Cosine Modulation Research Articles

Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer

The spatial second-order interference of two independent pseudothermal light beams in a Hong-Ou-Mandel interferometer is studied experimentally and theoretically. The similar cosine modulation in the second-order coherence function as the one with entangled-photon pairs in a Hong-Ou-Mandel interferometer is observed. Two-photon interference based on Feynman's path integral theory is employed to interpret the results. The experimental results and theoretical simulations agree with each other very well.

A Novel Window and Its Application in NPR Type Transmultiplexer Design

This paper proposes a new window based approach for the design of <i>M</i>-channel maximally decimated Near-Perfect Reconstruction (NPR) type transmultiplexer. Cosine modulation is used to design the synthesis and analysis sections of the transmultiplexer. The prototype filter is designed with high Side-Lobe-Fall-Off-Rate (SLFOR) combinational window functions. A gradient based optimization algorithm has been applied to minimize the interference parameters like Inter-Channel Interference (ICI) and Inter-Symbol Interference (ISI).The proposed method of design of transmultiplexers are showing the improvements in terms ICI and ISI.

Two Dimensional &lt;i&gt;M&lt;/i&gt;-Channel Non-separable Filter Banks Based on Cosine Modulated Filter Banks with Diagonal Shifts

Two Dimensional &lt;i&gt;M&lt;/i&gt;-Channel Non-separable Filter Banks Based on Cosine Modulated Filter Banks with Diagonal Shifts

Ultrasonic lateral modulation imaging, speckle reduction, and displacement vector measurements using simple single-beam scanning or plural crossed-beam scanning with new spectra frequency division processing methods

Ultrasonic lateral modulation imaging, speckle reduction, and displacement vector measurements using simple single-beam scanning or plural crossed-beam scanning with new spectra frequency division processing methods Chikayoshi Sumi, Yousuke IshiiDepartment of Information and Communication Sciences, Faculty of Science and Technology, Sophia University, Tokyo, JapanAbstract: The development of effective ultrasonic tissue displacement measurement methods increases the number of possible applications for various tissue displacement and strain measurements. These applications include measurements of spontaneous motions/deformations generated by heart motion; pulsations from phenomena such as blood flow (intracardiac, intravascular, and carotid); heart, blood vessel, and liver motion; and motion from artificial sources such as motions/deformations generated by applying static compression/stretching forces, vibration or acoustic radiation forces (breast and liver). For arbitrary orthogonal coordinate systems obtained using arbitrary transducer types (eg, linear, convex, sector, arc, or radial array types, or single aperture types with a mechanical scan), several lateral modulation (LM) methods (eg, scanning with plural crossed or steered beams over a region of interest) have been developed that can be used with new echo imaging methods for tissue displacement/deformation measurements. Specifically, by using such beamforming methods, in addition to highly accurate displacement vector and lateral displacement measurements, LM echo imaging with a high lateral carrier frequency and a high lateral resolution has been developed. Another new beamforming method, referred to as &ldquo;a steering angle (ASTA) method,&rdquo; ie, scanning with a defined steering angle, is also described. In addition to conventional non-steered-beam scanning (ie, a version of ASTA) and conventional steered-beam scanning with a variable steering angle (eg, sector, arc, radial scan), a simple, single-beam scanning method also permits the use of LM, which yields an accurate displacement vector measurement with fewer calculations than the original LM methods. This is accomplished by using a previously developed spectra frequency division method (SFDM). However, the lateral carrier frequency and the measurement accuracy acquired by using such a single-beam scanning method are lower than those achieved with the original LM scanning methods and should be increased (ie, by using a quasi-LM method). In this report, the effectiveness of the use of the new SFDMs is verified with experiments on agar phantoms, in which conventional non-steered, focused single-beam transmission/reception scanning is performed together with high-speed non-steered single plane-wave transmission and non-steered, focused single-beam reception scanning using a linear array-type transducer. For comparison, the original LMs, with their respective transmissions of crossed, steered focused beams and plane waves are also performed. Because the use of rectangular apodization functions (ie, no apodization) yields a larger bandwidth in a lateral direction than the effective use of parabolic functions with the original LM method, it is shown that disregarding the lateral low-frequency spectra yields useful quasi-LM echo imaging with a high lateral frequency, and further significantly increases the measurement accuracy of a displacement vector. In addition, when no apodization is used with the original version of LM, disregarding the low-frequency lateral spectra is effective. In addition, the interchangeability of cosine and sine modulations performed after completing beamforming can also be used for single-beam scanning as well as for the original LM scanning method. Specifically, the cosine and sine modulations, respectively, are used for LM and quasi-LM imaging and displacement vector measurements. It is concluded that the appropriate use of the new SFDMs with simple single-beam scanning or with simple plural crossed-beam scanning with no apodization can achieve almost the same accuracy as the original LM scanning method using plural crossed beams with the effective apodization. Another new application of SFDM is also described: an incoherent superposition of the frequency-divided spectra reduces speckles. The new methods will also be effective for other beamforming methods and with other types of transducers.Keywords: lateral modulation scanning, single-beam scanning, apodization, spectra frequency division method, low-frequency spectra, quasi-LM imaging, coherent superposition, incoherent superposition

A design of IFIR prototype filter for Cosine Modulated Filterbank and Transmultiplexer

This paper proposes a computational efficient approach for the design of M-band Cosine Modulated Filterbank (CMFB) and Transmultiplexer (TMUX) in Near Perfect Reconstruction (NPR) condition. The required prototype filter is formulated by using interpolated FIR (IFIR) technique. Suitable stretch factor is used for the reduction in computation cost and obtained minimum value of distortion parameters. The minimization of these parameters has been achieved by applying a single variable bisection type optimization technique. Design examples are included to prove superiority of performance over the existing work.

Design of Linear Phase Nonuniform Filter Banks with Interpolated Prototype Filters

Most of nonuniform filter banks designed by existing methods are not linear phase. In order to solving the problem, a novel method for designing linear-phase nonuniform filter banks is proposed in this paper. By analyzing the filter banks structure with block decimation transformed to rational decimation, we get an interpolated filter banks structure which removes the mirror frequency brought from interpolation. The filter banks are obtained by cosine modulation in this paper, and the prototype filters are interpolated and filtered before modulation. To make sure the significant aliasing distortions are cancelled completely, all prototype filters are designed with consistent transition band performance, using the optimization algorithm. Simulation results demonstrate that the linear-phase nonuniform filter banks designed by the proposed method have small amplitude distortions and aliasing distortions.

Design and performance analysis of various one dimensional codes using different data formats for OCDMA system

In this paper, the design, implementation and performance analysis of various one dimensional codes in an OCDMA system for different data formats is presented. A number of different codes are used with optical CDMA to improve its error performance. Here, three such codes, optical orthogonal codes (OOC), Walsh Hadamard codes and zero cross-correlation (ZCC) codes have been compared using different data formats, NRZ raised cosine, NRZ rectangular, RZ raised cosine and RZ rectangular. It is found that NRZ raised cosine has the best system performance for all the codes used. After that, the three codes have been compared in terms of the BER, eye diagrams and received optical power using NRZ raised cosine modulation format. It is analyzed that ZCC codes have zero cross-correlation property. The simulation results revealed that ZCC codes can provide a better BER compared to the OOC and Walsh Hadamard codes and it is most suitable to be employed in the OCDMA systems.

A simple design method for the cosine-modulated filter banks using weighted constrained least square technique

This paper presents a simple and efficient design method for cosine-modulated filter banks with prescribed stopband attenuation , passband ripple , and channel overlap. The method casts the design problem as a linear minimization of filter coefficients such that their value at ω = π /2 M is 0.707, which results in a simpler, more direct design procedure. The weighted constrained least squares technique is exploited for designing the prototype filter for cosine modulation (CM) filter banks. Several design examples are included to show the increased efficiency and flexibility of the proposed method over the exiting methods. An application of the proposed method is considered in the area of sub-band coding of the ECG and speech signals.

An Improved and Simplified Approach for Designing Cosine Modulated Filter Bank Using Window Technique

An improved and simplified approach is presented for design of nearly perfect reconstructed cosine-modulated (CM) filter banks with prescribed stopband attenuation and channel overlapping. The method employs Kaiser window technique to design the prototype filter for filter banks with the novelty of exploiting spline functions in the transition band of the ideal filter instead of using the conventional brick-wall filter based on linear optimization of filter coefficients such that their value at frequency (??=??/2M) is 0.707. The simulation results illustrate the proposed method and its improvement over other existing methods in terms of amplitude distortion (e am ), number of iterations (NOI), aliasing distortion (e a ) and computation time (CPU time).

Subband Vector Quantization with Trellis Coding

In this paper, a subband coding system consisting a combination of analysis filter bank, vector quantizer and trellis coding is designed. For the analysis filter bank, which decompose an input signal spectrum to bands we used a design method of cosine modulated filter bank with the perfect reconstruction. The analysis filters are obtained by cosine modulation of a prototype filter with the transfer function H(z), which optimization is performed right through the two-channel lossless lattice structure. Next block in this coding system is the vector quantizer with a full search, which perform quantization in the subband domain. The final block of the designed subband coding system is the block of trellis coding. This uses a block structured codebook of the vector quantizer with an extended set of the quantization vectors in accordance with Ungerboeck’s theory of clustering the set.

Compensating spectral loss variations in EDFA amplifiers for different modulation formats

In this paper, we investigate the performance of the optical system consisting of chain of EDFA amplifiers for different data formats such as non-return-to-zero (NRZ), return to zero (RZ) and Manchester. Their effect on the spectral loss variations produced in fiber output is analyzed. We show that when the RZ raised cosine and Manchester raised cosine modulation formats are used, the non-linear ties are produced in power spectrum plots which severely distort the signals obtained at the output of the chain of the EDFA amplifiers. On the other hand, the NRZ raised cosine modulation format best compensates the spectral loss variations in the power spectrum plots obtained at the output. We further show that NRZ raised cosine has good eye opening as compared to other modulation formats.

Design of Linear-Phase Nonuniform Filter Banks With Partial Cosine Modulation

The majority of the existing work on designing nonuniform filter banks (NUFBs) cannot achieve linear-phase (LP) property, because of the high complexity associated with phase distribution. This correspondence proposes an idea of partial cosine modulation to obtain the LP property of NUFBs with rational sampling factors. It makes the efficient modulation technique possible to be used to design LP NUFBs. Except the separately designed lowpass and highpass analysis/synthesis filters, we obtain the bandpass by cosine modulation of several prototypes, worth of the name ?partial cosine modulation.? By analyzing the phase issue of significant aliasing terms, we derive the matching conditions to make the required LP NUFB achievable. With these criteria being satisfied, the design problem becomes that of several prototypes as well as the lowpass and highpass filters, leading to a less design effort. By using the proposed method, near-perfect-reconstruction LP NUFBs can be obtained in a simple and efficient way as demonstrated by examples.

An optimized transmultiplexer using combinational window functions

This paper proposes an efficient approach for the design of M-channel maximally decimated near-perfect reconstruction (NPR) type transmultiplexer. Cosine modulation is used to design the synthesis and analysis sections of the transmultiplexer. The prototype filter is designed by using high sidelobe falloff rate (SLFOR) combinational window functions. A bisection-type optimization algorithm has been applied to minimize the interference parameters like inter-channel interference (ICI) and inter-symbol interference (ISI). The proposed algorithm has certain advantages than earlier reported work. The algorithm is of generalized nature, independent of the window function used in the design of the prototype filter. Second, it is fast and computationally efficient as only a single parameter is used as a variable which provides almost uniform interference level in all subchannels. Design examples are included for comparison with earlier reported work. Very small values of ICI and ISI have been obtained by using variable and combinational window functions.

A simple method for the design of cosine-modulated pseudo-QMF banks

In this paper, a simple and efficient iterative technique for designing of Cosine-Modulated (CM) filter banks with approximate reconstruction is presented. In the proposed technique, cut-off frequency is optimised to satisfy a new Perfect Reconstruction (PR) condition at frequency (ω = π/2M). Different window functions have been used to design the prototype filter for CM filter banks. The simulation results illustrate the improvement achieved through this method over other existing methods in terms of amplitude distortion (eam), Number of Iterations (NOI), aliasing distortion (ea) and computation time (CPU time). When it is exploited for subband coding of the Electrocardiogram (ECG) and speech signals, the proposed method yields good fidelity performance measuring parameters.

Determination of lateral modulation apodization functions using a regularized, weighted least squares estimation.

Recently, work in this group has focused on the lateral cosine modulation method (LCM) which can be used for next-generation ultrasound (US) echo imaging and tissue displacement vector/strain tensor measurements (blood, soft tissues, etc.). For instance, in US echo imaging, a high lateral spatial resolution as well as a high axial spatial resolution can be obtained, and in tissue displacement vector measurements, accurate measurements of lateral tissue displacements as well as of axial tissue displacements can be realized. For an optimal determination of an apodization function for the LCM method, the regularized, weighted minimum-norm least squares (WMNLSs) estimation method is presented in this study. For designed Gaussian-type point spread functions (PSFs) with lateral modulation as an example, the regularized WMNLS estimation in simulations yields better approximations of the designed PSFs having wider lateral bandwidths than a Fraunhofer approximation and a singular-value decomposition (SVD). The usefulness of the regularized WMNLS estimation for the determination of apodization functions is demonstrated.

1245: Lateral Cosine Modulation for Next-Generation Ultrasound Equipment

1245: Lateral Cosine Modulation for Next-Generation Ultrasound Equipment

A Demonstration of Optimal Apodization Determination for Proper Lateral Modulation

We have realized effective ultrasound (US) beamformings by the steering of plural beams and apodizations for B-mode imaging with a high lateral resolution and accurate measurement of tissue or blood displacement vector and/or strain tensor using the multidimensional cross-spectrum phase gradient method (MCSPGM), or multidimensional autocorrelation or Doppler methods (MAM and MDM) using multidimensional analytic signals. For instance, the coherent superposition of the steered beams performed in the lateral cosine modulation method (LCM) has a higher potential for realizing a more accurate measurement of a displacement vector than the synthesis of the displacement vector using the accurately measured axial displacements obtained by the multidimensional synthetic aperture method (MDSAM), multidirectional transmission method (MTM) or the use of plural US transducers. Originally, the apodization function to be used for realizing a designed point spread function (PSF) was obtained by the Fraunhofer approximation (FA). However, to obtain the best approximated, designed PSF in the least-squares sense, we proposed a linear optimization (LO) method. Furthermore, on the basis of the knowledge about the losts of US energy during the propagation, we have recently developed a nonlinear optimization (NLO) method, in which the feet of the main lobes in apodization function are properly truncated. Thus, NLO also allows the decrease in the number of channels or the confinement of the effective aperture. In this study, to gain insight into the ideal shape of the PSF, the accuracies of the two-dimensional (2D) displacement vector measurements were compared for typical PSFs with distinct lateral envelope shapes, particularly, in terms of full width at half maximum (FWHM) and the length of the feet, i.e., the Gaussian function, Hanning window and parabolic function. It was confirmed that a PSF having a wide FWHM and short feet was ideal. Such a PSF yielded an echo with a high signal-to-noise ratio (SNR), a large bandwidth and a large maximum spectrum of the center frequency. Moreover, for the three PSFs used, by calculating the PSFs using a typical transducer model and the apodization functions obtained by the respective LO and NLO methods and FA, we compare the approximation accuracies of the realized PSFs. NLO was effective for realizing such an ideal PSF. In addition, NLO allowed the significant decrease in the number of channels or the confinement of the effective aperture. Thus, in the comparisons of the three distinct PSFs, we obtain an appropriate apodization function. This study will assist the realization of the best lateral modulation.

Shear modulus reconstruction by strain tensor measurement using lateral modulation

Two-dimensional (2D) shear modulus reconstructions are performed on an agar phantom using our previously developed ultrasound lateral Gaussian envelope cosine modulation method (LGECMM) together with multidimensional displacement vector measurement methods, i.e., the multidimensional cross-spectrum phase gradient method (MCSPGM), the multidimensional autocorrelation method (MAM) and the multidimensional Doppler method (MDM). The accuracies of the obtained 2D reconstructions are compared with each other in addition to those of 1D reconstructions obtained from the respective ratios of lateral and axial strains.

Effective lateral modulations with applications to shear modulus reconstruction using displacement vector measurement

High accuracy in measuring target motions can be realized by combined use of our previously developed lateral Gaussian envelope cosine modulation method (LGECMM) and displacement vector measurement methods that enable simultaneous axial and lateral displacement measurements, such as the multidimensional autocorrelation method (MAM). In this paper, LGECMM is improved by using parabolic functions and Hanning windows instead of Gaussian functions in the apodization function, i.e., parabolic apodization and Hanning apodization. The new modulations enable decreases in effective aperture length (i.e., channels) and yield more accurate displacement vector measurements than LGECMM due to increased echo signal-to-noise ratio and lateral spatial resolution. That is, on the basis of a priori knowledge about ultrasound propagation using the focusing scheme and shape of the apodization function, we stopped using Fraunhofer approximation. As practical applications of the modulations, for an agar phantom that is deformed in a lateral direction, stable and accurate 2-D shear modulus reconstructions are performed using our previously developed direct inversion approach together with 2-D strain tensor measurements using MAM.

Inducing catastrophe in malignant growth

Mathematical catastrophe theory is used to describe cancer growth during any time-dependent program a(t) of therapeutic activity. The program may be actively imposed, e.g. as chemotherapy, or occur passively as an immune response. With constant therapy a(t), the theory predicts that cancer mass p(t) grows in time t as a cosine-modulated power law, with power = 1.618..., the Fibonacci constant. The cosine modulation predicts the familiar relapses and remissions of cancer growth. These fairly well agree with clinical data on breast cancer recurrences following mastectomy. Two such studies of 3183 Italian women consistently show an immune system's average activity level of about a = 2.8596 for the women. Fortunately, an optimum time-varying therapy program a(t) is found that effects a gradual approach to full remission over time, i.e. to a chronic disease. Both activity a(t) and cancer mass p(t) monotonically decrease with time, the activity a(t) as 1/(ln t) and mass remission as t--94{-0.382}. These predicted growth effects have a biological basis in the known presence of multiple alleles during cancer growth.