Pole Filter Research Articles

On Determination of Laguerre Filter Pole through Step or Impulse Response Data

Any stable transfer function can be expanded by using Laguerre series. However, a finite Laguerre series is only an approximation of the true plant and the model error is a function of the filter pole. This paper summarizes some methods for the determination of Laguerre filter pole from step response or impulse response signals. The importance of a proper Laguerre filter pole for good model approximation and robust control is also discussed.

Switched-current filter design using cascaded sections

A new analogue sampled-data active device, named as a switched-current operational amplifier (SIOA), is presented. The use of active circuit elements may simplify drawing the circuit diagram significantly greatly and may permit easier analysis and synthesis of SI networks. A number of all pole and elliptic (second- or third-order) switched-current (SI) filters are derived from the switched capacitor prototypes. These can be used as simple, self-contained filters or as filter sections in the cascaded realizations of a higher order transfer functions. To illustrate the approach, a fifth-order low-pass filter is designed.

An optimization approach to the design of frequency sampling filters implemented with finite word length architectures

Many digital signal processing applications require linear phase filtering. Under certain conditions, a frequency sampling filter can implement a linear phase filter more efficiently than an equivalent filter implemented by a direct convolution structure. However, frequency sampling filter structures require pole-zero cancellations on the unit circle. For practical implementations of frequency sampling filters, finite word length effects usually prevent exact pole-zero cancellation. An uncancelled pole on the unit circle causes the filter to be unstable. Therefore, designers move the filter's poles and zeros off the unit circle and onto a circle of radius r where r < 1, by replacing z −1 with rz −1 in the filter's system function. As a result of this modification, the frequency response of the new filter using rz −1 where r < 1 is different from the frequency response of the original filterwhere r = 1. As r decreases, the frequency response of the modified frequency sampling filter increasingly differs from the frequency response of the original filter, and thus values of r close to 1 are usually chosen. However, it has been shown that the filter's output roundoff noise decreases as r decreases. Thus, there is a need for a design technique which chooses a value of r which renders an acceptable roundoff noise level while satisfying various frequency response design constraints. This paper develops an optimization method for designing a frequency sampling filter with r < 1 such that a linear combination of the mean square error between the desired and actual frequency responses in the passband and stopband and the sum of the square error of the impulse response symmetry is minimized while the stopband frequency samples are constrained to zero.

Extremely low phase noise UHF oscillators utilizing high-overtone, bulk-acoustic resonators

High-overtone, bulk acoustic resonators (HBAR) have been designed that exhibit 9-dB insertion loss and loaded Q values of 80000 at 640 MHz with out-of-phase resonances occurring every 2.5 MHz. These resonators have been used as ovenized frequency-control elements in very low phase noise oscillators. The oscillator sustaining stage circuitry incorporates low-1/f noise modular RF amplifiers, Schottky-diode ALC, and a miniature 2-pole helical filter for suppression of HBAR adjacent resonant responses. Measurement of oscillator output signal flicker-of-frequency noise confirms that state-of-the-art levels of short-term frequency stability have been obtained. Sustaining stage circuit contribution to resulting oscillator flicker-of-frequency noise is 7-10 dB below that due to the resonators themselves. At 16-dBm resonator drive, an oscillator output signal white phase noise floor level of -175 dBc/Hz is achieved.

Method of encoding speech signals involving the extraction of speech formant candidates in real time

Method of encoding speech signals which is based upon determining the roots of the linear prediction polynomial describing the spectrum of an analog speech signal, wherein the roots are candidates in determining the formants of the speech signal. The method involves the analysis of respective frames of sampled digital speech data using a linear predictive technique to determine a set of reflection coefficients or K-parameters which are then converted into the equivalent predictor coefficients or A-parameters describing a prediction polynomial having a plurality of roots corresponding to the poles of an all-pole filter characterizing the vocal tract. A modified Bairstow technique is then empolyed for factoring out quadratic factors which are then sorted in an ordered arrangement in terms of ascending bandwidths. In performing the modified Bairstow technique, initial estimates of the successive quadratic factors for a current frame of digital speech data are made in sequence, and the prediction polynomial is successively deflated to a reduced order polynomial in determining the respective quadratic factors thereof. The initial estimate of the first quadratic factor is the same as the smallest bandwidth root as determined from the previous frame of digital speech data. These removed quadratic factors or roots are candidates for determining the formants of the speech signal.

A method for exceptionally low noise single channel recordings.

We present a method whereby, with integrating electronics, quartz patch electrodes and a novel use of silicone oil, background noise levels as low as .083 pA RMS in a 5 kHz bandwidth (4-pole Butterworth filter) have been achieved in single channel patch clamp recordings. These approaches result in much higher signal to noise ratios for single channel recording than have previously been reported and should allow many investigators to significantly reduce noise at a constant bandwidth or to increase their recording bandwidths by several kHz.

A novel approach to the design of 2-d recursive digital filters

An efficient method is presented for the design of 2-D circular symmetric recursive digital filters satisfying prescribed magnitude and constant group-delay responses. The transfer function of this class of 2-D filters has a zero-phase non-separable numerator and separable denominator 2-variable polynomials in z 1 and z 2 . In the proposed technique the coefficients of the 2-D filters are calculated in two steps. In the first step the parameters of two 1-D all pole filters 1/D 1(z 1) and 1/D 2(z 2) are calculated by minimizing a multicriterion objective function using a suitable optimization technique so that the magnitude and group- delay responses of the desired 2-D filter along the ω 1 , ω 2 axes are obtained. Essentially, the first step of the proposed design method yields a 2-D all pole separable product filter with rectangular cutoff boundaries with or without constant group-delay responses in the passband of the above filter. In the second step, the parameters of the zero-phase 2-variable non- separable polynomial in z 1 and z 2 in the numerator can be determined through minimization of a cost function using a linear programming approach. Note that the second step acts as a magnitude equalizer to convert a rectangular cutoff boundary to a circular one. An example illustrates the usefulness of the proposed algorithm.

A NEW COMPREHENSIVE PROCEDURE FOR THE EXACT DESIGN OF CANONIC LDI-TYPE SC LADDER FILTERS

A new procedure is given for the exact design of canonic LDI-type SC ladder filters realizing any elliptic discrete-time transfer function, including highpass functions. We show that, in contrast to known exact design procedures, the underlying prototype network should be terminated with so-called half-unit delays in order to preserve the capability of realizing any filter type. We will show, based on such ladder prototypes, simple and stray-insensitive LDI-type SC ladder filters can be derived, which are canonical for any filter type (i.e., every filter pole requires for its realization one stray-insensitive SC integrator without the need for additional amplifiers). Compared to common exact design procedures, simpler SC ladder structures are obtained, in particular, for highpass-type filters. Exact designs of canonic SC highpass ladder filters are presented and compared with corresponding biquad designs.

On robust eigenvalue configuration

This study focuses on a class of disconnected subsets of the complex plane, of interest in the context of dominant pole assignment and filter design. It is first observed that the robust stability conditions originally put forth are in fact necessary and sufficient for the number of eigenvalues (matrices) or zeros (polynomials) in any given connected component to be the same for all the members of the given family. Polynomic semiguardian maps are then identified for a class of disconnected regions of interest. These maps are in fact essentially guarding with respect to one-parameter families.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Formant‐based speech synthesizer

A formant-based multi-path speech synthesizer is reconfigurable to use common elements for different types of sounds. A pitch generator or a noise generator is connected to a glottal signal path for vowel or aspirate sound, respectively. The pole and zero filters normally part of the fricative signal path which produces fricative or stop sounds are used in the glottal signal path for nasal sounds. The output of a spectral filter in the glottal signal path bypasses the cascaded formant filters and is connected directly to the glottal path attenuator for voice bar sounds. The output of the first formant filter is rectified and modulates the noise signal in the fricative path and the glottal and fricative signal paths are summed for voiced fricative sounds. To minimize spectral tilt, the third and fourth formant filters and the pole filter are peak filters. The glottal path attenuator is at the end of the glottal signal path to maximize the signal-to-noise ratio.

Polytopes of polynomials with zeros in a prescribed set

In the publication by A.C. Bartlett, C.V. Holot, and H. Lin (Proc. Amer. Contr. Conf., Minneapolis, MN, 1987) a fundamental result is established on the zero locations of a family of polynomials. It is shown that the zeros of a polytope P of nth-order real polynomials are contained in a simply connected set D if and only if the zeros of all polynomials along the edges of P are contained in D. The present authors are motivated by the fact that the requirement of simple connectedness of D may be too restrictive and applications such as dominant pole assignment and filter design where the separation of zeros is required. They extend the edge criterion of Bartlett et al. to handle any set D whose complement D/sup c/ has the following property: every point D in D/sup c/ lies on some continuous path which remains within D/sup c/ and is unbounded. This requirement is typically verified by inspection and allows for a large class of disconnected sets. >

One extending hypersphere method to handle dominant pole assignment

It is pointed out that the stability hypersphere approach presented by C.B. Soh et al. (see ibid vol.AC-32, p.239-244, Mar. 1987), can be extended to handle the case where the region is not simply connected. The extension is useful in application such as dominant pole assignment and filter design where the separation of zeros is required. >

Correction of (sin x )/ x distortion introduced by discrete-time/continuous-time signal conversion

A new analytical method is proposed for the correction of the (sin x)/x distortion which is characteristic of the spectra of discrete-time signals converted to continuous-time waveforms. The method is based on the adjustment of the quality factors associated with the poles of the reconstruction filter transform function. Simulation results show that, in spite of its simplicity, the new technique yields significant improvements in the frequency spectrum of the continuous-time signal after the conversion.

A 6-pole filter for improving the readability of muscle contaminated EEGs

A multi-channel switched-capacitor 6-pole filter for significantly reducing the EMG artifact present during seizures recorded by long-term monitoring procedures has been implemented for routine use. This permits repeated replay of the seizures with different filter settings. All of the channels can be simultaneously dialed to any cut-off frequency (3 dB down) between 8 Hz and 70 Hz and the event replayed for filtering and write-out onto any standard EEG machine. The advantage of the 6-pole switched-capacitor filter is that it does not require a complex design with high precision RC components. The cut-off frequency is determined by the frequency of a simple clock that is used to select the same cut-off point for all 16 channels. By changing the clock frequency, the operator moves the cut-off point linearly. The dramatic improvement obtained by off-line digital filtering that was recently reported (Gotman et al. 1981) indicates that more efficient filtering of EMG contaminated seizures is diagnostically significant in selected cases. This approach is limited by the availability and expense of not only the computer's hardware but also the dedicated software. Specially designed 4-pole analog filters (Barlow 1984) are less expensive than digital filtering, but are difficult to design even at specific frequencies and do not allow for a range of frequencies. The switched-capacitor 6-pole filters have all the advantages of the above but are even more efficient in reducing EMG artifact. They also do not have any of the above disadvantages and cost only a few dollars per channel.

Order-recursive spectrum estimation

The use of a multiple-pole filter in the time-average estimation of the autocorrelation allows the power spectrum estimates to be recursive in the order of multiplicity of the filter pole. The recursive generation of the estimates from various filter orders provides the flexibility to select the estimator of interest in terms of the variance and spectral and temporal resolution. >

Topics in Multiple-Loop Regulators and Current-Mode Programming

Some general considerations about multiple-loop feedback are discussed, and it is concluded that incorporation of a current-programmed power stage into a ``new'' power stage model is both justified and useful. A new circuit-oriented model of the current feedback path is derived which augments the well-known power stage canonical circuit model. The current loop gain, though wide-band, is always stable if the conventional stabilizing ramp is employed but has a relatively small low-frequency value. Consequently, the ``new'' power stage is more usefully modeled by a y-parameter model in which the current loop is not explicit. Expressions for the y parameters are given that are extensions of those previously derived. Another form of the model resembles the original canonical form for duty ratio programming, and shows that current programming effectively introduces lossless series damping that separates widely the two poles of the power stage LC filter. Therefore, although current programming tends to make the power stage output behave as a current source, the contol-to-output voltage transfer function exhibits, in addition to the familiar dominant pole, a second pole at the current loop gain crossover frequency, which may lie anywhere from one-sixth to two-thirds of the switching frequency.

A 12-bit sigma-delta analog-to-digital converter with a 15-MHz clock rate

A sigma-delta analog-to-digital converter that achieves 12-bit integral and differential linearity and nearly 13-bit resolution without trimming is described. The baseband width is 120 kHz with a first filter pole at 60 kHz, the clock frequency is 15 MHz, and only one 5-V power supply is needed. The circuit was realized in a p-well CMOS technology with 3-/spl mu/m minimum feature size. Compared with previous sigma-delta modulators, the input signal frequency and clock rate limit have been increased by one order of magnitude. To achieve this increase, a novel integrator concept was developed using bidirectional current sources. The circuit is fully self-contained, requiring only a 15-MHz crystal and one blocking capacitor as external elements. This converter was developed as the analog front end of a digital echo cancellation circuit for an integrated services digital network.

Corrections to "Finding the poles of lattice filter"

Corrections to "Finding the poles of lattice filter"

Speech analysis and synthesis methods developed at ECL in NTT — From LPC to LSP —

Speech analysis and synthesis methods developed at ECL in NTT are described. Starting from the LPC method the PARCOR and LSP schemes based on all pole filter are explained. The principles and physical interpretations of these methods are presented in comparison with each other. The characteristics of the feature parameters in these methods are clarified by means of several experiments. Synthesized speech quality is also shown by objective and subjective experiments. High quality synthesized speech can be achieved by these methods at a low bit rate transmission under 9600 bps.

Finding the poles of the lattice filter

The lattice filter is often used in spectral analysis problems. Once the reflection coefficients <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{c_{k}}</tex> are found, the task remains of extracting spectral information from them. Frequently this is done by DFT methods. An appealing alternative is to find the poles (modes) of the lattice directly. In this paper, we present an algorithm for computing the poles of the lattice directly from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{c_{k}}</tex> . The algorithm is based on the continued fraction expansion representation for the transfer function of the lattice. When applied to a sinusoid in noise, the algorithm found the poles, and hence the sinusoid's frequency, in less time than it took using a DFT-based peak detector. Another efficient algorithm is presented which computes the number of poles lying outside the unit circle. It is also based on information obtained directly from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{c_{k}}</tex> and employs only integer addition. Finally, it is shown that, by an adaptation of this algorithm, the number of poles lying in an annulus <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R &lt; |z| &lt; 1</tex> can be determined.