Dolph Chebyshev Research Articles

Design of fir filters using exponential--Hamming window family

In this paper, a new two-parameter window obtained by the combination of two windows, known as exponential and Hamming, is proposed and applied for the design of finite impulse response (FIR) digital filters. First of all, the quality of the proposed window is analyzed in terms of window spectral parameters and then compared with other two-parameter windows, namely Kaiser, cosh, and exponential. The window simulation results show that the proposed window can provide better ripple ratio than other windows for fixed window length and mainlobe width. Secondly, the performance of the proposed window is analyzed in digital filter design. The filter numerical comparison with Saramaki, Kaiser, Dolph–Chebyshev, cosh, and exponential windows confirms that the filter designed by the proposed window can exhibit a better filtering performance compared to well-known two-parameter windows in the literature because it can provide better minimum stopband attenuation for fixed filter length and transition width.

Adaptive Dolph–Chebyshev window‐based S transform in time‐frequency analysis

The S transform is widely used in time-frequency analysis (TFA). However, the standard S transform suffers from the poor energy concentration in time-frequency distribution (TFD). In this study, an adaptive Dolph–Chebyshev window instead of the Gaussian window-based S transform and its fast realisation strategy are introduced for non-stationary signal TFA. By controlling the shape of the Dolph–Chebyshev window adaptively to signal, the new TFA method is able to achieve a high energy concentration in TFD. In addition, the new method is superior to other classical methods for instantaneous frequency estimation. Several examples are presented to illustrate its behaviour on different signals and demonstrate its validity.

Analysis of absorption in situ with a spherical microphone array

Measured values of acoustic absorption often vary between the laboratory and the field due to deficiencies in standard measurement methods. This paper introduces a new method of measuring acoustic absorption in the field using a spherical microphone array. Plane-wave decomposition is used to separate direct energy from reflected energy when the array is placed adjacent to the absorptive sample. Additional signal processing techniques including the Dolph–Chebyshev beampattern and Delay-and-Sum processing are introduced and used to improve the method. The method is verified by simulation for normal and oblique incidence and by experiment for normal incidence.

Performance enhancement of high-altitude platforms wireless sensor networks using concentric circular arrays

In this paper, a concentric circular antenna array (CCA) is proposed to improve the performance of High-Altitude Platform Wireless Sensor Network (HAPWSN). This CCA is optimized using a modified Dolph–Chebyshev feeding function and designed for two cell sizes. The WSN is formed by a HAP, which acts as a global sink and a set of ground sensors. The communications performance of this network is examined using existing practical sensor technologies at two different frequencies (2.4GHz and 868MHz) and two corresponding bit rates (250kbps and 38.4kbps) where it shows the capability of establishing communications link between the HAP sink and the ground sensors. A comparison between the proposed CCA and conventional antenna techniques that give the same cell specifications shows that the link performance in terms of the bit energy-to-noise power spectral density ratio can be increased by 11.37dB for cells of 8km radius and by 16.8dB in the case of 30km radius cells which indicates the capability of establishing HAPWSN at 2.4GHz.

Synthesis of a Linear Antenna Array for Maximum Side-lobe Level Reduction

are number of Techniques used to reduce Side Lobe Level (SLL) of antenna arrays to save power and improve Quality of Service (QoS) by ensuring maximum radiation in desired direction, several methods are available in literature. It is a well known fact that when an attempt is made to reduce the first sidelobe level of an antenna array, the beamwidth increases. However, in the present work, an array for a specified first side lobe level of -35dB was synthesized using Dolph Chebyshev method. A real-value Genetic Algorithm (RGA) was also used to optimize the current excitations. The weighting vectors are compared. Using these vectors, patterns are generated for arrays of different elements. The resultant patterns are compared and the result shows greater improvement in the SLL reduction from the RGA method without deteriorating the main beamwidth. Keywordslobe level, Quality of Service, beamwidth, Dolph Chebyshev, and Real-Value Genetic Algorithm 1. INTRODUCTION antenna array is a group of identical antenna elements

Hybrid MUSIC Dolph–Chebyshev algorithm for a smart antenna system

ABSTRACTThis paper presents practical design of a smart antenna system based on direction‐of‐arrival estimation and Dolph–Chebyshev beam forming. Direction‐of‐arrival estimation is based on the multiple signal classification algorithm for identifying the directions of the source signals incident on the sensor array comprising the smart antenna system. The smart antenna system design involves a hardware part, which provides real data measurements of the incident signals received by the sensor array. This paper presents the Dolph–Chebyshev method for the synthesis and design of antenna arrays with periodic element spacing. A Field‐Programmable Gate Array implementation is presented for an antenna array application employing digital beamforming. The array comprises 10 elements, equal in number receiving radio frequency and intermediate frequency components, as well as a Spartan‐3E Field‐Programmable Gate Array‐based unit, which is responsible for the control of the array. Low‐cost and switched‐beam, and fully adaptive antenna array suitable for 2‐GHz applications are proposed in this paper. Copyright © 2013 John Wiley & Sons, Ltd.

Time-selective windowing technique in free-field microphone reciprocity calibration

Time-selective windowing techniques, which effectively remove multi-path noise, have been widely utilized for reciprocity calibration of microphone there are still limitations imposed by overlapping signals, particularly at low frequencies and for high Q microphones. Based on a fast Fourier transform analysis, the leakage due to a limited frequency range makes the overlap problem worse, not be perfectly separated. Instead of using conventional low-pass filters that are designed to have a flat response in the frequency range of interest, in this study, a filter with a Dolph-Chebyshev window shape was proposed because it has low sidelobe levels. After removing multi-path noise with a time-selective window, an inverse filter should be applied to compensate for distortion created by the applied filter. The method suggested in this paper extends the possible frequency range of free-field reciprocity calibration to frequencies below 2 kHz.

Linear array modules with prescribed excitations using waveguide shunt slot-fed microstrip patch elements

A waveguide shunt slot-fed microstrip patch antenna (WGMPA) element is proposed and analyzed with method of moments (MOM) using entire-domain basis functions. The developed analysis has been utilized to obtain parametric observation of power-coupling versus transverse offset of feeding slot from the waveguide axis. Expressions for the radiation pattern as a summation of contributions of individual basis functions are reported. The proposed element is amenable to building-up series-fed linear arrays by a simple cascading of elements at the through-end of the feeding waveguide. The authors propose that arbitrary amplitude excitations may be applied to such linear arrays for desired tailored array pattern characteristics. The required transverse offsets for each array element may be computed using the reported parametric result. As a demonstration of concept, two distributions are designed – uniform amplitudes and Dolph–Chebyshev for reduced side lobes. Computed element patterns from MOM are used with an array factor formulation for arbitrary element positions. Both modules show radiation characteristics closely matching the expected directivity and sidelobe envelopes. Analysis validation is achieved using a proven finite element method (FEM)-based solver; the comparison is close and is reported. Efficacy of the waveguide shunt-slot fed patch element for building linear array modules with prescribed amplitude distributions is thus established.

An optimized design of nonuniform filter bank using variable-combinational window function

This paper proposes an optimized tree structure technique for the design of near perfect reconstruction (NPR) non-uniform filterbank. Popular variable window functions like Kaiser, Dolph-Chebyshev (DC) and Parzen-cos6 (nπ/N) (PC6) are used in the design of prototype filter. The NPR condition, results the distortion at the output. Therefore a linear iterative optimization technique is used to minimize the distortion. The proposed algorithm provides lowest value of distortion parameter than earlier reported publications with minimum computation overhead.

DIFFERENTIAL EVOLUTION ALGORITHM FOR OPTIMIZING THE CONFLICTING PARAMETERS IN TIME-MODULATED LINEAR ARRAY ANTENNAS

In this paper, a new technique is proposed to optimize the con∞icting parameters like low value of maximum side lobe level (SLL), narrow beam-width of the main beam and low value of maximum sideband radiation level (SRL) of time-modulated linear antenna arrays (TMLAAs). The method is based on minimizing a multi-objective fltness function by using single-objective difierential evolution algorithm (DEA) technique. The method is applied to both uniformly excited TMLAA (UE-TMLAA) and non-uniformly excited TMLAA (NUE-TMLAA) to synthesize low side lobe optimum pattern at operating frequency by suppressing the sideband radiation level to a su-ciently low value. For UE-TMLAA only the switch- on time durations of the array elements and for NUE-TMLAA the switch-on time durations and the static amplitudes with predetermined dynamic range ratio (DRR) of static amplitudes are taken as the optimization parameters for the DEA. To show efiectiveness of the proposed approach, the single-objective DEA optimized results are compared with those obtained by other single objective and multi- objective techniques that has been reported previously. Also, flrst null beam width (FNBW) and half power beam width (HPBW) of the DEA optimized patterns at fundamental radiation are compared with those of the Dolph-Chebyshev (D-C) pattern of same SLL.

New Window Functions for the Design of Narrowband Lowpass Differentiators

New window functions are studied for the design of FIR narrowband lowpass differentiators (FNLD). The ideal lowpass differentiator is truncated by window functions. Using the sinc sum function, the frequency responses of the truncated lowpass differentiators are changed to a new form, which contains two parts. The first part is the integral of the sum of weighted sinc sum functions and the second one is the direct sum of other weighted sinc sum functions. According to the properties of the sinc sum function, the properties of the two parts are analyzed and differentiator errors are mainly dictated by the second part. As a result, the stopband error of FIR lowpass differentiators is approximately proportional to the cutoff frequency of their corresponding ideal differentiators. It is deduced that window constants can be derived according to the second part. Examples are given on how to get optimized windows for the design of FNLD. Three new windows as a family are obtained. The performances of FNLD obtained by using these new windows are concluded. Consequently, FNLD can be designed conveniently. Comparisons show that theses new windows are much better than the Hanning, Hamming, Blackman, and Dolph–Chebyshev windows and more optimized than the Kaiser window in terms of the performances of FNLD.

Enhanced ultrasound strain imaging using chirp-coded pulse excitation

To improve the quality of ultrasound strain imaging, chirp-coded pulse excitation which can enhance echo signal-to-noise ratio (eSNR) was used. The effects of various factors on chirp-coded strain imaging were investigated. Five chirp schemes were designed to investigate the relationship of the range side lobe level (RSLL), main lobe width and energy for strain imaging. We use phase zero method with amplitude modulation correction as strain estimator. The simulation results demonstrate that elastographic signal-to-noise ratio (SNRe) for chirp pulse decreases with the RSLL and the main lobe width, and that there is a tradeoff among choosing a high-energy tapering window function, reducing the RSLL and narrowing the main lobe in designing a chirp scheme for strain imaging. Chirp pulse performs much better than conventional short pulse in low eSNR, great depth or high attenuation conditions due to the increased eSNR with it. However, in high eSNR condition, the increased eSNR with chirp pulse does not improve SNRe, and the performance of chirp pulse mainly depends on the RSLL and main lobe width. Some chirp schemes still achieve higher SNRe than short pulse in high eSNR condition, because these chirp schemes have narrower main lobe than short pulse and have very low RSLL. Chirp pulse has better lesion detectability and axial strain resolution than short pulse especially in low eSNR condition, because chirp pulse can use shorter window length to get the same SNRe that is achieved by short pulse. Within the scope of five window functions (Tukey, Lanczos, Parzen, Dolph–Chebyshev and Kaiser), we tried to find the optimal chirp scheme which is possibly the combination of chirp pulse excitation with 40% tapered Tukey window and matched compression filter. A commercial elastic phantom experiment on a freehand strain imaging system further validates the superior performance of chirp pulse.

Pulse compression technique for simultaneous HIFU surgery and ultrasonic imaging: A preliminary study

In an ultrasound image-guided High Intensity Focused Ultrasound (HIFU) surgery, reflected HIFU waves received by an imaging transducer should be suppressed for real-time simultaneous imaging and therapy. In this paper, we investigate the feasibility of pulse compression scheme combined with notch filtering in order to minimize these HIFU interference signals. A chirp signal modulated by the Dolph–Chebyshev window with 3–9MHz frequency sweep range is used for B-mode imaging and 4MHz continuous wave is used for HIFU. The second order infinite impulse response notch filters are employed to suppress reflected HIFU waves whose center frequencies are 4MHz and 8MHz. The prototype integrated HIFU/imaging transducer that composed of three rectangular elements with a spherically con-focused aperture was fabricated. The center element has the ability to transmit and receive 6MHz imaging signals and two outer elements are only used for transmitting 4MHz continuous HIFU wave. When the chirp signal and 4MHz HIFU wave are simultaneously transmitted to the target, the reflected chirp signals mixed with 4MHz and 8MHz HIFU waves are detected by the imaging transducer. After the application of notch filtering with pulse compression process, HIFU interference waves in this mixed signal are significantly reduced while maintaining original imaging signal. In the single scanline test using a strong reflector, the amplitude of the reflected HIFU wave is reduced to −45dB. In vitro test, with a sliced porcine muscle shows that the speckle pattern of the restored B-mode image is close to that of the original image. These preliminary results demonstrate the potential for the pulse compression scheme with notch filtering to achieve real-time ultrasound image-guided HIFU surgery.

A Projection-Based Approach for Ultra-Low Side-Lobe Pattern Synthesis in Time-Modulated Spherical Arrays

The time-modulation approach is extended to spherical antenna arrays to synthesize ultra-low side-lobe patterns. A projection approach combined with the generalized Tseng–Cheng distributions, which generate axis-symmetric patterns in all ϕ-cuts for planar arrays with square lattices and boundaries, is utilized in the synthesis of time-modulated spherical arrays. Patterns with an approximately Dolph–Chebyshev profile for all ϕ-cuts are successfully synthesized by phase compensation using the differential evolution algorithm. Numerical results show that ultra-low side-lobes can be synthesized for time-modulated spherical arrays, with very low dynamic-range ratios, low sideband levels, and minimal reduction in directivity and efficiency.

Pattern Synthesis using Genetic Algorithm for Low Sidelobe Levels

For pattern synthesis of arrays, it is required to find out appropriate weighting vectors to yield a desired radiation pattern. It is well known that several methods for above purpose are available in literature. It is an established fact that when an attempt is made to reduce the first sidelobe level, the beamwidth increases. However, it is of interest in the present work to synthesize an array for a specified first side lobe level without deteriorating the beamwidth. For this purpose, well known analytical technique for array synthesis to control side lobe level, Dolph Chebyshev method is used with the application of WIPL-D Microwave EM software, and the excitation levels are found out. They are also found out using Genetic Algorithm (GA). The weighting vectors are compared in the form of a Table. Using these vectors, the patterns are generated for arrays of different elements. The resultant patterns are compared for the above methods.

DFT Interpolation Algorithm for Kaiser–Bessel and Dolph–Chebyshev Windows

This paper describes the discrete Fourier transform (DFT) interpolation algorithm for arbitrary windows and its application and performance for optimal noncosine Kaiser-Bessel and Dolph-Chebyshev windows. The interpolation algorithm is based on the polynomial approximation of the window's spectrum that is computed numerically. Two- and three-point (2p and 3p) interpolations are considered. Systematic errors and noise sensitivity are analyzed for the chosen Kaiser-Bessel and Dolph-Chebyshev windows and compared with Rife-Vincent class I windows.

New efficient window function, replacement for the Hamming window

A new simple window function is presented, which for the same window order (M), has a main-lobe width less than or equal to that of the Hamming window, while offering about 2–4.5 dB smaller peak side-lobe amplitude. Furthermore, just like the Hamming window, it is computationally efficient for signal spectrum analysis; this is because of the fact that, the sum of window coefficients with its shifted version by M/2 samples (i.e. 50% overlap) is constant for the overlapped region. The new window is obtained by adding the third harmonic of the cosine function to the Hamming window, and finding the appropriate amplitudes of DC term, cosine function, and its third harmonic to minimise the peak side-lobe amplitude. A comparison with the Kaiser and Dolph–Chebyshev windows is also performed. Finite impulse response filters designed by windowing method show the efficiency of the new window.

Dolph–Chebyshev Beampattern Design for Spherical Arrays

Spherical arrays with array processing based on spherical harmonics have been recently studied for a wide range of applications that require three-dimensional beamforming. In this correspondence, a Dolph-Chebychev beampattern design, widely used in array processing due to the direct control over main-lobe width and maximum sidelobe level, is developed for spherical arrays within the spherical harmonics framework. We show that due to the similarity between the Legendre polynomials that define the spherical array beampattern and the Chebyshev polynomials that define the desired Dolph-Chebyshev beampattern, spherical array weights can be computed directly and accurately given desired main-lobe width or sidelobe level.

A new efficient approach to the design of parametric windows with arbitrary sidelobe profiles

Based on a simple variable transformation in the spectral domain, a new method to parametrize any window in the same way as Kaiser–Bessel or Dolph–Chebyshev windows is presented, allowing a very flexible trade-off between the width of the main lobe and the height of the sidelobes. The derivation of the method is a generalization of the procedure used for the design of Kaiser–Bessel window and van der Maas function, which is related to the Dolph–Chebyshev window. The properties of this spectral transformation are studied. New bases of functions are presented, which can be used to easily design families of windows having a specific asymptotic decrease rate of the sidelobes. Links are made between this work and windows found in the literature.

Anti-image FIR filters for large interpolation factors

In this paper, the design of FIR filters using novel window families is introduced. These window functions are having high side-lobe-fall-off-rate (SLFOR). The designed filters can be used as anti-imaging filters for large interpolation factors used in multirate signal processing. The performance of the proposed filters is compared with similar filters designed with Kaiser window, Dolph–Chebyshev window and optimum filters designed using Parks–McClellan method. It is observed that, filters designed with high SLFOR combinational window families are providing better image suppression with large interpolation factor. These filters provide smaller aliasing and imaging errors at the cost of smaller initial stopband attenuation.