Impulse Invariant Transformation Research Articles

A novel two-channel continuous-time time-interleaved 3rd-order sigma-delta modulator with integrator-sharing topology

This paper presents a 3rd-order two-path continuous-time time-interleaved (CTTI) delta-sigma modulator which is implemented in standard 90 nm CMOS technology. The architecture uses a novel method to resolve the delayless feedback path issue arising from the sharing of integrators between paths. By exploiting the concept of the time-interleaving techniques and through the use time domain equations, a conventional single path 3rd-order discrete-time (DT) ΔΣ modulator is converted into a corresponding two-path discrete-time time-interleaved (DTTI) counterpart. The equivalent CTTI version derived from the DTTI ΔΣ modulator by determining the DT loop filters and converting them to the equivalent continuous-time loop filters through the use of the Impulse Invariant Transformation. Sharing the integrators between two paths of the reported modulator makes it robust to path mismatch effects compared to the typical time-interleaved modulators which have individual integrators in all paths. The modulator achieves a dynamic range of 12 bits with an OverSampling Ratio of 16 over a bandwidth of 10 MHz and dissipates only 28 mW of power from a 1.8-V supply. The clock frequency of the modulator is 320 MHz but integrators, quantizers and DACs operate at 160 MHz.

A compact digital gamma-tone filter processor

Area consumption is one of the most important design constrains in the development of compact digital systems. Several authors have proposed making compact Cochlear Implant processors using Gamma-tone filter banks. These model aspects of the cochlea spectral filtering. A good area-efficient design of the Gamma-tone Filter Bank could reduce the amount of circuitry allowing patients to wear these cochlear implants more easily. In consequence, many authors have reduced the area by using the minimum number of registers when implementing this type of filter. However, critical paths limit their performance. Here a compact Gamma-tone Filter processor, formulated using the impulse invariant transformation together with a normalization method, is presented. The normalization method in the model guarantees the same precision for any filter order. In addition, area resources are kept low due to the implementation of a single Second Order Section (SOS) IIR stage for processing several SOS IIR stages and several channels at different times. Results show that the combination of the properties of the model and the implementation techniques generate a processor with high processing speed, expending less resources than reported in the literature.

Introduction to digital signal processing and filter design

Preface. 1. Introduction. 1.1 Introduction. 1.2 Application of DSP. 1.3 Discrete-Time Signals. 1.4 History of Filter Design. 1.5 Analog and Digital Signal Processing. 1.6 Summary. Problems. References. 2. Time-Domain Analysis and z Transform. 2.1 A Linear, Time-Invariant System. 2.2 z Transform Theory. 2.3 Using z Transform to Solve Difference Equations. 2.4 Solving Difference Equations Using the Classical Method. 2.5 z Transform Method Revisited. 2.6 Convolution Revisited. 2.7 A Model from Other Models. 2.8 Stability. 2.9 Solution Using MATLAB Functions. 2.10 Summary. Problems. References. 3. Frequency-Domain Analysis. 3.1 Introduction. 3.2 Theory of Sampling. 3.3 DTFT and IDTFT. 3.4 DTFT of Unit Step Sequence. 3.5 Use of MATLAB to Compute DTFT. 3.6 DTFS and DFT. 3.7 Fast Fourier Transform. 3.8 Use of MATLAB to Compute DFT and IDFT. 3.9 Summary/ Problems. References. 4. Infinite Impulse Response Filters. 4.1 Introduction. 4.2 Magnitude Approximation of Analog Filters. 4.3 Analog Frequency Transformations. 4.4 Digital Filters. 4.5 Impulse-Invariant Transformation. 4.6 Bilinear Transformation. 4.7 Digital Spectral Transformation. 4.8 Allpass Filters. 4.9 IIR Filter Design Using MATLAB. 4.10 Yule-Walker Approximation. 4.11 Summary. Problems. References. 5. Finite Impulse Response Filters. 5.1 Introduction. 5.2 Linear Phase Fir Filters. 5.3 Fourier Series Method Modified by Windows. 5.4 Design of Windowed FIR Filter Using MATLAB. 5.5 Equiripple Linear Phase FIR Filters. 5.6 Design of Equiripple FIR Filters Using MATLAB. 5.7 Frequency Sampling Method. 5.8 Summary. Problems. References. 6. Filter Realizations. 6.1 Introduction. 6.2 FIR Filter Realizations. 6.3 IIR Filter Realizations. 6.4 Allpass Filters in Parallel. 6.5 Realization of FIR and IIR Filters Using MATLAB. 6.6 Summary. Problems. References. 7. Quantized Filter Analysis. 7.1 Introduction. 7.2 Filter Design-Analysis Tool. 7.3 Quantized Filter Analysis. 7.4 Binary Numbers and Arithmetic. 7.5 Quantization Analysis of IIR Filters. 7.6 Quantization Analyis of FIR Filters. 7.7 Summary. Problems. References. 8. Hardware Design Using DSP Chips. 8.1 Introduction. 8.2 Simulink and Real-Time Workshop. 8.3 Design Preliminaries. 8.4 Code Generation. 8.5 Code Composer Studio. 8.6 Simulator and Emulator. 8.7 Conclusion. References. 9. MATLAB Primer. 9.1 Introduction. 9.2 Signal Processing Toolbox. References. Index.

Analysis of Charge-Pump Phase-Locked Loops

In this paper, we present an exact analysis for third-order charge-pump phase-locked loops using state equations. Both the large-signal lock acquisition process and the small-signal linear tracking behavior are described using this analysis. The nonlinear state equations are linearized for the small-signal condition and the z-domain noise transfer functions are derived. A comparison to some of the existing analysis methods such as the impulse-invariant transformation and s-domain analysis is provided. The effect of the loop parameters and the reference frequency on the loop phase margin and stability is analyzed. The analysis is verified using behavioral simulations in MATLAB and SPECTRE.

Digital implementation of linear gammatone filters: Comparison of design methods

Digital implementations of linear gammatone filters are regularly part of auditory models and can be used in the sound processing in cochlear implants. How close digital impulse, magnitude, and phase responses match the corresponding properties of the analog gammatone filter is evaluated for one, finite-impulse response filter design, and for five, infinite-impulse response filter designs: base-band impulse invariant transformation, impulse invariant transformation, matched z transformation, bilinear transformation, and mapping of differentials with backward differences. Filter properties and computational cost are compared as a function of the filter’s order and center frequency, and sampling frequency. Results show that filters designed with the base-band impulse invariant transformation give the best overall approximation of the analog properties with reasonable computational cost.

Discrete type dynamic synapses neural network: Speech recognition application

A discrete type of the Dynamic Synapses Neural Network (DSNN) has been developed and applied to speech recognition. In order to speed up the training time of the network, a new discrete time implementation of the original DSNN [J.-S. Liaw and T. W. Berger, 1996] has been introduced based on the impulse invariant transformation. The new architecture of the network was trained with the Genetic Algorithms [H. H. Namarvar et al., 2001] and tested against the continues-type DSNN. The overall speed of the new algorithm with discrete-time difference equation set is about 13 times faster than the same algorithm with the continuous differential equation set. This significant reduction of processing time not only decreases the training time but also makes the system better suited for real-time speech recognition tasks. [Work supported by DARPA.]

Discretization effects in TLM diffusion models

The standard methods for bringing a TLM diffusion model to convergence are necessary but tedious. However, much time and effort can be saved if the initial choices of elemental size and iteration timestep are appropriate. Here we consider the general form of the solution to the diffusion equation and sample the component dynamics to determine the impulse invariant response. We then derive a convenient method for charting the discrepancy between the coefficients of the continuous description and the impulse invariant transformation, as this discrepancy varies with discretization of space and time. The use of the curves in estimating appropriate elemental size and iteration timestep is described. Copyright © 2000 John Wiley & Sons, Ltd.

Accurate model of the semiconductor laser nonuniform FM response for the study of coherent optical systems

This paper proposes an accurate simulation model of the semiconductor laser nonuniform FM response, to be used in the computer-aided design of coherent optical communication systems. The FM response of the laser is modeled as a recursive digital filter derived directly from measurements. Least squares fitting and the impulse invariant transformation method are used to calculate digital filter coefficients. The procedure is applied in the case of a conventional DFB laser. The calculated model of the DFB is used to study the influence of the nonuniform FM response on the performance of a coherent heterodyne CPFSK system with differential receiver operating at 1 Gb/s. Theoretical and experimental results are in excellent agreement. >

Fault Detection of Dynamical Systems with Nonstationary Inputs

The paper presents a practical fault detection method for dynamical systems with some arbitrary and nonstationary inputs. The method implies an impulse invariant transformation for obtaining the equivalent system having as input a stationary uncorrelated sequence, and as output the response for this input. The transformation uses the AR filters of the quasi-stationary data blocks of the original input, resulted by a segmentation procedure. A similar procedure is used to segment the processed output in quasi-stationary data blocks. Each transition from one data block to another marks a change in the dynamic properties of the system. The method is applied for detection of changes in dynamic characteristics of a vibrating structure subject to a transient natural excitation.