Frequency Domain Interpretation Research Articles

Applying velocity specification techniques to control robotic positioning systems

Abstract Residual vibration limits the terminal positioning precision of robotic manipulators. The residual vibration exhibited by robotic manipulators can be due to low frequency structural modes, self-excited by the manipulator during operations. In these cases, redesigning the structure to modify the resonant frequency(ies) causing residual vibration can be impractical or too costly. In this paper, an intelligent controller scheme is developed to measure and control residual vibration caused by the principal structural resonance. The controller tests the robot structure for critical resonant modes, calculates a drive profile using motion specification techniques to control the residual vibration, and then evaluates its effectiveness. A frequency domain interpretation is used to select the preferred input driver waveform. A breadboard controller is also developed for a single-degree-of-freedom drive system and it is used to validate the proposed strategy. Test results for a simple cantilever beam system and for a desktop articular-arm robot are presented.

Asymptotic error performance of modulation codes in the presence of severe intersymbol interference

The minimum distance and hence the asymptotic error probability of trellis modulation codes that have been subjected to severe channel filtering are evaluated. A general algorithm is proposed for this purpose and applied to one class of coded modulations. Using a frequency-domain interpretation of the Euclidean distance, it is shown that under extreme channel band limitations, the error event that causes the minimum distance is characterized by a spectral null at DC. Numerical results show that for filtered continuous-phase-modulation codes, decreasing the modulation index or smoothing the frequency pulse does not improve the error performance. For some of these modulations, channel filtering can actually improve the minimum distance. Bandpass and low-pass filtering are contrasted. The numerical results are explained by power spectrum considerations. >

A study on the speaker-independent feature extractinn of Japanese vowels by neural networks

The feature extraction characteristics of three-layer back propagation neural networks, when applied to speaker-independent vowel/gender recognition tasks, are investigated. Speech samples are monosyllabic vowels extracted from a syllablic data base of 100 Japanese syllables digitized at a sampling rate of 16 kHz spoken by 100 different speakers. Several LPC-based parameters and physiology-based parameters are tested for input representations. The results reveal that three hidden units are necessary to discriminate five Japanese vowels. Close investigation of hidden unit functions reveals that distributed representations of the targets are developed as hidden unit activation patterns. The frequency domain interpretation of the input weights of hidden units, using autocorrelation inputs, shows that the network extracts conventional knowledge on vowel formant structure. The relations between hidden unit activation patterns and descriptive features, as well as their implications to speech perception research, are also discussed.

Time domain harmonic matching pitch estimation using time-dependent speech modeling

A new formulation of the pitch estimation problem is proposed. A speech signal is modeled as a sequence of a specified function in a time-dependent manner which allows the period and the amplitude of excitation of the signal to be time varying. The asymmetry of the signal distribution with respect to the time axis is profited from. A statistically optimized resemblance function derived from an energy criterion is obtained. The estimation of pitch period is achieved by maximizing this function. An estimation of the position and the amplitude of the maximum peak in each period for voiced speech segments is simultaneously provided. An interpretation in frequency domain shows that this approach is equivalent to the harmonic structure matching process of the recently proposed biological pitch perception. Experiments on the performances of the algorithm are presented for clean, noisy, and simulated telephone-line filtered speech, respectively. The result is extremely encouraging: the estimation is almost free from error for clean speech, no presence of the first harmonic is necessary, the estimation is of high noise immunity, and the speech model is sufficient for following rapid pitch variations. It appears that the method is at least as efficient as any existing pitch determination methods based on harmonic structure searching.

Algebraic characterizations of almost invariance

This paper stresses the algebraic (as opposed to analytic) nature of the concept of almost invarianoe, which has been introduced by Willems (1980) as a means of studying asymptotic aspects of linear systems. Based on an interpretation' in terms of difference equations, it is shown that the basic properties and a number of characterizations of tho four fundamental classes of subspaces can be derived in a relatively simple and purely algebraic fashion. Among other things, this paper also extends the results of Hautus on the frequency-domain interpretation of ordinary ( A, B)-invariant subspaces, re-derives the pencil characterization of Jaffe and Karcanias (1981), and obtains a new ‘ hybrid ’ type of characterization. The last result also loads to a rank test for almost invariance.

A Frequency-Domain Interpretation of Echoes and their Effect on Teletext Data Reception

The interpretation of echoes in terms of ripples in the amplitude and group delay of a system is analyzed and discussed. Simple relationships are given, valid for most practical purposes for echo levels up to at least 10-20 percent. Scre general applications are considered, including determination of SAW filter triple transit frcm group delay ripple rate and amplitude. For this paper the relationships were used to represent echoes due to multipath. A computer program for television system analysis used these echoes as an input and eye diagrams were plotted for different echo levels and tines, for both ideal and real systems. Computer simulation of a data decoder, which extends the analytical approach to include direct assessrent of errors as a function of decoding threshold, is described but not used herein. Ihe analytical approach appears to be promising and will be applied to a greater number of echo and real system combinations as time permits.

Second‐Order Stochastic Input‐Output Stability and Instability of Interconnected Systems

AbstractNew results for the second‐order stochastic input‐output stability and instability of large classes of continuous time and discrete time interconnected stochastic systems are established. The analysis is accomplished in terms of lower order subsystems and in terms of system interconnecting structure. When appropriate, frequency domain interpretations are emphasized. The method of analysis advanced herein is applied to three specific examples.

Digital Control Law Synthesis in the w' Domain

Utility of w' transform domain analysis/synthesis procedures for linear, constant, single-rate sampled-data systems is explored. Basic properties of the wf domain are reviewed and compared with corresponding Z-,H>-, and s-domain properties. The main contribution of the paper is recognition that sampling and data-hold operations are modeled exactly in the w' domain, regardless of the sampling rate employed, and that the w' variable is analogous to the s variable in the sense that all familiar frequency domain design concepts, procedures, and interpretations can be carried over directly. Moreover, the imaginary part of w' approximates angular frequency to for Ico 1 < ir/lT, which further facilitates interpretation. Two example applications illustrate the procedure and make clear (by means of transfer functions and Bode plots) the nonminimum phase effects of sampling and data-hold operations and of sampling rate. It is demonstrated that acceptable closed-loop performance can be achieved at sampling rates that are an order of magnitude less than those employed when an emulation design approach is used.

Distance measures for speech processing

The properties and interrelationships among four measures of distance in speech processing are theoretically and experimentally discussed. The root mean square (rms) log spectral distance, cepstral distance, likelihood ratio (minimum residual principle or delta coding (DELCO) algorithm), and a cosh measure (based upon two nonsymmetrical likelihood ratios) are considered. It is shown that the cepstral measure bounds the rms log spectral measure from below, while the cosh measure bounds it from above. A simple nonlinear transformation of the likelihood ratio is shown to be highly correlated with the rms log spectral measure over expected ranges. Relationships between distance measure values and perception are also considered. The likelihood ratio, cepstral measure, and cosh measure are easily evaluated recursively from linear prediction filter coefficients, and each has a meaningful and interrelated frequency domain interpretation. Fortran programs are presented for computing the recursively evaluated distance measures.

Input-output stability of interconnected systems

New results for input-output stability of multiple input-multiple output systems, viewed as interconnected systems, are established. In the present approach, which can also be utilized in stabilization and compensation procedures, large-scale systems are analyzed in terms of their subsystems and interconnecting structure. The method advanced is applied to a specific example. The present results differ appreciably from earlier ones by Porter and Michel because they are applicable to a larger class of problems, they are simpler to apply when conicity conditions are used, and in addition to circle criteria, they also utilize Popov-type conditions. The present procedure differs significantly from existing methods concerned with the analysis of systems having several nonlinearities. Many of these earlier results (multidimensional Popov criteria) usually involve frequency dependent test matrices and graphical frequency domain interpretations are generally not possible. The present results require frequency independent test matrices and yield graphical frequency domain interpretations.

Frequency-Domain Interpretation of Oscillator Phase Stability

A frequency-domain interpretation of the phase stability of an oscillator is discussed. From a knowledge of the time dependence of an oscillator phase during a time interval T* it is possible to give the characteristics of this oscillator, not only for this time interval, but also for subsequent time intervals. Since the use of a Fourier transform for the computation of a continuous power spectrum is unrealistic, a discrete-spectrum approach will be taken. Usually, in the calculation of power spectra, stationarity of the fluctuations is assumed, although experiment indicates that this is often not the case. A more realistic approach is adopted. Analytical phenomena and random walk are separated from white noise on the basis of statistical criteria using discrete Fourier transforms. The white noise is then interpreted in the frequency domain. Both random walk and specific signals are studied in the time domain and can be separated by digital filtering. Two different sets of experimental results are analyzed by this method, one derived from measurements on a quartz-crystal oscillator locked to a low-frequency transmitter and the second from measurements on an ammonia maser. In both cases, measurement precision and ease of prediction of the behavior of the oscillator are improved.