Ideal Frequency Response Research Articles

Correcting the dynamic response of a commercial esophageal balloon-catheter.

It is generally recommended that an esophageal balloon-catheter possess an adequate frequency response up to 15 Hz, such that parameters of respiratory mechanics may be quantified with precision. In our experience, however, we have observed that some commercially available systems do not display an ideal frequency response (<8-10 Hz). We therefore investigated whether the poor frequency response of a commercially available esophageal catheter may be adequately compensated using two numerical techniques: 1) an exponential model correction, and 2) Wiener deconvolution. These two numerical techniques were performed on a commercial balloon-catheter interfaced with 0, 1, and 2 lengths of extension tubing (90 cm each), referred to as configurations L0, L90, and L180, respectively. The frequency response of the balloon-catheter in these configurations was assessed by empirical transfer function analysis, and its "working" range was defined as the frequency beyond which more than 5% amplitude and/or phase distortion was observed. The working frequency range of the uncorrected balloon-catheter extended up to only 10 Hz for L0, and progressively worsened with additional tubing length (L90 = 3 Hz, L180 = 2 Hz). Although both numerical methods of correction adequately enhanced the working frequency range of the balloon-catheter to beyond 25 Hz for all length configurations (L0, L90, and L180), Wiener deconvolution consistently provided more accurate corrections. Our data indicate that Wiener deconvolution provides a superior correction of the balloon-catheter's dynamic response, and is relatively more robust to extensions in catheter tube length compared with the exponential correction method.

Control parameter design for automatic carrier landing system via pigeon-inspired optimization

In this paper, a novel control parameter design method is presented for the automatic carrier landing system. To overcome difficulties in the manual parameter adjustment task, the pigeon-inspired optimization algorithm is utilized by converting the parameter design problem to an optimization problem. The modified version is proposed to avoid the lack of the diversity of pigeon population in the basic version. Parameters in the inner loop are optimized by computing the fitting difference between an ideal frequency response curve and the frequency response curve of the optimized control system. To optimize control parameters in the H-dot autopilot and the approach power compensation system, a weighted linear cost function in the time domain is adopted. Series of experiments are conducted to demonstrate the feasibility and effectiveness of our method. Comparative results indicate that out method is much better than other methods.

A new computer-aided tuning scheme for general lossy coupled-resonator bandpass filters based on the Cauchy method

In this paper, a novel analytical circuit model extraction scheme for the computer-aided tuning (CAT) of general lossy coupled-resonator bandpass filters is proposed based on the Cauchy total least squares (TLS) method. The new approach enforces the realisable condition of a set of scattering rational functions that is required for a lossy two-port network in extracting the transfer and reflection characteristics of a filter. Thus, a lossy circuit model can be synthesised from the extracted scattering polynomials using the well-known coupling matrix synthesis method from the literature. To illustrate the effectiveness of the new scheme, measured data of two different kinds of dual-mode filters are used. Using the proposed method, the extracted coupling matrix can give nearly identical frequency responses with the measured data, regardless of whether the filter is well-tuned or badly detuned.

α-Spline design of finite impulse response digital filters

The use of transition functions to connect the passband and the stopband in the ideal amplitude frequency response of an FIR filter reduces the oscillations near the band edges caused by the Gibbs phenomenon in filters designed by windowing. To this end, several methods based on β-splines have been proposed, in which an integer order of the spline is used to properly shape the transition band of the filter. However, it has been reported in the literature that the optimal value of the spline order that minimizes the approximation׳s mean square error may take non-integer values. Therefore, there is a lack of a precise formulation that allows the use of real positive numbers to properly design spline-based digital filters. The aim of this paper is to solve this problem, presenting a new formulation based on α-splines. By means of the proposed approach, non-integer values for the spline order can be employed in an appropriate mathematical framework, allowing its use as a real variable in any design procedure. Design examples demonstrate that smaller approximation errors than other approaches based on conventional windows can be obtained.

Optimal fractional delay-IIR filter design using cuckoo search algorithm

This paper applied a novel global meta-heuristic optimization algorithm, cuckoo search algorithm (CSA) to determine optimal coefficients of a fractional delay-infinite impulse response (FD-IIR) filter and trying to meet the ideal frequency response characteristics. Since fractional delay-IIR filter design is a multi-modal optimization problem, it cannot be computed efficiently using conventional gradient based optimization techniques. A weighted least square (WLS) based fitness function is used to improve the performance to a great extent. FD-IIR filters of different orders have been designed using the CSA. The simulation results of the proposed CSA based approach have been compared to those of well accepted evolutionary algorithms like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The performance of the CSA based FD-IIR filter is superior to those obtained by GA and PSO. The simulation and statistical results affirm that the proposed approach using CSA outperforms GA and PSO, not only in the convergence rate but also in optimal performance of the designed FD-IIR filter (i.e., smaller magnitude error, smaller phase error, higher percentage improvement in magnitude and phase error, fast convergence rate). The absolute magnitude and phase error obtained for the designed 5th order FD-IIR filter are as low as 0.0037 and 0.0046, respectively. The percentage improvement in magnitude error for CSA based 5th order FD-IIR design with respect to GA and PSO are 80.93% and 74.83% respectively, and phase error are 76.04% and 71.25%, respectively.

Contact resonance atomic force microscopy imaging in air and water using photothermal excitation.

Contact Resonance Force Microscopy (CR-FM) is a leading atomic force microscopy technique for measuring viscoelastic nano-mechanical properties. Conventional piezo-excited CR-FM measurements have been limited to imaging in air, since the "forest of peaks" frequency response associated with acoustic excitation methods effectively masks the true cantilever resonance. Using photothermal excitation results in clean contact, resonance spectra that closely match the ideal frequency response of the cantilever, allowing unambiguous and simple resonance frequency and quality factor measurements in air and liquids alike. This extends the capabilities of CR-FM to biologically relevant and other soft samples in liquid environments. We demonstrate CR-FM in air and water on both stiff silicon/titanium samples and softer polystyrene-polyethylene-polypropylene polymer samples with the quantitative moduli having very good agreement between expected and measured values.

Spatially uniform harmonic acoustic radiation force excitation using one-dimensional linear array

Low frequency harmonic force excitation can be used for both imaging and tissue characterization. This type of excitation can be achieved via intersecting two beams that slightly differ in frequency. One requirement of this technique is creating focused intersecting beams using available hardware. Previous studies have suggested different configurations for creating harmonic radiation force using linear arrays. However, these methods rely on identical frequency response assumption across all elements of the aperture. In practice, this assumption can be easily violated, especially if the transmit frequencies are not around the center frequency of the probe. When using electronic steering and focusing at different locations, this can result in a non-uniform radiation force pattern due to frequency changes in the sub-aperture. When used for vibro-acoustography, this manifests as vertical streaks in the final image that can severely degrade the quality of the image. We present a novel technique that minimizes element transmit frequency switching which in turn results in a more uniform excitation intensity. The results of applying this aperture configuration for vibro-acoustography imaging of breast phantoms with hard inclusions show significant improvements over previous methods. [This work was supported by NIH Grant R01 EB17213.]

Coupled-Line Filters With Stub-Embedded Resonators Using Accurate Admittance-Transformer Feeds for Flexible Terminations

Accurate admittance-transformer (Y-TF) feeds along with short-circuited stub-embedded resonators (SCSERs) are proposed in this study to design the improved parallel coupled-line (PCL) filters with structure-inherent transmission zeros (TZs). The proposed Y-TF feeds for flexible terminations are thoroughly analyzed and found more accurate than conventional approximate tapped-line feedings. Specifically, two basic parallel-coupled bandpass filters with conventional λ/2 stepped-impedance resonators are first successfully implemented to validate the proposed Y-TF feedings. The ideal frequency responses of the two filters by a circuit simulator are compared with those transformed from the coupling matrix. Furthermore, an SCSER-based filter with multiple TZs is designed to verify the feasibility of the described design procedure. The adopted resonating components are composed of two short-circuited stepped-impedance stubs and multiple open-circuited ones all extended from a common joining point. The interstage couplings of the filter are achieved by the short-ended PCLs, while the input/output couplings are realized by the proposed Y-TF feedings. Through the fabrication of the proposed filters, the measured results along with the simulated ones validate the theoretical derivations.

Improving the time domain response of fractional order digital differentiators by windowing

In this paper, the limitation of using (jω)ν as the ideal frequency response of fractional order digital differentiators for non-bandlimited signals is discussed. High frequency error enhanced by (jω)ν, along with the cause of time domain response degradation, is presented. Windows are proposed, which can help to improve the time domain response of fractional order digital differentiator and greatly reduce the filter order if the differentiator is approximated by finite impulse response (FIR) filter. Simulation results show that windowing the output of fractional order digital differentiator in frequency domain is effective in improving the time domain response of signals.

Two high accuracy digital integrators for Rogowski current transducers

The Rogowski current transducers have been widely used in AC current measurement, but their accuracy is mainly subject to the analog integrators, which have typical problems such as poor long-term stability and being susceptible to environmental conditions. The digital integrators can be another choice, but they cannot obtain a stable and accurate output for the reason that the DC component in original signal can be accumulated, which will lead to output DC drift. Unknown initial conditions can also result in integral output DC offset. This paper proposes two improved digital integrators used in Rogowski current transducers instead of traditional analog integrators for high measuring accuracy. A proportional-integral-derivative (PID) feedback controller and an attenuation coefficient have been applied in improving the Al-Alaoui integrator to change its DC response and get an ideal frequency response. For the special design in the field of digital signal processing, the improved digital integrators have better performance than analog integrators. Simulation models are built for the purpose of verification and comparison. The experiments prove that the designed integrators can achieve higher accuracy than analog integrators in steady-state response, transient-state response, and temperature changing condition.

Cat Swarm Optimization algorithm for optimal linear phase FIR filter design

In this paper a new meta-heuristic search method, called Cat Swarm Optimization (CSO) algorithm is applied to determine the best optimal impulse response coefficients of FIR low pass, high pass, band pass and band stop filters, trying to meet the respective ideal frequency response characteristics. CSO is generated by observing the behaviour of cats and composed of two sub-models. In CSO, one can decide how many cats are used in the iteration. Every cat has its′ own position composed of M dimensions, velocities for each dimension, a fitness value which represents the accommodation of the cat to the fitness function, and a flag to identify whether the cat is in seeking mode or tracing mode. The final solution would be the best position of one of the cats. CSO keeps the best solution until it reaches the end of the iteration. The results of the proposed CSO based approach have been compared to those of other well-known optimization methods such as Real Coded Genetic Algorithm (RGA), standard Particle Swarm Optimization (PSO) and Differential Evolution (DE). The CSO based results confirm the superiority of the proposed CSO for solving FIR filter design problems. The performances of the CSO based designed FIR filters have proven to be superior as compared to those obtained by RGA, conventional PSO and DE. The simulation results also demonstrate that the CSO is the best optimizer among other relevant techniques, not only in the convergence speed but also in the optimal performances of the designed filters.

Extension of Bandstop Filter Topology With Inter-Resonator Coupling Structures to Higher-Order Filters

This letter presents a rigorous extension of the concept for the bandstop filter (BSF) with inter-resonator couplings to a higher order filter. We show that a BSF topology with inter-resonator couplings can exhibit the frequency response that a conventional BSF topology without inter-resonator couplings generates. Equivalence between the coupling matrices of the two topologies are shown. As an example, this letter shows that fourth-order BSFs with and without inter-resonator couplings can exhibit identical frequency responses.

A Novel Firefly Algorithm for Optimal Linear Phase FIR Filter Design

Optimal digital filter design in digital signal processing has thrown a growing influence on communication systems. FIR filter design involves multi-parameter optimization, on which the existing optimization algorithms do not work efficiently. For which different optimization techniques can be utilized to determine the impulse response coefficient of a filter and try to meet the ideal frequency response characteristics. In this paper, FIR low pass, high pass, band pass and band stop filters have been designed using a new meta-heuristic search method, called firefly algorithm. Firefly Algorithm is inspired by the flash pattern and characteristics of fireflies. The performance of the designed filters has been compared with that obtained by real coded genetic algorithm (RGA), standard PSO and differential evolution (DE) optimization techniques. Differential evolution (DE) is already one of the most powerful stochastic real-parameter optimization algorithms in current use. Here the firefly algorithm (FA) technique has proven a significant advantage. For the problem at hand, the simulation of designing FIR filters has been done and the simulation results demonstrate that Firefly algorithm is better than other relevant algorithms, not only in the convergence speed but also in the performance of the designed filter.

Broadband photonic radio frequency (RF) channelization based on coherent optical frequency combs and polarization I/Q demodulation

In this work, we analyze and demonstrate a novel photonic-assisted broadband and high-resolution radio frequency (RF) channelization scheme based on dual coherent optical frequency combs (OFCs), regular optical de-muxes, and polarization I/Q demodulators in theory and experiment. The use of two coherent combs avoids precise optical alignment, and a numerical filter in digital signal processor (DSP) enables an ideal rectangular frequency response in each channel without any ultra-narrow optical filters. Besides, due to the use of polarization I/Q demodulation, ambiguous frequency estimate in direct detection can be avoided and the amplitude, phase mismatch in traditional I/Q demodulation can be mitigated. In experiment, we use two coherent OFCs with the free spectrum range (FSR) of about 40 GHz to demonstrate the channelization scheme with seven channels, 500 MHz channel spacing and frequency coverage from 3.75 GHz to 7.25 GHz. The input RF tones are accurately down-converted to an intermediate frequency (IF) with a maximum frequency error of 110 kHz. Meanwhile, crosstalk and spurious free dynamic range (SFDR) of the scheme are also discussed.

Theoretical and experimental determination of bandwidth for a two-axis fast steering mirror

Fast steering mirror (FSM) system is a precise beam steering mechanism which modulates the beam between a light source and a receiver using its reflecting surface. High bandwidth is an important property of FSM, which is associated with the response speed and stable precision. It is difficult to design the closed-loop bandwidth for FSM, which relies on the open-loop frequency response of the system and the design of the controller. A theoretical analysis, simulation, and testing method to determine an appropriate bandwidth designation for a two-axis FSM are developed in this paper. An ideal open-loop plant frequency response is compared to a final closed-loop bandwidth requirement, and then, stiffness of elastic support in each direction is researched and idea of stiffness design of elastic support is put forward. An integrated mechanical control simulation (IMCS) method is introduced to simulate the structural response and controller design synchronously to predict the final closed-loop control performance of the two-axis FSM system. Finally, the open-loop plant frequency response and closed-loop bandwidth of the assembled two-axis FSM system are tested with the results confirming the general validity of the analysis and simulation method presented in this paper.

Broadband Photonic RF Channelization Based on Coherent Optical Frequency Combs and I/Q Demodulators

In this paper, a novel photonic-assisted broadband and high-resolution radio-frequency (RF) channelization scheme based on dual coherent optical frequency combs (OFCs), regular optical de-muxes, and I/Q demodulators is analyzed and experimentally demonstrated. The use of two coherent combs avoids precise optical alignment, and a numerical filter in digital signal processor (DSP) enables an ideal rectangular frequency response in each channel without any ultranarrow optical filters. Besides, due to the use of I/Q demodulators, ambiguous frequency estimate in direct detection is avoided. By using two coherent OFCs with the free spectrum range (FSR) of about 40 GHz, we experimentally demonstrate the channelization scheme with seven channels, 500-MHz channel spacing, and frequency coverage from 3.75 to 7.25 GHz. The input RF tones are accurately downconverted to an intermediate frequency (IF) with a maximum frequency error of 125 kHz. Meanwhile, the channel frequency response and crosstalk of the scheme are also evaluated experimentally.

Closed Form Variable Fractional Time Delay Using FFT

In this letter, a novel tunable frequency response is proposed for variable fractional delay filter with careful consideration on conjugate symmetry. This proposed fractional delay method can be efficiently realized by FFT using the tunable fractional delay parameter. Its equivalent closed form to windowing method is derived and presented. Several comparisons to other windowing methods are also demonstrated, such as the magnitude response, group delay, and approximation error between ideal frequency response.

Novel Method for Frequency Response Measurement of Optoelectronic Devices

We develop a novel method to measure the frequency response of the optoelectronic devices. In this method, an electro-absorption modulator is utilized not only as a modulator but also as a photodetector with the identical frequency response. Based on this property, the frequency responses of the optoelectronic devices can be obtained and the results show good consistency with the measurement results by traditional methods. Instead of using broadband modulators or photodetectors, the frequency response of high bandwidth optoelectronic devices can be measured by using the low bandwidth optoelectronic devices.

An Effective Approach to Finding Differentiator Window Functions Based on Sinc Sum Function

An approach to finding digital differentiator window functions is studied. The frequency response of the truncated ideal differentiator is expressed by two parts. One is the ideal frequency response and the other is the deviation on the interval from ω=0 to ω=π. The deviation expression is the sum of weighted functions, where the general expression of these functions is equal to the half-sum of a pair of sinc sum functions plus π, and each weight is a window constant. Using the properties of the sinc sum function eight properties of the general expression and six properties of the deviation expression are deduced. By these properties both the relative errors of the passband and the change of their ripples can be small if each weight is proper and the truncated ideal differentiator is ideal at ω=0. From the expression of the deviation a matrix equation with window constants as unknowns can be written. Examples are given about how to write the matrix equations and how to find the optimized window constants. Four new differentiator windows as a family are obtained. These windows belong to the fixed window. Different from existing windows, the new windows are optimized in terms of reducing the relative errors of the passband. Comparisons show that new windows are better or much better than the Hanning, Hamming, Blackman, Kaiser, Chebyshev and polynomial windows in terms of differentiator performances.

Optimal linear phase finite impulse response band pass filter design using craziness based particle swarm optimization algorithm

An efficient method is proposed for the design of finite impulse response (FIR) filter with arbitrary pass band edge, stop band edge frequencies and transition width. The proposed FIR band stop filter is designed using craziness based particle swarm optimization (CRPSO) approach. Given the filter specifications to be realized, the CRPSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristics. In this paper, for the given problem, the realizations of the optimal FIR band pass filters of different orders have been performed. The simulation results have been compared with those obtained by the well accepted evolutionary algorithms, such as Parks and McClellan algorithm (PMA), genetic algorithm (GA) and classical particle swarm optimization (PSO). Several numerical design examples justify that the proposed optimal filter design approach using CRPSO outperforms PMA and PSO, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.