Pub Date : 1955-06-01DOI: 10.1109/TCT.1955.1085234
L. Ule
IN THIS PAPER the concept of a minimum weighted squared error that has often been used in curve fitting1 is applied to a filter operating upon an input signal. The filter output is required to be a weighted least-squared-fit to its input. The steady-state error of the filter in reproducing its input is then zero when the input signal is contained in the ensemble of the chosen. fitting functions. The statistical aspects of the problem2 are subordinated to the requirement of zero steady state error to a proper input. The separate provinces of time-independent and time-varying filters in this sort of problem are defined; a slight generalization leads to a solution in the time-varying case. The proper domain of nonlinear least-squares filters is pointed out, but no general solution is given.
{"title":"Weighted least-squares smoothing filters","authors":"L. Ule","doi":"10.1109/TCT.1955.1085234","DOIUrl":"https://doi.org/10.1109/TCT.1955.1085234","url":null,"abstract":"IN THIS PAPER the concept of a minimum weighted squared error that has often been used in curve fitting1 is applied to a filter operating upon an input signal. The filter output is required to be a weighted least-squared-fit to its input. The steady-state error of the filter in reproducing its input is then zero when the input signal is contained in the ensemble of the chosen. fitting functions. The statistical aspects of the problem2 are subordinated to the requirement of zero steady state error to a proper input. The separate provinces of time-independent and time-varying filters in this sort of problem are defined; a slight generalization leads to a solution in the time-varying case. The proper domain of nonlinear least-squares filters is pointed out, but no general solution is given.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114493046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-06-01DOI: 10.1109/TCT.1955.6373417
E. Ho
THIS PAPER considers a new matrix factorization method for the synthesis of RLC two terminal-pair-networks. Equivalent matrices suitable for the synthesis of RLC ladder and parallel ladder networks are developed by linear transformations of matrix multiplication. The application of the method is demonstrated through the synthesis of a general minimum-phase transmission function as ladder networks 1‾4 and a general nonminimum-phase transmission function as parallel ladder networks. The advantage of the present method is that superfluous elements in the realized ladder networks are reduced considerably. Furthermore, an unbalanced form can be obtained for realizing a nonminimum-phase transmission function which has generally been realized in the lattice form.1, 5‾7
{"title":"A general matrix factorization method for network synthesis","authors":"E. Ho","doi":"10.1109/TCT.1955.6373417","DOIUrl":"https://doi.org/10.1109/TCT.1955.6373417","url":null,"abstract":"THIS PAPER considers a new matrix factorization method for the synthesis of RLC two terminal-pair-networks. Equivalent matrices suitable for the synthesis of RLC ladder and parallel ladder networks are developed by linear transformations of matrix multiplication. The application of the method is demonstrated through the synthesis of a general minimum-phase transmission function as ladder networks 1‾4 and a general nonminimum-phase transmission function as parallel ladder networks. The advantage of the present method is that superfluous elements in the realized ladder networks are reduced considerably. Furthermore, an unbalanced form can be obtained for realizing a nonminimum-phase transmission function which has generally been realized in the lattice form.1, 5‾7","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134214311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-06-01DOI: 10.1109/TCT.1955.1085222
A. Perry
{"title":"Review of 'The Complete Specification of a Network by a Single Parameter'","authors":"A. Perry","doi":"10.1109/TCT.1955.1085222","DOIUrl":"https://doi.org/10.1109/TCT.1955.1085222","url":null,"abstract":"","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"238 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131826074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500166
A. Papoulis
{"title":"On the expansion of a network response into a series of orthogonal functions","authors":"A. Papoulis","doi":"10.1109/TCT.1955.6500166","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500166","url":null,"abstract":"","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122935971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500163
L. Tasny
{"title":"The application of statistical methods to servomechanisms","authors":"L. Tasny","doi":"10.1109/TCT.1955.6500163","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500163","url":null,"abstract":"","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117000533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500162
H. Orchard
{"title":"Improved matrix and determinant methods for solving networks","authors":"H. Orchard","doi":"10.1109/TCT.1955.6500162","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500162","url":null,"abstract":"","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128673318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500146
L. A. Pipes
THE GENERAL theory of electric circuits whose component parameters are linear and constant has been extensively developed and is well understood. In recent years, considerable attention and effort has been directed to the analysis and performance of circuits whose parameters vary with the time. Many of the most important and interesting problems of circuit theory involve variable. parameters. For example, the equivalent circuits of the microphone transmitter, the condenser microphone, the induction generator, the superregenerator and of many other practical devices contain parameters that are time-varying. Many systems in mechanical and acoustical engineering in which the compliance or the inertia parameters vary with the time lead to the same mathematical formulation of their behavior as do the time-varying circuit problems.
{"title":"Four methods for the analysis of time-variable circuits","authors":"L. A. Pipes","doi":"10.1109/TCT.1955.6500146","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500146","url":null,"abstract":"THE GENERAL theory of electric circuits whose component parameters are linear and constant has been extensively developed and is well understood. In recent years, considerable attention and effort has been directed to the analysis and performance of circuits whose parameters vary with the time. Many of the most important and interesting problems of circuit theory involve variable. parameters. For example, the equivalent circuits of the microphone transmitter, the condenser microphone, the induction generator, the superregenerator and of many other practical devices contain parameters that are time-varying. Many systems in mechanical and acoustical engineering in which the compliance or the inertia parameters vary with the time lead to the same mathematical formulation of their behavior as do the time-varying circuit problems.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125478899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500155
D. Lampard
IN RECENT years time-varying circuits have attracted considerable attention in the literature,1 but little seems to have been done2 for those cases in which the input to such circuits is a random one.
近年来，时变电路在文献中引起了相当大的关注，但对于这种电路的输入是随机的情况，似乎很少有人做。
{"title":"The response of linear networks to suddenly applied stationary random noise","authors":"D. Lampard","doi":"10.1109/TCT.1955.6500155","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500155","url":null,"abstract":"IN RECENT years time-varying circuits have attracted considerable attention in the literature,1 but little seems to have been done2 for those cases in which the input to such circuits is a random one.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122611714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500154
J. H. Laning, R. Battin
IN RECENT years an extensive body of mathematical techniques has been developed for the analysis of the response of linear constant coefficient control systems to stationary random processes as inputs. In many cases it is possible to achieve direct synthesis of the optimum system for an assigned task. For nonstationary inputs or variable coefficient systems, no corresponding theory exists, even though problems of this nature arise quite often in practice. In the present paper an analog method is presented for the rms error analysis of a class of nonstationary problems. However, no attempt is made at the synthesis of an optimum system. Following a brief discussion of analog methods applicable to the general nonstationary case, our attention is concentrated on the special problem of a variable coefficient linear system with a stationary random input. Exploitation of the properties of the adjoint system in this case is shown to reduce considerably the labor in computing rms errors in comparison with the general method for nonstationary inputs. The simulation of the adjoint system is shown to be readily obtainable from the simulation of the original system.
{"title":"An application of analog computers to the statistical analysis of time-variable networks","authors":"J. H. Laning, R. Battin","doi":"10.1109/TCT.1955.6500154","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500154","url":null,"abstract":"IN RECENT years an extensive body of mathematical techniques has been developed for the analysis of the response of linear constant coefficient control systems to stationary random processes as inputs. In many cases it is possible to achieve direct synthesis of the optimum system for an assigned task. For nonstationary inputs or variable coefficient systems, no corresponding theory exists, even though problems of this nature arise quite often in practice. In the present paper an analog method is presented for the rms error analysis of a class of nonstationary problems. However, no attempt is made at the synthesis of an optimum system. Following a brief discussion of analog methods applicable to the general nonstationary case, our attention is concentrated on the special problem of a variable coefficient linear system with a stationary random input. Exploitation of the properties of the adjoint system in this case is shown to reduce considerably the labor in computing rms errors in comparison with the general method for nonstationary inputs. The simulation of the adjoint system is shown to be readily obtainable from the simulation of the original system.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121488237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-03-01DOI: 10.1109/TCT.1955.6500147
J. Brodin
LET $bar f$ (an overbarred letter) denote the operator of a linear system; x(τ) an input signal, which depends on time τ and y(t) the output response, as recorded at time t. The functional relationship between x(τ) and y(t) will be written $y = {bar f} x. eqno{hbox{(1)}}$.
{"title":"Analysis of time-dependent linear networks","authors":"J. Brodin","doi":"10.1109/TCT.1955.6500147","DOIUrl":"https://doi.org/10.1109/TCT.1955.6500147","url":null,"abstract":"LET <tex>$bar f$</tex> (an overbarred letter) denote the operator of a linear system; x(τ) an input signal, which depends on time τ and y(t) the output response, as recorded at time t. The functional relationship between x(τ) and y(t) will be written <tex>$y = {bar f} x. eqno{hbox{(1)}}$</tex>.","PeriodicalId":232856,"journal":{"name":"IRE Transactions on Circuit Theory","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1955-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129732357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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