of implementations of digital filters for typical applications with requirements on high throughput and low power consumption. The first involves the design and implementation of a digital down converter (DDC) for a multiple antenna element radar receiver. The DDC is used to convert a real IF input signal into a complex baseband signal composed of an inphase and a quadrature component. The DDC includes bandpass sampling, digital I/Q demodulation, decimation, and filtering and three different DDC realizations are proposed and evaluated. The second case study is a combined interpolator and decimator filter for use in an OFDM system. The analog-to-digital converters (ADCs) and the digital-to-analog converters (DACs) work at a sample rate twice as high as the Nyquist rate. Hence, interpolation and decimation by a factor of two is required. Also, some channel shaping is performed which complicates the filter design as well as the implementation. Frequency masking techniques and novel filter structures was used for the implementation. The combined interpolator and decimator was successfully implemented using an LWDF in a 0.35 mm CMOS process using carry-save arithmetic. The third case study is the implementation of a high-speed decimation filter for a SD ADC. The decimator has an input data rate of 16 Gsample/s and the decimation factor is 128. The decimation is performed using two cascaded digital filters, a comb filter followed by a linear-phase FIR filter. A novel hardware structure for single-bit input digital filters is proposed. The proposed structure was found to be competitive and was used for the implementation. The decimator filter was successfully implemented in a 0.18 mm CMOS process using standard cells. In the third part of the thesis we discuss efficient realization of sum-of-products and multiple-constant multiplications that are used in, for example, FIR filters. We propose several new difference methods that result in realizations with a low number of adders. The proposed design methods have low complexity, i.e., they can be included in the search for quantized filter coefficients.

International Telemetering Conference Proceedings / October 28-31, 1996 / Town and Country Hotel and Convention Center, San Diego, California / The traditional use of active RC-type filters as anti-aliasing filters in Pulse Code Modulation (PCM) systems is being replaced by the use of Digital Signal Processing (DSP) filters, especially when performance requirements are tight and when operation over a wide environmental temperature range is required. In order to keep systems more flexible, it is often desired to let the DSP filters run asynchronous to the PCM sample clock. This results in the PCM output signal being a sampling of the output of the DSP, which is itself a sampling of the input signal. In the analysis of the PCM data, the signal will have a periodic repeat of a previous sample, or a missing sample, depending on the relative sampling rates of the DSP and the PCM. This paper analyzes what effects can be expected in the analysis of the PCM data when these anomalies are present. Results are presented which allow the telemetry engineer to make an effective value judgment based on the type of filtering technology to be employed and on the desired system performance.

International Telemetering Conference Proceedings / October 30-November 02, 1995 / Riviera Hotel, Las Vegas, Nevada / The need for precise gain and phase matching in multi-channel data sampling systems can result in very strict design requirements for presample or anti-aliasing filters. The traditional use of active RC-type filters is expensive, especially when performance requirements are tight and when operation over a wide environmental temperature range is required. New Digital Signal Processing (DSP) techniques have provided an opportunity for cost reduction and/or performance improvements in these types of applications. This paper summarizes the results of an evaluation of various digital filter types used as matched presample filters in data sampling systems.