Terms Of Transfer Function Research Articles

First-Order Estimation and Precorrection of Parasitic Loss Effects in Ladder Filters

A method of estimation and approximate precompensation for the effects of element losses in resistance-terminated LC circuits is presented. Some new theorems are utilized for the special case of ladder networks. The process is valid for a nonuniform distribution of losses; there is, however, a limit to the amount of loss that can be compensated for. The procedure is based on a simple expression giving the firstorder increment of the complex transfer function in terms of quantities normally available from the lossless design. A formula is derived for the lossy response of the network; this has a form which brings out the individual effects of the different parasitic elements in producing distortion, and shows the effects of Q-tolerances of each lossy element. The predistorted transmission function is also given explicitly. The method'is not restricted to treating the effects of dissipation. It is also applicable to other parasitic phenomena (stray capacitances, element tolerances, etc.). The formulas become especially simple and useful for ladder networks. In the case of equal loss factors in elements of the same kind, they present an alternative to Darlington's design equations. Examples are given to illustrate the relative simplicity and accuracy of the method for practical network synthesis.

Optimization of the Flight-Control, Airframe System

The analysis of a system composed of a flight control and an airframe is ordinarily accomplished by using servoanalysis techniques in which the airframe and controller are described in terms of transfer functions. Optimization of such a system at the analytical level involves the selection of desirable relative locations for the poles and zeros of the airframe and controller transfer functions. The appropriate airframe pole and zero locations thus selected are then reflected back into the airframe geometrical characteristics. To achieve such an optimum system thus demands an overall approach which considers both the airframe and flight controller to be alterable system elements. This paper develops the optimization concept and illustrates the procedure with practical examples.

Responses of Temperature-Sensing-Element Analogs

Abstract From the standpoint of stability, temperature-sensing elements used in control systems should not contribute much phase lag at the frequency where the open-loop phase lag is 180 deg. For those cases where the temperature-sensing element does not contribute appreciable (less than 30 deg) phase lag around 180 deg, it would be advantageous to have a low-frequency approximation which works for complicated thermal systems. This paper presents such an approximation and establishes its validity for the electrical analogs of many sensing elements. In addition, it shows how the approximation is related to the thermal lag measured during a ramp input and the 63 per cent response time. These results, which are obtained in terms of transfer functions, can be applied to other systems having the same analogs.

Envelope transfer function analysis in A-C servo systems

IN THE ANALYSIS of a-c servo systems for stability and performance, attention is centered upon the carrier “envelope,” i.e., the signal proper. Extension of the convenient transfer function description used in direct-signal (low-pass) servo systems thus requires that the dynamic behavior of each element in the a-c system be described in terms of its effect on the carrier envelope by “envelope transfer functions” which are functions of signal frequency. In general, three types of elements are encountered in a-c servo systems: type-1 elements in which both input and output are modulated carriers; type-2 elements which have inputs at signal frequencies and outputs which are modulated carriers, and are called ”modulators” and type-3 elements which accept modulated carriers as inputs, produce outputs at signal frequencies, and are called “demodulators.” Both type-2 and type-3 elements readily lend themselves to simple envelope transfer function description if their dynamic behavior occurs on the signal side. Type-1 elements, however, have known transfer functions in terms of actual frequency, rather than signal frequency, and the envelope or signal transfer function must be derived.

Closed-Loop Control Systems Containing a Digital Computer

A discussion is given of the concepts of delay and distortion in feedback loops, with special reference to some of the special features incurred by digital control. Simple examples are given. Various approximations are presented for the ``starred'' transfer function in terms of the original analog transfer function, both in signal order to facilitate stability computations for digitally controlled loops, and also to illustrate the dependence of the properties of such loops on the analog and digital parameters.

Minimum-phase Transfer-Function synthesis

The Transfer Function in Terms of the General Circuit Parameters

Minimum-Phase Transfer-Function Synthesis

The Transfer Function in Terms of the General Circuit Parameters

Newer concepts of the pitch, the loudness and the timbre of musical tones

It is not widely realised that the first paper on cepstrum analysis was published two years before the FFT algorithm, despite having Tukey as a common author, and its definition was such that it was not reversible even to the log spectrum. After publication of the FFT in 1965, the cepstrum was redefined so as to be reversible to the log spectrum, and shortly afterwards Oppenheim and Schafer defined the “complex cepstrum”, which was reversible to the time domain. They also derived the analytical form of the complex cepstrum of a transfer function in terms of its poles and zeros. The cepstrum had been used in speech analysis for determining voice pitch (by accurately measuring the harmonic spacing), but also for separating the formants (transfer function of the vocal tract) from voiced and unvoiced sources, and this led quite early to similar applications in mechanics. The first was to gear diagnostics (Randall), where the cepstrum greatly simplified the interpretation of the sideband families associated with local faults in gears, and the second was to extraction of diesel engine cylinder pressure signals from acoustic response measurements (Lyon and Ordubadi). Later Polydoros defined the differential cepstrum, which had an analytical form similar to the impulse response function, and Gao and Randall used this and the complex cepstrum in the application of cepstrum analysis to modal analysis of mechanical structures. Antoni proposed the mean differential cepstrum, which gave a smoothed result. The cepstrum can be applied to MIMO systems if at least one SIMO response can be separated, and a number of blind source separation techniques have been proposed for this. Most recently it has been shown that even though it is not possible to apply the complex cepstrum to stationary signals, it is possible to use the real cepstrum to edit their (log) amplitude spectrum, and combine this with the original phase to obtain edited time signals. This has already been used for a wide range of mechanical applications. A very powerful processing tool is an exponential “lifter” (window) applied to the cepstrum, which is shown to extract the modal part of the response (with a small extra damping of each mode corresponding to the window). This can then be used to repress or enhance the modal information in the response according to the application.