Fast cross-correlation algorithm with application to spectral analysis

Based on the light curves at 22 and 37 GHz from the Metsahovi monitoring program, we investigate the time lags between the two radio bands for 48 radio-loud AGNs. DCF and ZDCF analyses are applied to the data. Our results show that there is a strong correlation between the two radio frequencies for all the sources, with the variations in the light curves at 37 GHz leading the ones at 22 GHz in general. There is no obvious differences between different sub-class AGNs as regards the time lag. In two sources, it was found that the bursts at the lower frequency lead the ones at the higher frequency. One possible explanation is that electron acceleration dominates the light curve until the radiation reaches the maximum. Some sources, such as 3C 273, 3C 279, 3C 345 and 3C 454.3, have good enough data, so we can calculate their lags burst-by-burst. Our calculations show that different outbursts have different lags. Some bursts have positive lags, most of bursts have no clear lags, and a few have negative lags. This result means that different bursts are triggered by different mechanisms, and the interpretation for the result involves both an intrinsic and a geometric mechanism. The positive lags are well consistent with the shock model, and we use these lags to calculate the typical magnetic field strength of the radiating region.

The fast algorithms of discrete sinusoidal transform of the fourth type (DST-IV) for small-length input data in the range of lengths from 2 to 9 are developed. Fast algorithms for short input data sequences are subsequently used as building blocks for designing fast algorithms of large-sized discrete transforms. Applying the fast DST-IV algorithms for small-size block processing can reduce overall system complexity and delay, allowing detailed signal processing. As a result of the literature review, two main approaches to developing fast discrete sine transform (DST) algorithms were identified, namely, the polynomial algebraic approach and the matrix factorization approach. In the paper, the last approach is exploited. A matrix-vector product expression of the DST-IV is the starting point for designing the fast algorithms. Then based on the repetition and arranging of the matrix elements, the factorisation of the matrices of coefficients of DST-IV is produced to reduce computational complexity. The correctness of the obtained algorithmic solutions was justified theoretically using a strict mathematical background of each of them. The elaborated algorithms were then further tested using MATLAB R2023b software to finally confirm their performance. The resulting factorizations of the DST-IV matrices reduce the number of multiplications by 63% but increase the number of additions by 8% on average in the range of signal sample numbers from 3 to 9. It has been observed that for even-length input sequences, the reduction in the number of multiplications is not as significant as for odd-length sequences. For some other well-known discrete trigonometric transforms (discrete Fourier transform, discrete Hartley transform) the opposite situation holds. The proposed DST-IV fast algorithms do not limit the length of the input data sequence to powers of two or three. The data flow graphs constructed for the proposed algorithms reveal their modular space-time structure suitable for VLSI implementation. Keywords: discrete sine transform; matrix factorization; fast algorithms; computational complexity; digital signal processing.

The approximation of a fractional order PIλDμ-controller transfer function using a chain fraction theory is considered. Analytical expressions for the approximation of s±α components of the transfer functions of PIλDμ-controllers were obtained through the application of the chain fraction theory. Graphs of transition functions and frequency characteristics of Dμ (α = μ = 0.5) and Iλ (α = λ = −0.5) parts for five different decomposition orders were obtained and analyzed. The results showed the possibility of applying the approximation of the PIλDμ-controller transfer function by the method of chain fractions with different valuesof λ and μ. For comparison, the transfer functions with the same order polynomials, obtained by the methods of Oustaloup transformation and chain fractions, were approximated for α = ±0.5. The analysis proved the advantages of using the chain fraction method to approximate the transfer function of the PIλDμ-controller. The performed approximation opens up the possibility of developing engineering methods for the technical implementation of PIλDμ-controllers. The accuracy of the same order transfer function approximation is higher when the method of chain fractions is used. It has been established that the adequacy of the frequency characteristics of the transfer functions obtained by the chain fraction method also depends on the approximation order.

The electrical impedance of trigeminal ganglion cells (in vivo) and hippocampal CA1 neurons (in vitro) of guinea pigs was measured in the frequency range of 5-1250 Hz using intracellular recording techniques with single microelectrodes and computerized methodology. The transfer functions of the electrode and the electrode-neuron system were computed from the ratio of fast Fourier transforms of the output voltage response from the neuron and input current composed of sine waves with rapidly increasing frequency which displaced membrane potential by 2-5 mV. We believe these to be the first measurements of complex impedance and transfer functions in peripheral and central neurons of vertebrates and the first use of such input current functions. The majority of trigeminal ganglion cells did not exhibit electrical behaviour ascribable to a simple resistance-capacitance (RC) circuit but showed a hump at low frequencies (5-250 Hz) in the computed transfer function, probably attributable to resonance. The transfer function in less than 20% of the trigeminal neurons could be fitted approximately to a theoretical transfer function (resistance in series with a parallel RC circuit model) providing values for electrode resistance, effective input resistance, and effective input capacitance. The transfer functions measured in hippocampal CA1 neurons were characterized by a rapid fall-off in the low frequency range (less than 200 Hz). Impedance locus plots approximate the locus corresponding to a series RC circuit in parallel with a parallel RC circuit.

Parameter estimation is one of the most challenging tasks in large‐scale distributed modeling, because of the high dimensionality of the parameter space. Relating model parameters to catchment/landscape characteristics reduces the number of parameters, enhances physical realism, and allows the transfer of hydrological model parameters in time and space. This study presents the first large‐scale application of automatic parameter transfer function (TF) estimation for a complex hydrological model. The Function Space Optimization (FSO) method can automatically estimate TF structures and coefficients for distributed models. We apply FSO to the mesoscale Hydrologic Model (mHM, mhm-ufz.org), which is the only available distributed model that includes a priori defined TFs for all its parameters. FSO is used to estimate new TFs for the parameters “saturated hydraulic conductivity” and “field capacity,” which both influence a range of hydrological processes. The setup of mHM from a previous study serves as a benchmark. The estimated TFs resulted in predictions in 222 validation basins with a median NSE of 0.68, showing that even with 5 years of calibration data, high performance in ungauged basins can be achieved. The performance is similar to the benchmark results, showing that the automatic TFs can achieve comparable results to TFs that were developed over years using expert knowledge. In summary, the findings present a step toward automatic TF estimation of model parameters for distributed models.

A digital twin is a promising evolving tool for prognostic health monitoring. However, in rotating machinery, the transfer function between the rotating components and the sensor distorts the vibration signal, hence, complicating the ability to apply a digital twin to new systems. This paper demonstrates the importance of estimating the transfer function for a successful transfer across different machines (TDM). Furthermore, there are few algorithms in the literature for transfer function estimation. The current algorithms can estimate the magnitude of the transfer function without its original phase. In this study, a new approach is presented that enables the estimation of the transfer function with its phase for a gear signal. The performance of the new algorithm is demonstrated by measured signals and by a simulated transfer function.

This paper addresses the blind dereverberation problem of a single-input multiple-output acoustic system. Many conventional approaches require a precise order of the transfer functions. In this paper, we propose an equalization algorithm that is less sensitive to the order misadjustment of the transfer functions. First, the transfer functions are estimated using an overestimated order, and the inverse filter set for these estimated transfer functions is calculated. Since the estimated transfer functions contain a common polynomial, the signal processed by the inverse filter set suffers from the effect of this common polynomial. Then, we extract this polynomial to compensate for the distortion. The proposed algorithm recovers input signal as long as the channel is overestimated. Simulation results show that the proposed method works well even when the order is highly overestimated.

Extratropical sea surface temperature (SST) and surface turbulent heat flux monthly anomalies in the central and eastern part of the North Atlantic are considered for the period 1952–92 on a 5° × 5° grid. In this region where the mean surface current is small, the SST anomalies are well simulated by a simple one-dimensional mixed layer model that is stochastically forced by the day-to-day changes in the local air–sea fluxes. A statistical signature of the stochastic model is that the cross correlation between surface heat flux and SST anomalies changes sign between negative and positive lags when the heat flux feedback is negative. This is observed at each grid point of the domain for the turbulent heat flux, which thus contributes both to generating the midlatitude SST anomalies and to damping them, once they are generated. Using properties of the lag covariance between SST and heat flux anomalies, the turbulent heat flux feedback is estimated from the observations. It averages to about 20 W m−2 K−1 in the investigated domain, increasing toward the northwest and the northeast and decreasing southward. It also varies seasonally, being generally largest in the fall and smaller and more uniform in summer. There is no indication that it can become significantly positive. A negative turbulent heat flux feedback is also suggested by the lag relation between the dominant modes of SST and turbulent heat flux variability over the whole North Atlantic, and it is found that the spatial patterns of the associated SST and turbulent heat flux anomalies are remarkably similar whether the atmosphere leads or lags, with only a change of heat flux sign between lead and lag situations. This analysis provides some observational support for the use on short timescales of a restoring condition for SST in ocean-only simulations, but the coupling coefficient should be weaker than usually assumed and a function of latitude and season. The associated SST–evaporation feedback has little effect on interannual surface salinity changes. It should be significant on longer timescales, but then the restoring temperature should be allowed to vary and nonlocal influences should be considered.

SUMMARY In the presence of large and continuous correlated noise signals in measured electric and magnetic time-series, even robust remote-reference methods give erroneous estimates of MT transfer functions. If clean remote time-series are available, it is possible to separate MT and correlated noise signals and to derive unbiased MT transfer functions with the signal–noise separation method (SNS) (Larsen et al. 1996). In practice, the remote time series also contain some noise and the results can be improved by using a second remote data set and the SNS-remote-reference technique. We tested this method with data from the Saxonian Granulite Massif (SGM), Germany, where strong correlated noise signals were detected. We used remote data which were recorded 350 km away and, for short periods, data from sites of the profile across the SGM itself (distance 5 km). To show the efficiency of the signal–noise separation we first determined a ‘true’ MT transfer function from time-series with low noise level. In a second step we reproduced the results from processing very noisy data sections. We were able to determine useful MT transfer functions even when the MT variations have less than 10 per cent share of the measured variations. We identified dominant noise in the measured time-series from pipelines and trains.

This paper presents a detailed study on the impact source identification of a plate structure using time-reversal (T-R) method. Prior to impact monitoring, the plate is calibrated (or characterized) by transfer functions at discrete locations on the plate surface. Both impact location and impact loading time-history are identified using T-R technique and associated signal processing algorithms. Numerical verification for finite-size isotropic plates under low velocity impacts is performed to demonstrate the versatility of T-R method for impact source identification. The tradeoff between accuracy of the impact location detection and calibration spacing is studied in detail. In particular, the effect of plate thickness on calibration spacing has been examined. A number of parameters selected for determining the impact location, approximated transfer functions and steps taken for reconstructing the impact loading time-history are also examined. Two types of noise with various intensities contaminated in strain response and/or transfer functions are investigated for demonstrating the stability and reliability of the T-R method. The results show that T-R method is robust against noise in impact location detection and force reconstruction in circumventing the inherent ill-conditioned inverse problem. Only transfer functions are needed to be calibrated and four sensors are requested in T-R method for impact identification.

Baroreflex modulates both the ventricular and vascular properties and stabilizes arterial pressure (AP). However, how changes in those mechanical properties quantitatively impact the dynamic AP regulation remains unknown. We developed a framework of circulatory equilibrium, in which both venous return and cardiac output are expressed as functions of left ventricular (LV) end-systolic elastance (Ees), heart rate (HR), systemic vascular resistance (R), and stressed blood volume (V). We investigated the contribution of each mechanical property using the framework of circulatory equilibrium. In six anesthetized dogs, we vascularly isolated carotid sinuses and randomly changed carotid sinus pressure (CSP), while measuring the LV Ees, aortic flow, right and left atrial pressure, and AP for at least 60 min. We estimated transfer functions from CSP to Ees, HR, R, and V in each dog. We then predicted these parameters in response to changes in CSP from the transfer functions using a data set not used for identifying transfer functions and predicted changes in AP using the equilibrium framework. Predicted APs matched reasonably well with those measured (r2=0.85-0.96, P<0.001). Sensitivity analyses indicated that Ees and HR (ventricular properties) accounted for 14±4 and 4±2%, respectively, whereas R and V (vascular properties) accounted for 32±4 and 39±4%, respectively, of baroreflex-induced AP regulation. We concluded that baroreflex-induced dynamic AP changes can be accurately predicted by the transfer functions from CSP to mechanical properties using our framework of circulatory equilibrium. Changes in the vascular properties, not the ventricular properties, predominantly determine baroreflex-induced AP regulation.

An efficient two-dimensional finite-element (FE) model is developed for the calculation of synchronous machine transfer functions. The numerical model uses two equivalent sinusoidally distributed stator windings substituting the actual three-phase machine by an equivalent two-phase one, leading to simplified FE simulations. Just two complex solutions per frequency are needed to obtain the three transfer functions that completely describe the two-port nature of the d axis network. A new FE-based method is proposed to accurately establish the rotor base quantities, allowing the calculated transfer functions to be in per-unit. Results are validated by comparing the performance of a two-axis equivalent circuit, derived from the FE transfer functions, with a reference transient FE program.

The manual design of Switched-Capacitor (SC) filters can be a strenuous process. This task becomes even more complex when the high gain amplifier is replaced by a low gain amplifier due to the loss of the virtual ground node, increasing the complexity of the filter's transfer function and requiring the compensation of the parasitic capacitances during the design phase. This paper proposes an automatic procedure for the design of high order SC filters using low gain amplifiers. The design methodology is based on a Genetic Algorithm (GA) using hybrid cost functions with varying goal specifications. The cost function first uses equations for the estimation of the filter's transfer function and, once the specifications are met, the filter is further optimized in order to increase its robustness to random variations. Afterwards, the gain and settling time of the amplifier is also estimated using equations and optimized against several process corners. The use of equation-based cost functions reduces the computation time, allowing the use of larger populations to cover the entire design space. Once all specifications are met, the GA uses transient electrical simulations of the circuit in the cost functions, resulting in the accurate determination of the filter's transfer function, and obtaining the final design solution within a reasonable amount of computation time.

This paper describes a simple procedure for synthesizing an active distributed RC network which, by using dominant poles and zeros, realizes a very accurate approximation of an arbitrary stable rational transfer function. The network uses a single uniformly distributed RC line with taps spaced along its length. A linear combination of tap voltages is added to the input signal to form the driving voltage for the RC line; the output signal is also a linear combination of the tap voltages. The network offers a number of significant advantages. Since it realizes a nearly rational transfer function, the approximation problem can be conveniently solved using readily available results on rational function approximation. Also, the network uses only one uniform RC line, the transfer function can be changed simply by changing resistor values, and the frequency can be scaled by minor connection changes. Thus one standard network with minor modification is useful for a wide variety of applications. This paper develops the design procedure and derives the various sensitivity functions of importance. Two example designs are carried out: an approximation to a second-order low-pass transfer function and an approximation to a second-order band-pass transfer function with a Q of 100. The sensitivities for the examples are very reasonable and the measurements made on laboratory models indicate excellent agreement with theoretical predictions.

Significant arterio-venous differences in nicotine concentrations have been observed during and after cigarette smoking, nicotine nasal spray, and intravenous nicotine administration. In this paper we describe a novel mathematical method for estimating arterial blood levels from venous blood level data. The model allows to quantify: (i) the influence of the microcirculation in the hands and forearm on the distribution of nicotine, and (ii) the influence of disregarding the venous to arterial circulation in the estimate of systemic inputs. We also (iii) propose a general method to predict arterial concentrations and inputs given venous data. The basic model we adopt is based on the relationship Cv = T * Ca, where Cv and Ca are the concentration in the venous and arterial site, respectively, T is the arterio-venous transfer function and * indicates convolution. We use empirical data to estimate T. We then compare estimates of systemic inputs to the venous site obtained taking into account the transfer function or, as usually done, disregarding it. The relationship we use to compare estimated inputs are: Cv = T * ka * A (where Ka is the arterial disposition function and A the systemic input), and Cv = Kv * A (where Kv is the venous disposition function), respectively. Finally, the estimated transfer function allows to estimate (average) Ca or A given arbitrary venous data. (i) Our analysis suggests that a bi-exponential T is needed to describe observed arterial-venous differences. The estimated transfer function indicates that no elimination of nicotine is involved in the forearm. (ii) Disregarding T, as usually done, erroneously obtains too complex venous input functions (because these input functions incorporate T). (iii) Disregarding T erroneously estimates significantly higher total inputs. (iv) Using the proposed model and previously published venous nicotine level data we predict substantial arterial-venous differences in blood nicotine levels for smokeless tobacco and nicotine gum. The use of disposition functions obtained from venous data may lead to erroneous estimation of the rates of entry into the circulation and systemic bioavailability for many drugs.