The convolution operation used in deterministic network calculus differs from its counterpart known from the classic systems theory. A reason for this lies in the fact that the former is defined in terms of the so-called min-plus algebra. Therefore, it is oft difficult to realize how it really works. In these cases, its graphical interpretation can be very helpful. This paper is devoted to a topic of construction of the min-plus convolution curve. This is done here in a systematic way to avoid arriving at non-transparent figures that are presented in publications. Contrary to this, our procedure is very transparent and removes shortcomings of constructions known in the literature. Some examples illustrate its usefulness.
A high accurate electronic instrument transformer calibration system is introduced in this paper. The system uses the fourth-order convolution window algorithm for the error calculation method. Compared with Fast Fourier Transform, which is recommended by standard IEC-60044-8 (Electronic current transformers), it has higher accuracy. The relative measuring errors caused by asynchronous sampling could be reduced effectively without any special hardware technique adopted. The results show that the ratio error caused by asynchronous sampling can be reduced to 10-4, and the phase error can be reduced to 10-3 degrees when the deviation of frequency is within ±0.5 Hz. The present method of measurement processing is achieved by a high-accuracy USB multifunction data acquisition (DAQ) card and virtual measurement devices, with low cost, short exploitation period and high stability.
At present, most of the existing target detection algorithms use the method of region proposal to search for the target in the image. The most effective regional proposal method usually requires thousands of target prediction areas to achieve high recall rate.This lowers the detection efficiency. Even though recent region proposal network approach have yielded good results by using hundreds of proposals, it still faces the challenge when applied to small objects and precise locations. This is mainly because these approaches use coarse feature. Therefore, we propose a new method for extracting more efficient global features and multi-scale features to provide target detection performance. Given that feature maps under continuous convolution lose the resolution required to detect small objects when obtaining deeper semantic information; hence, we use rolling convolution (RC) to maintain the high resolution of low-level feature maps to explore objects in greater detail, even if there is no structure dedicated to combining the features of multiple convolutional layers. Furthermore, we use a recurrent neural network of multiple gated recurrent units (GRUs) at the top of the convolutional layer to highlight useful global context locations for assisting in the detection of objects. Through experiments in the benchmark data set, our proposed method achieved 78.2% mAP in PASCAL VOC 2007 and 72.3% mAP in PASCAL VOC 2012 dataset. It has been verified through many experiments that this method has reached a more advanced level of detection.
Active acoustics offers potential benefits in music halls having acoustical short-comings and is a relatively inexpensive alternative to physical modifications of the enclosures. One critical benefit of active architecture is the controlled variability of acoustics. Although many improvements have been made over the last 60 years in the quality and usability of active acoustics, some problems still persist and the acceptance of this technology is advancing cautiously. McGill's Virtual Acoustic Technology (VAT) offers new solutions in the key areas of performance by focusing on the electroacoustic coupling between the existing room acoustics and the simulation acoustics. All control parameters of the active acoustics are implemented in the Space Builder engine by employing multichannel parallel mixing, routing, and processing. The virtual acoustic response is created using low-latency convolution and a three-way temporal segmentation of the measured impulse responses. This method facilitates a sooner release of the virtual room response and its radiation into the surrounding space. Field tests are currently underway at McGill University involving performing musicians and the audience in order to fully assess and quantify the benefits of this new approach in active acoustics.
In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo and Riemann-Liouvile equations and we also show an explicit formula for the solution of systems of time-invariant Caputo equations.
In the present paper, we investigate a multi-server Erlang queueing system with heterogeneous servers, non-homogeneous customers and limited memory space. The arriving customers appear according to a stationary Poisson process and are additionally characterized by some random volume. The service time of the customer depends on his volume and the joint distribution function of the customer volume and his service time can be different for different servers. The total customers volume is limited by some constant value. For the analyzed model, steady-state distribution of number of customers present in the system and loss probability are calculated. An analysis of some special cases and some numerical examples are attached as well.
Virtual or active acoustics refers to the generation of a simulated room response by means of electroacoustics and digital signal processing. An artificial room response may include sound reflections and reverberation as well as other acoustic features mimicking the actual room. They will cause the listener to have an impression of being immersed in virtual acoustics of another simulated room that coexists with the actual physical room. Using low-latency broadband multi-channel convolution and carefully measured room data, optimized transducers for rendering of sound fields, and an intuitive touch control user interface, it is possible to achieve a very high perceived quality of active acoustics, with a straightforward adjustability. The electroacoustically coupled room resulting from such optimization does not merely produce an equivalent of a back-door reverberation chamber, but rather a fully functional complete room superimposed on the physical room, yet with highly selectable and adjustable acoustic response. The utility of such active system for music recording and performance is discussed and supported with examples.