where f mn is the resonant frequency of the TM mn0 mode, μ mn the corresponding zero of the Bessel function ( m and n are non-negative integers), c the light velocity in free space, R the radius of the circular SIW resonator, and ε r and μ r are the relative dielectric constant and permeability of the substrate, respectively. The resonant frequency f 11 of the ﬁrst higher-order mode TM 110 occurs at the
The extended particle filter (EKPF) algorithm was initially given by Freitas in , under the framework of EKPF algorithm. This algorithm applies recursive formula of EKF to update each particle and will get an ap- proximate posterior probability density of ξ t . By the posterior probability distribution, new samples from the distribution are represented by a set of particles. Each particle has a weight assigned to it that represents the probability of that particle being sampled from the probability density function. In the resampling step, the par- ticles with negligible weights are replaced by new particles in the proximity of the particles with higher weights. EKPF, SEKPF and SLEKPF algorithm are as follows :
The LF used in the design of CP-PLLs is a secondorder low pass filter, which converts the current generate from charge pump (𝐼 𝑐𝑝 ) into a controlled voltage signal (𝑉 𝑐𝑡𝑟𝑙 ) for control the VCO after it filters the alternating current component. Also, the LF is used to suppress the noise and high frequency signal components from the CP, and to stabilize the loop . The topology of a low pass filter used in this design is shown in Fig.5 , where H (p) is the loop transfer function (1) for Loop Filter.
The extensive literature on DPLLs has many architectures and implementation techniques for the block diagram of Figure 2. The various approaches depend upon the target application and the system implementation technology. A DPLL architecture that has a number of desirable attributes, which include linearity and insensitivity to variations in input signal power, is the time delay digital tanlock loop (TDTL) . The TDTL solved the practical implementation issues that affected its predecessor, the digital tanlock loop (DTL), by replacing the Hilbert transformation (HT) block with a simple time delay unit . Essentially, the TDTL consists of two sample and hold blocks, a phase detector, a digital filter, a digitally controlled oscillator, and a time-delay block. This mixed-signal system accepts an analogue signal at its input but performs all the processing digitally. This means that the system can be easily implemented in a digital or a mixed-signal process. However, the replacement of the HT by a time delay unit led to a slight degradation in the linearity of the locking range characteristic [12,13]. A number of possible solutions have been proposed in the literature to overcome this problem including the use of a variable time delay block [14-16]. This paper proposes an improved TDTL architecture that overcomes the nonlinearity problem through the elimination of the time delay block. This new no-delay DTL architecture is referred to as NDTL. The NDTL system modifies the design of the DCO circuitry so that two sampling signals with 90 o phase shift are generated in order to maintain the quadrature relationship between the two channels of the system.
The loudspeaker will be assumed sealed to interrupt the radiation from the rear of the diaphragm thus reducing the complexity of the model. The intention is that the same model should apply to all loudspeaker units with adjustment of parameter values. Treble units are almost always sealed and midrange units most often include a can at the rear side. The bass loudspeakers are never sealed and must be placed within a closed cabinet. As will be shown later in this section, the loudspeaker is a transducer where the transfer function is a band-pass filter with a frequency range determined by the moving system and the voice coil. The sound pressure is downward limited by the resonance frequency below which any closed-box loudspeaker systems will drop off at 12 dB/octave and the sound pressure is upward limited by the electrical low-pass filter of the voice coil resistance and inductance above which the response drops off by –6 dB/octave.
From measurement software to be developed, the PDF and cumulative density function (CDF) can be obtained. For noise pattern detection the inverse CDF can be used since this concept has been accepted in the technical community worldwide . To obtain the PDF, results of the inverse accumulative function will be differentiated i.e.
OTA-C filters are one of the most widely used as continuous time filters. It is because they are fast active integrators, provides low-power operation and tuning of the filter characteristics at higher frequencies. At high frequencies, the OP AMP based active filters has limited performance. We cannot change the values of resistors and inductors but OTA-C filter provides ability to change their values by changing the transconductance of OTA. Secondorder low and high pass filter structures have widespread applications. The double gate MOSFETs show better performance in the nanometer range of operation. Because it has better control over short channel effects (SCE’s) and other scaling related problems like gate leakage, sub-threshold conduction. Double gate MOSFET is four terminal device and back gate can be used for biasing which can tune the characteristics of circuit. This will provide additional advantage of low power and reduced area. This paper presents secondorder low pass and high pass filter based on double gate OTA for VHF and UHF frequency applications. The proposed filter consists of two OTAs and two capacitors. This filter shows low sensitivity to passive components, low component count and ease in design. The simulation results shows pass band frequency of 14MHz and power consumption of 153.4 µwatt. The simulations are done using Tanner EDA version 13.0 at 90nm technology.
Passive filters are essential components in a vast array of electronic systems. By definition, networks consisting only of passive filters contain no active elements and do not require an external power supply. They have become increasingly important to the development of television, cellular and satellite radio components. These devices typically operate in the VHF (30-300 MHz) and UHF (300-3000 MHz) frequency ranges. Consequently, advancement of VHF and UHF passive filter designs for signal processing has become a crucial topic. There are four main types of filter passive responses: lowpass, highpass, bandpass and bandstop. This work focuses on bandpass filters.
In experiment, the common grounded inductor is the manual helix coil of high Q, and the capacitors of the 100 B serials of ATC are chosen as the capacitor array, and the PIN diodes of the MA4Pxxx serials of MA/COM are chosen as the switches. Using programmable logic device (PLD), the digital circuits of FH filter produce low or high voltage to control the PIN diodes forward or reverse bias, then select different capacitors combining with resonance circuit to accomplish different operating frequency filter characteristic. At last, the 3D EM simulation and experiment results are shown in Fig. 4.
In this paper, we mainly consider the stochastic second-order cone complementarity problem (SSOCCP). Due to the existence of stochastic variable, the SSOCCP may have no solutions. In order to deal with this problem, we ﬁrst regard the merit function of the stochastic second-order cone complementarity problem as the loss function and then present a low-risk deterministic model that is a conditional value-at-risk (CVaR) model. However, there may be two diﬃculties for solving the CVaR model directly: One is that the objective function is a non-smoothing function. The other is that the objective function contains expectation. (In general, the value of expectation is not easy to be calculated.) In view of these two problems, we present the approximation problems of the model by using a smoothing method and a sample average approximation technique. Furthermore, we give the convergence results of global optimal solutions and the convergence results of stationary points of the
This research focuses on estimation of the spectrum and the spectral power density function of non- Gaussian secondorder autoregressive model AR(2) through performing simulation’s experiments to calculate the values of power spectral density function (PSD) for different sample sizes and various frequencies.
ends of the interval (0, ∞). The second question is positivity of solutions of the equation Lu = f under boundary conditions u(0) = 0, u (∞) = 0. The used abstract scheme is close to the well-known MS Birman’s method in the spectral theory of self-adjoint operators. Conditions for discreteness of spectrum and positivity of the Green’s operator are obtained. The result relates to the MS Birman’s result on the necessary and suﬃcient condition for discreteness of spectrum of a polar-diﬀerential operation. The results may be interesting for researchers in qualitative theory of functional-diﬀerential equations and spectral theory of self-adjoint operators. MSC: Primary 34K08; 34K10; secondary 34K12
Abstract. In the paper we study the Green function for 2n-th order differential equation with a normal operator coefficient on the semi-axis. To this end, at first we construct the Green function of the equation with ”frozen” coefficients. Then we use the Levi method and obtain an integral equation for the Green function of the given equation. We prove the solvability of the integral equation. Using the integral equation we establish the main properties of the Green function.
®7Exactly where the differences lie between the system of the Begriffsschrift and second-order logic is not entirely straightforward to determine. This is mainly because exactly what constitutes second-order logic is not a settled issue. What we do know, for example, is that in the system of the Begriffsschrift there is quantification over second-order variables. We also know that Frege did not have an axiom of comprehension, the need for such an axiom was not pressing until Frege wanted to ground Hume's principle. To do this Frege introduced axiom V. This is an abstaction principle, which is not quite the same as a comprehension principle. As far as I know, a clear discussion of the exact differences is absent from the literature. Furthermore, insofar as a reconception of logicism is needed in the light of the many formal systems which present themselves as logic, what is being argued for here is that second-order logic, in its modern guise, can be characterised as logic, and this constitutes a partial vindication of logicism. To what extent the vindication is loyal to Frege's original project, in part, depends on the perceived rapport between modern second-order logic and the formal system of the Begj'iffsschrift. For exmple, whether or not what Frege explicitly proves in the system of the Begriffsschrift could also be proven in a weaker system than that of second-order logic, such as many-sorted logic, is an open question, as far as I know, Many-sorted logic is an obvious choice because it also has quantifcation over second-order variables, but it is complete.
In our consideration of second-order systems, the natural frequencies are in general complex-valued. We only need a limited set of complex mathematics, but you will need to have good facility with complex number manipulations and identities. For a review of complex numbers, take a look at the handout on the course web page.
The large belief-elicitation literature focuses on eliciting beliefs on events that are observ- able. The entire scoring rule literature fits into this category. Here, on the other hand, we elicit (second-order) beliefs on unobservable belief-states. A few recent papers do also address problems pertaining to belief-elicitation on unobservable states, but these require the agent to be SEU maximizer at some decision making stage. In this paper, in contrast, we consider the more standard problem of eliciting first and second-order be-
These cyberneticians' emphasis on such epistemological, psychological and social issues was a welcome complement to the reductionist climate which followed on the great progress in science and engineering of the day. However, it may have led them to overemphasize the novelty of their "second-order" approach. First, it must be noted that most founding fathers of cybernetics, such as Ashby, McCulloch and Bateson, explicitly or implicitly agreed with the importance of autonomy, self-organization and the subjectivity of modelling. Therefore, they can hardly be portrayed as "first order" reductionists. Second, the intellectual standard bearers of the secondorder approach during the 1970's, such as von Foerster, Pask, and Maturana, were themselves directly involved in the development of "first order" cybernetics in the 1950's and 1960's. In fact, if we look more closely at the history of the field, we see a continuous development towards a stronger focus on autonomy and the role of the observer, rather than a clean break between generations or approaches. Finally, the secondorder perspective is now firmly ingrained in the foundations of cybernetics overall. For those reasons, the present article will discuss the basic concepts and principles of cybernetics as a whole, without explicitly distinguishing between "first order" and "secondorder" ideas, and introduce cybernetic concepts through a series of models of classes of systems.
Abstract. Classification of Symmetric Positive Definite (SPD) matrices is gaining momentum in a variety machine learning application fields. In this work we propose a Python library which implements neural networks on SPD matrices, based on the popular deep learning framework Pytorch. Keywords: SPD matrix, covariance, second-order neural network, Rie- mannian machine learning
Second-order Abstract Categorial Grammar (Kanazawa, 2009b) is one such framework, equivalent to MSO in tree-transforming power (Kanazawa, 2009a). ACG tree transductions, which are expressed as linear λ-term homo- morphisms and thus have the same complexity as linear λ-term normalization, can be imple- mented in Haskell in the manner of Kiselyov and Shan (2010). A function extensionally equivalent to that defined logically above can be defined in a simple ACG consisting of a composed pair of homomorphisms and implemented in Haskell in a pair of type classes.