In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. There are obtained the analytical solutions of the equations and also the maximal positive values of these solutions. The obtained sufficient conditions of the positivity of these solutions are defined by the Theorems. There are also formulated the necessary conditions of the positivity of these solutions. The analytical formulae enable the design of the system with prescribed properties [3].
Source/filter models have frequently been used to model sound production of the vocal apparatus and musical instruments. Beginning in 1968, in an effort to measure the transfer function (i.e., transmission response or filter characteristic) of a trombone while being played by expert musicians, sound pressure signals from the mouthpiece and the trombone bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the signals’ harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s transfer function. The first such recordings were made on analog 1/4 inch stereo magnetic tape. In 2000 digital recordings of trombone mouthpiece and anechoic output signals were made that provide a more accurate measurement of the trombone filter characteristic. Results show that the filter is a high-pass type with a cutoff frequency around 1000 Hz. Whereas the characteristic below cutoff is quite stable, above cutoff it is extremely variable, depending on level. In addition, measurements made using a swept-sine-wave system in 1972 verified the high-pass behavior, but they also showed a series of resonances whose minima correspond to the harmonic frequencies which occur under performance conditions. For frequencies below cutoff the two types of measurements corresponded well, but above cutoff there was a considerable difference. The general effect is that output harmonics above cutoff are greater than would be expected from linear filter theory, and this effect becomes stronger as input pressure increases. In the 1990s and early 2000s this nonlinear effect was verified by theory and measurements which showed that nonlinear propagation takes place in the trombone, causing a wave steepening effect at high amplitudes, thus increasing the relative strengths of the upper harmonics.
Sound and vibrations are often perceived via the auditory and tactile senses simultaneously, e.g., in a car or train. During a rock concert, the body vibrates with the rhythm of the music. Even in a concert hall or a church, sound can excite vibrations in the ground or seats. These vibrations might not be perceived separately because they integrate with the other sensory modalities into one multi-modal perception.
This paper discusses the relation between sound and vibration for frequencies up to 1 kHz in an opera house and a church. Therefore, the transfer function between sound pressure and acceleration was measured at different exemplary listening positions. A dodecahedron loudspeaker on the stage was used as a sound source. Accelerometers on the ground, seat and arm rest measured the resulting vibrations. It was found that vibrations were excited over a broad frequency range via airborne sound. The transfer function was measured using various sound pressure levels. Thereby, no dependence on level was found. The acceleration level at the seat corresponds approximately to the sound pressure level and is independent of the receiver position. Stronger differences were measured for vibrations on the ground.
Since a few years ago, there is an increasing interest for utilization of transfer functions (TF) as a reliable method for diagnosing of mechanical faults in transformer structure. However, this paper aims to develop the application of TF method in order to evaluate the drying quality of active part during the manufacturing process of transformer. To reach this goal, the required measurements are carried out on 50 MVA 132 KV/33 KV power transformer when active part is placed in the drying chamber. Two different features extracted from the measured TFs are then used as the inputs to artificial neural network (ANN) to give an estimate for required time in drying process. Results show that this new represented method could well forecast the required time. The results obtained from this method are valid for all the transformers which have the same design.
As it is found in the related published literatures, the transfer function (TF) evaluation method is the most feasible method for detection of winding mechanical faults in transformers. Therefore, investigation of an accurate method for evaluation of the TFs is very important. This paper presents three new indices to compare the transformer TFs and consequently to detect the winding mechanical faults. These indices are based on estimated rational functions. To develop the method, the necessary measurements are carried out on a 1.3 MVA transformer winding, under intact condition, as well as different fault conditions (axial displacement of winding). The obtained results demonstrate the high potential of proposed method in comparison with two other well-known indices. Additionally, two important methods for describing TFs by rational functions are studied and compared in this paper.
The transfer function (TF) method is presently a well-known method used to detect various types of winding damage in power transformers. Although abundant research has been done on this subject using laboratory windings as test objects, it is hard to find one, whose test objects are actual large-power transformer windings. Hence, a 400 kV disc winding consisting of 86 discs is used in this paper to study turn-to-turn short circuit with the help of the TF method. To evaluate the effects of this type of fault on TF curves, some mathematical comparison algorithms are used in this research.
The measurement of frequency characteristics, like magnitude and phase, related to a specific transfer function of DC–DC converters, can be a difficult task – especially when the measured signal approaches the boundary of a small-signal model validity (i:e. 1/3 of the switching frequency fS). It is hard to find a paper where authors mention the measurement techniques they use to draw frequency characteristics. Meanwhile the presence of noise in the output signal does not enable to directly measure the gain and the phase shift between the input and output signals. In such situations additional analysis is required in order to achieve a reliable result. This paper contains a description of a few methods that can be used to analyse measured signals in order to determine the gain and the phase shift of a specific transfer function. They enable to verify mathematical models in a wide range of frequencies (up to 1/3 fS). The methods use signals measured in the time domain and can be implemented in mathematical software such as Matlab or Scilab.
This paper analyses the performance of Differential Head-Related Transfer Function (DHRTF), an alternative transfer function for headphone-based virtual sound source positioning within a horizontal plane. This experimental one-channel function is used to reduce processing and avoid timbre affection while preserving signal features important for sound localisation. The use of positioning algorithm employing the DHRTF is compared to two other common positioning methods: amplitude panning and HRTF processing. Results of theoretical comparison and quality assessment of the methods by subjective listening tests are presented. The tests focus on distinctive aspects of the positioning methods: spatial impression, timbre affection, and loudness fluctuations. The results show that the DHRTF positioning method is applicable with very promising performance; it avoids perceptible channel coloration that occurs within the HRTF method, and it delivers spatial impression more successfully than the simple amplitude panning method.
This paper proposes a generalized fractional controller for integer order systems with time delay. The fractional controller structure is so adopted to have a combined effect of fractional filter and Smith predictor. Interestingly, the resulting novel controller can be decomposed into fractional filter cascaded with an integer order PID controller. The method is applied to two practical examples i.e. liquid level system and Shell control fractionator system. The closed- loop responses resulting from the proposed method are compared with that of the available methods in the literature. For quantitative evaluations of the proposed method, Integral Absolute Error (IAE) and Integral Square Control Input (ISCI) performance criteria are employed. The proposed method effectively enhances the closed-loop response by improving the IAE values, reducing the control effort inputs to achieve the desired output. The disturbance rejection and robustness tests are also carried out. The robustness test reveals a significant improvement in the maximum absolute sensitivity measure. That is displayed in numerical simulations of the paper.
The head-related transfer function (HRTF) is dependent on the position of the sound source (both direction and distance) and is also affected by individual anatomical parameters. Individualized HRTFs have been shown to affect the perception of sound direction, but have not been considered in distance perception. This work aims to discover, by means of psychoacoustic experiments for a virtual reproduction system through a pair of in-ear headphones, the effect of individualized HRTF on auditory distance perception for a nearby sound source. The individualized HRTFs of six subjects and the non-individualized HRTFs of a mannequin at seven distances between 0.2 and 1.0 m and five lateral azimuths between 45X and 135X in the horizontal plane were processed with white noise to generate binaural signals. Further, the individualized and non-individualized HRTFs were used in the auditory distance perception experiments. Results of distance perception show that the variance of distance perception results among subjects is significant, the reason could be the stimuli are lack of dynamic cue and early reflections, or the auditory difference of distance perception among subjects. However, via the analyses of mean slope of perceptual distance and correlation between the perceptual and real distance, we find that the individualized HRTF cue has insignificant influence on distance perception.
In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. The analytical solutions of the equations and also the maximal positive values of these solutions are obtained. The analytical formulae enable the design of the system with prescribed properties. The complementary case to the earlier paper is presented. In an earlier paper it was assumed that the roots si are different, and now we consider the case when s1 = s2 = … = sn.
The parameters of sigma-delta audio DAC depend mainly on digital sigma-delta modulator's features, especially on its noise transfer function (NTF). Many methods of design and optimization of the loop filter's coefficients in sigma-delta modulators have been proposed so far. These methods enable the designer to get suitable noise transfer functions for specific application. This paper reviews NTF design and optimization methods which are particularly useful in audio applications.