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 [9], 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 [10]:

Show more
The LF used in the design of CP-PLLs is a **second** **order** 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 [8]. The topology of a low pass **filter** used in this design is shown in Fig.5 [2], where H (p) is the loop transfer **function** (1) for Loop **Filter**.

Show more
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) [10]. 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 [11]. 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.

Show more
24 Read more

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.

Show more
100 Read more

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. **Second** **order** 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 **second** **order** 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.

Show more
13 Read more

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.

Show more
92 Read more

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.

Show more
10 Read more

transputer network, clock synchronization, second order filter, clock rate adjustment, simulation, distributed algo- rithms.. Introduction.[r]

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

Show more
14 Read more

This research focuses on estimation of the spectrum and the spectral power density **function** of non- Gaussian **second** **order** 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

Show more
18 Read more

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.

Show more
226 Read more

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.

26 Read more

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-

40 Read more

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 **second** **order** 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 **second** **order** 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 "**second** **order**" ideas, and introduce cybernetic concepts through a series of models of classes of systems.

Show more
24 Read more

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

11 Read more