When a filter transfer function in s is replaced with the bilinear transform in z, the resulting discrete model represents the original continuous model within a second order accuracy of integration. A unique set of recently discovered minimum memory algorithms that perform the bilinear transform on a continuous transfer function are implemented on an INTEL 8080 microprocessor system. Scaling techniques are used to frequency scale all transfer functions to a standardized frequency. All data words are represented in a signed binary double precision format to maintain higher calculation speed and accuracy. Three test case transfer functions of different order are implemented using the bilinear transform algorithms. First, the algorithms are used to generate the three discrete models. Second, the continuous time models are driven by a step input function, generating a continuous time output. Third, the step function input is discretized and used to drive the bilinear algorithm derived models. Finally, the discrete outputs are compared with the continuous time outputs to validate and evaluate the software techniques used to implement the bilinear algorithms, which imply that the techniques provide a basis for new hardware designs.

Digital signal processing (DSP) is widely used in many applications spanning the spectrum from audio processing to image and video processing to radar and sonar processing. At the core of digital signal processing applications is the digital filter which are implemented in two ways, using either finite impulse response (FIR) filters or infinite impulse response (IIR) filters. The primary difference between FIR and IIR is that for FIR filters, the output is dependent only on the inputs, while for IIR filters the output is dependent on the inputs and the previous outputs. FIR filters also do not sur from stability issues stemming from the feedback of the output to the input that aect IIR filters. In this thesis, an architecture for FIR filtering based on distributed arithmetic is presented. The proposed architecture has the ability to implement large FIR filters using minimal hardware and at the same time is able to complete the FIR filtering operation in minimal amount of time and delay when compared to typical FIR filter implementations. The proposed architecture is then used to implement the fast affine projection adaptive algorithm, an algorithm that is typically used with large filter sizes. The fast affine projection algorithm has a high computational burden that limits the throughput, which in turn restricts the number of applications. However, using the proposed FIR filtering architecture, the limitations on throughput are removed. The implementation of the fast affine projection adaptive algorithm using distributed arithmetic is unique to this thesis. The constructed adaptive filter shares all the benefits of the proposed FIR filter: low hardware requirements, high speed, and minimal delay.

[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.

published_or_final_version / Speech and Hearing Sciences / Doctoral / Doctor of Philosophy

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.

This thesis proposes to estimate the speed of a moving acoustic source by either linear or non linear processing of the resulting Doppler shift present in a high-frequency pilot tone. The source is an acoustic modem (Hermes) which currently uses moving average to estimate and compensate for Doppler shift. A new auto regressive approach to Doppler estimation (labeled IIR method in the text) promises to give a better estimate. The results for a simulated peak velocity of 2 m/s in the presence of additive noise showed an RMSE of 0.23 m/s using moving average vs. 0.00018 m/s for the auto regressive approach. The SNR was 75 dB. The next objective was to compare the estimated Doppler velocity obtained using the two algorithms with the experimental values recorded in real time. The setup consisted of a receiver hydrophone attached to a towing carriage that moved with a known velocity with respect to a stationary acoustic source. The source transmitted 375 kHz pilot tone. The received pilot tone data were preprocessed using the two algorithms to estimate both Doppler shift and Doppler velocity. The accuracy of the algorithms was compared against the true velocity values of the carriage. The RMSE for a message from experiments conducted indoor for constant velocity of 0.4 m/s was 0.6055 m/s using moving average, 0.0780 m/s using auto regressive approach. The SNIR was 6.3 dB. / by Poorani Kathiroli. / Thesis (M.S.C.S.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

A maior parte do sinal propagante para oeste nos oceanos é explicada pelas ondas de Rossby baroclínicas. Porém, vórtices de mesoescala podem interferir na identificação dessas ondas. A maior adversidade em se distinguir o sinal dessas feições é que os vórtices parecem propagar-se com uma velocidade aproximada à velocidade de fase das ondas. Um dos objetivos do presente trabalho é caracterizar os sinais propagantes para oeste em termos da sua velocidade de fase no Atlântico. A análise se baseia em de dados das anomalias da altura da superfície do mar (ASM) e da temperatura de superfície do mar (TSM) derivados dos altímetros TOPEX/Poseidon e Jason-1 e radiômetro TRMM/TMI. As anomalias de ASM e TSM foram filtradas por um conjunto de filtros de resposta impulsiva finita (FIR) para eliminar o sinais sazonais, interanuais e sinais de alta frequência. A análise de correlação cruzada entre as matrizes zonais-temporais de ASM e TSM foi feita para limitar as conclusões aos sinais presentes simultaneamente em ambas as bases de dados. A velocidade de fase das ondas de Rossby foi estimada via transformada de Radon aplicada às matrizes de correlação cruzada. Um máximo local solitário sobre a origem foi observado nos diagramas de correlação e associado à presença de vórtices de mesoescala. Porém este máximo se alonga com a mesma inclinação correspondente à velocidade de fase das ondas de Rossby. Isto sugere que estes vórtices podem propagar-se sobrepostos às ondas. As velocidades de propagação dos vórtices são estimadas através do ajuste de uma função de decaimento exponencial no tempo e na distância zonal. Análises preliminares da transformada de Fourier mostraram que os sinais propagantes para oeste são predominantemente anuais, embora picos de frequências semi-anuais são observadas nestes espectros. Em decorrência da evidência de que os sinais propagantes para oeste são compostos simultaneamente por vórtices e ondas de Rossby, um filtro baseado na transformada de Radon e sua inversa foi desenvolvido para separar o sinal de feições com simetria circular. O filtro de vórtice circular foi aplicado em três áreas onde se localizam a Corrente das Agulhas, Confluências Brasil-Malvinas e Corrente do Golfo. Com base na análise visual pode-se afirmar que o filtro identificou com sucesso vórtices circulares nas três áreas estudadas, tanto nos dados de ASM como nos de TSM. As velocidades de fase das ondas de Rossby foram ligeiramente mais rápidas, em média, que as velocidades dos vórtices em todas as três áreas, cerca de 10% na ASM e 13% na TSM. As velocidades calculadas após a aplicação do filtro de vórtice circular apresentaram um viés positivo em relação as obtidas via correlações cruzadas. A maior diferença na estimativa das velocidades dos vórtices foi de 21% e nas ondas 25%, ambas na região da Corrente das Agulhas. Baseado nas evidências apresentadas é possível afirmar que vórtices podem se propagar com velocidades semelhantes à velocidade das ondas de Rossby do primeiro modo baroclínico. O lag das correlações cruzadas indicaram que o processo físico que relaciona a variabilidade nos dados de ASM à dos TSM é a advecção causada pela passagem de uma onda planet´aria do primeiro modo baroclínico. Esta advecção pode ser horizontal ou vertical dependendo do processo dominante que ocorre numa dada região. / In the oceans, most of the westward propagating signal is explained by baroclinic Rossby waves. However, mesoscale vortices can interfere in the identification of these waves. The main observational issue is to distinguish eddies from the wave-like propagating signals, since the former propagates with a speed that approximately matches the phase speed of baroclinic Rossby waves. The objective of the present study is to characterize the westward propagating signals in terms of their propagation speeds in the Atlantic. The analysis is based on satellite derived sea surface height (SSH) and sea surface temperature (SST) anomalies from the TOPEX/Poseidon and Jason-1 altimeters and TRMM/TMI radiometer records. The SSH and SST anomaly maps were filtered with a set of finite impulse response filters to eliminate the seasonal and interannual cycles and high frequency signals. The cross-correlation analysis between SSH and SST longitude-time matrices was performed to limit the conclusions to the features that appear simultaneously in both datasets. The of Rossby wave phase speed was estimated via Radon transform applied to the longitude-time cross-correlation matrices. A single local maximum was was observed at the origin of the cross-correlation diagrams and associated to mesoscale vortices. However, this maximum spreads along the same slope that characterizes the the westward Rossby wave phase speed. This suggests that vortices propagate superimposed to Rossby waves. The propagating speed of the vortices is estimated from the linear fit of an exponential decay function. A preliminary Fourier analysis show that the westward propagating signals are predominantly annual, yet peaks in the semiannual frequencies are observed. The evidence that the westward propagating signals are composed simultaneously of vortices and Rossby waves motivated the development of a filter based in the Radon transform and its inverse, to isolate the signal associated to circularly symmetric features. This circular vortex filter was applied in three areas that portray the Agulhas Current, the Brazil-Malvinas Confluence, and the Gulf Stream. Based on visual analysis one can affirm that the circular filter sucessfully identified vortices in three areas, both in the SSH and in the SST data. The phase speeds of Rossby waves were, on average, slightly faster than vortices speeds in the three areas, approximately 10% in SSH and 13% in SST. The speeds calculated after the circular vortex filter was applied presented a positive bias in relation to those obtain from cross correlations. The largest difference in the vortices speeds was 21% and in the wave speeds 25%, both in Agulhas Current region. Based on the present evidences it is possible to state that vortices can propagate with speeds similar to those of first-mode baroclinic Rossby waves. The cross-correlation lag suggests that the physical process that links the variability of the SSH to that of the SST is the advection generated by the passage of a first-mode baroclinic planetary wave. This advection can be horizontal or vertical depending of the dominant process in a given region.