A note on digital filter synthesis

A novel method is presented for the exact design and synthesis of lossless discrete-integrator (LDI) digital filters. In this method, the entire digital filter synthesis is performed directly in the discrete-time z-domain without any recourse to the concept of a continuous-time analog prototype reference filter. The proposed design method lends itself in a straightforward fashion to the synthesis of high-quality LDI digital filters having ladder, lattice, or other similar practical configurations. In addition, it is capable of realizing a wide class of practical digital transfer functions, including the classical Butterworth Chebyshev, inverse Chebyshev, and, most importantly, elliptic transfer functions. >

When discretizing continuous-time systems or signals, one is often interested in preserving a property termed covariance-invariance. In this paper a technique is outlined for synthesizing discrete-time systems and signals which are covariance-invariant with corresponding continuous-time systems and signals. Applications of the technique to process simulation, minimum mean-squared error estimation, and digital filter synthesis are outlined, with example designs presented for covariance-invariant Butterworth and Chebychev digital filters. Based on the frequency response of these designs it is argued that the method of covariance-invariance is superior to the methods of impulse-invariance and bilinear-z as a response matching design technique for the synthesis of digital filters. This superiority is especially apparent at sampling rates that are marginal with respect to filter critical frequencies.

A novel framework for retiming using evolutionary computation for high level synthesis of digital filters

Genetic algorithms are exploited and applied to the development of a novel approach to the high-level synthesis of digit-serial digital filters. The salient feature of this approach is that it permits the digit-size to be taken into account as a variable of optimization, facilitating global data-path optimization with respect to both area and time. Moreover, it conforms closely to an actual hardware implementation, taking into account not only the cost of the required arithmetic functional units but also that of the required registers and multiplexors. The proposed approach is particularly efficient as it preserves the data-dependency relationships in the original digital filter data flow-graph under the operations of crossover and mutation performed by the constituent genetic algorithm. The effectiveness of this approach is demonstrated by comparing its results to those obtained by using the existing techniques for the high-level synthesis of a benchmark wave digital filter implemented as a bit-parallel architecture, and by presenting the results for the corresponding digital filter implemented as a digit-serial architecture.

We present the experimental application and comparison of two methods for the synthesis of digital filters, which represent the state-of-the-art of optimum digital processing of shaped signals with arbitrary constraints in time and frequency domain and any kind of stationary noise power spectral density. The methods are implemented in experimental measurement setups and optimum filters are synthesized with regard to assigned constraints (e.g. finite duration, flat top, peaking time, zero area, etc.) and by taking into account the real environmental noise or disturbance present in the system, identified from datasets of straightforward signal experimental acquisitions. Implementation issues are detailed and design rules for digital signal processors based on these techniques are derived.

As the complexity of digital filters is dominated by the number of multiplications, many works have focused on minimizing the complexity of multiplier blocks that compute the constant coefficient multiplications required in filters. The complexity of multiplier blocks can be significantly reduced by using an efficient number system. Although the canonical signed digit representation is commonly used as it guarantees the minimal number of additions for a constant multiplication, we propose in this paper a digital filter synthesis algorithm that is based on the minimal signed digit (MSD) representation. The MSD representation is attractive because it provides a number of forms that have the minimal number of non-zero digits for a constant. This redundancy can lead to efficient filters if a proper MSD representation is selected for each constant. In experimental results, the proposed algorithm resulted in superior filters to those generated from the CSD representation.

Methods of digital signal processing in control and monitoring systems are relevant today and largely replace the classic analog methods. This article discusses the main methods of digital signal processing and synthesis of appropriate devices, primarily digital filters.

This book is Volume III of the series DSP for MATLAB™ and LabVIEW™. Volume III covers digital filter design, including the specific topics of FIR design via windowed-ideal-lowpass filter, FIR highpass, bandpass, and bandstop filter design from windowed-ideal lowpass filters, FIR design using the transition-band-optimized Frequency Sampling technique (implemented by Inverse-DFT or Cosine/Sine Summation Formulas), design of equiripple FIRs of all standard types including Hilbert Transformers and Differentiators via the Remez Exchange Algorithm, design of Butterworth, Chebyshev (Types I and II), and Elliptic analog prototype lowpass filters, conversion of analog lowpass prototype filters to highpass, bandpass, and bandstop filters, and conversion of analog filters to digital filters using the Impulse Invariance and Bilinear Transform techniques. Certain filter topologies specific to FIRs are also discussed, as are two simple FIR types, the Comb and Moving Average filters. The entire series consists of four volumes that collectively cover basic digital signal processing in a practical and accessible manner, but which nonetheless include all essential foundation mathematics. As the series title implies, the scripts (of which there are more than 200) described in the text and supplied in code form here will run on both MATLAB™ and LabVIEW™. The text for all volumes contains many examples, and many useful computational scripts, augmented by demonstration scripts and LabVIEW™ Virtual Instruments (VIs) that can be run to illustrate various signal processing concepts graphically on the user's computer screen. Volume I consists of four chapters that collectively set forth a brief overview of the field of digital signal processing, useful signals and concepts (including convolution, recursion, difference equations, LTI systems, etc), conversion from the continuous to discrete domain and back (i.e., analog-to-digital and digital-to-analog conversion), aliasing, the Nyquist rate, normalized frequency, sample rate conversion and Mu-law compression, and signal processing principles including correlation, the correlation sequence, the Real DFT, correlation by convolution, matched filtering, simple FIR filters, and simple IIR filters. Chapter four of Volume I, in particular, provides an intuitive or first principle understanding of how digital filtering and frequency transforms work. Volume II provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z-Transform (including definition and properties, the inverse z-transform, frequency response via z-transform, and alternate filter realization topologies including Direct Form, Direct Form Transposed, Cascade Form, Parallel Form, and Lattice Form), and the Discrete Fourier Transform (DFT) (including Discrete Fourier Series, the DFT-IDFT pair, DFT of common signals, bin width, sampling duration, and sample rate, the FFT, the Goertzel Algorithm, Linear, Periodic, and Circular convolution, DFT Leakage, and computation of the Inverse DFT). Volume IV, the culmination of the series, is an introductory treatment of LMS Adaptive Filtering and applications, and covers cost functions, performance surfaces, coefficient perturbation to estimate the gradient, the LMS algorithm, response of the LMS algorithm to narrow-band signals, and various topologies such as ANC (Active Noise Cancelling) or system modeling, Periodic Signal Removal/Prediction/Adaptive Line Enhancement (ALE), Interference Cancellation, Echo Cancellation (with single- and dual-H topologies), and Inverse Filtering/Deconvolution/Equalization. Table of Contents: Principles of FIR Design / FIR Design Techniques / Classical IIR Design

This paper introduces a class of hybrid analog/digital filter banks with approximately perfect magnitude reconstruction. The filter bank consists of analog analysis and digital synthesis filter banks. The analog analysis filters are formed as a sum and difference of two allpass subfilters, respectively, resulting in filters with low orders and few free parameters, which is advantageous from implementation and design points of view. The digital synthesis filters are odd-order linear-phase FIR filters with symmetric and anti-symmetric impulse responses, respectively. The filter design is performed by first optimizing the analog analysis filters. Then, with the analog filters fixed, optimum digital synthesis filters, in the minimax sense, are obtained with the aid of linear programming.

Digital filter is an important component of analog-to-digital converter. The speed and complexity of digital decimation filter have a great influence on Sigma Delta analog-to-digital converter. In view of this situation, a design of high speed and low complexity digital filter is presented in this paper. A three stages cascaded architecture is adopted to reduce the number of half-band filters by increasing the downsampling rate of cascaded integrator-comb filter. The cascaded integrator-comb filter adopts a serial-parallel mixed structure to improve the speed of data processing. In order to reduce the complexity of digital filter, a novel sine compensation filter is proposed to compensate the passband attenuation and the multipliers of half-band filter are designed by time division multiplexing technique. The simulation results and analysis show that this design meets the performance requirements and its speed is increased by four times. Compared with the same type of filters, the number of multipliers, adders and registers has decreased by 45%, 31% and 26% respectively.

The design of digital filter transfer functions is facilitated by taking advantage of well-established design techniques developed for continuous (analog) filters. Digital approximations to continuous filter functions may be found by applying an appropriate sampled-data (z) transformation to the continuous filter transfer function. Three mathematical transformations are described that find the most application: 1) the standard z-transform, 2) the bilinear z-transform, and 3) the matched z-transform. The applicability of the three transformations is discussed and examples are presented of digital filters designed using these transformations.

Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style treatment, existing recursive techniques are reviewed, explained and compared within a coherent framework; some fresh insights are provided and new enhancements/modifications are proposed. It is shown that the replacement of resonators by (non-recursive) modulators in sliding DFT (SDFT) analyzers with either a finite impulse response (FIR), or an infinite impulse response (IIR), does improve performance somewhat; however, stability is not guaranteed as the cancellation of marginally stable poles by zeros is still involved. The FIR deadbeat observer is shown to be more reliable than the SDFT methods, an IIR variant is presented, and ways of fine-tuning its response are discussed. A novel technique for stabilizing IIR SDFT analyzers with a fading memory, so that all poles are inside the unit circle, is also derived. Slepian and sum-of-cosine windows are adapted to improve the frequency responses for the various FIR and IIR DFT methods.

It is well known that perfectly circularly-symmetric 2-D digital filters cannot be implemented in practice. This paper makes an attempt to develop computer-aided approximation of circularly-symmetric 2-D digital filters. The starting point is the configuration with separable 1-D transfer functions in the forward path along with a multiplier k in the feedback path. Computer programs are developed so that when the transfer functions are prescribed, one can obtain the range of possible values of k for which the error does not exceed a prescribed value of cc percent. Different types of low-pass filters and other types of filters like high-pass, band-pass and band-elimination filters are considered as examples.

In this work, we have studied the integration of an optical signal-based Indoor Positioning System (IPS) capable of supporting multi-access discrimination techniques. The research analyzes the different techniques and conditions that can be used to develop an IPS using a microcontroller unit (MCU)-based system-on-chip (SoC) systems. The main goal is to be able to integrate into the MCU both the hardware and software requirements for an IPS detector. In this way, different strategies that can implement multi-access discrimination using Frequency-division multiple access (FDMA) have been tested, such as I/Q demodulation, digital filtering, and discrete Fourier transform (DFT). This analysis has found a good technique to be executed in an MCU-based SoC, the DFT implemented through the Goertzel’s algorithm. The empirical tests carried out concluded that, using only one an MCU with the required HW and tuned SW, 15 position measurements per second were computed, with high accuracy in the 3-D positioning, with errors of less than 1 cm in a test area of 3.5 × 3.5 m 2 . The main contribution of the paper is the implementation of the optical signal based IPS in an MCU-SoC that includes signal acquisition and processing. The digital filtering or spectral processing for up to 16 received signals makes this IPS system very attractive from a design and cost point of view.

This work presents the methodology utilized for the development of the numerical module of SIPREX, an expert system for digital filter design. This system integrates knowledge on the different techniques and application areas of digital signal processing with powerful numerical algorithms, representing a valuable tool for the solution of problems involving analysis and synthesis of digital filters.