Separation of Overlapping Linear Frequency Modulated (LFM) Signals Using the Fractional Fourier Transform

Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with +/-0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe

Scaling Factor Inconsistencies in Neutrinoless Double Beta Decay

The modern theory of neutrinoless double beta decay includes a scaling factor that has often been treated inconsistently in the literature. The nuclear contribution to the decay half life can be suppressed by 15-20% when scaling factors are mismatched. Correspondingly, $$ is overestimated.Comment: 4 page

Identification and separation of DNA mixtures using peak area information

We introduce a new methodology, based upon probabilistic expert systems, for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for ascertaining whether individuals, whose profiles have been measured, have contributed to the mixture. It can also be used to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our probabilistic methodology is illustrated on case data examples and compared with alternative approaches. The advantages are that identification and separation issues can be handled in a unified way within a single probabilistic model and the uncertainty associated with the analysis is quantified. Further work, required to bring the methodology to a point where it could be applied to the routine analysis of casework, is discussed.

Probabilistic expert systems for handling artifacts in complex DNA mixtures

This paper presents a coherent probabilistic framework for taking account of allelic dropout, stutter bands and silent alleles when interpreting STR DNA profiles from a mixture sample using peak size information arising from a PCR analysis. This information can be exploited for evaluating the evidential strength for a hypothesis that DNA from a particular person is present in the mixture. It extends an earlier Bayesian network approach that ignored such artifacts. We illustrate the use of the extended network on a published casework example

Identification and separation of DNA mixtures using peak area information (Updated version of Statistical Research Paper No. 25)

We introduce a new methodology, based upon probabilistic expert systems, for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for ascertaining whether individuals, whose profiles have been measured, have contributed to the mixture, but also to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our probabilistic methodology is illustrated on case data examples and compared with alternative approaches. The advantages are that identification and separation issues can be handled in a unified way within a single probabilistic model and the uncertainty associated with the analysis is quantified. Further work, required to bring the methodology to a point where it could be applied to the routine analysis of casework, is discussed

Extraction of an Overlapped Second Harmonic Chirp Component using the Fractional Fourier Transform

In ultrasound harmonic imaging with chirp coded excitation, the axial resolution can be improved by increasing the excitation signal bandwidth. However, increasing the bandwidth will cause overlapping between the received nonlinear second harmonic chirp component (SHCC) and the fundamental component. For the spectrally overlapping harmonics, signal decoding using the second harmonic matched filter (SHMF) typically produces higher range sidelobes level (RSLL), which reduces the image contrast. A multi-pulse detection scheme such as pulse inversion can be used to extract the overlapped SHCC; however it is susceptible to motion artifacts and reduced system frame-rate. In this study, the fractional Fourier transform (FrFT) is proposed with chirp coded excitation for the extraction of the overlapped SHCC. The experimental results indicate at least a 13 dB improvement in the RSLL of the FrFT filtered compressed SHCC when compared with the unfiltered compressed SHCC

Ultrasound array transmitter architecture with high timing resolution using embedded phase-locked loops

Coarse time quantization of delay profiles within ultrasound array systems can produce undesirable sidelobes in the radiated beam profile. The severity of these sidelobes is dependent upon the magnitude of phase quantization error - the deviation from ideal delay profiles to the achievable quantized case. This paper describes a method to improve inter channel delay accuracy without increasing system clock frequency by utilising embedded Phase-Locked Loop (PLL) components within commercial Field Programmable Gate Arrays (FPGAs). Precise delays are achieved by shifting the relative phases of embedded PLL output clocks in 208 ps steps. The described architecture can achieve the necessary inter element timing resolution required for driving ultrasound arrays up to 50 MHz. The applicability of the proposed method at higher frequencies is demonstrated by means of extrapolating experimental results obtained using a 5 MHz array transducer. Results indicate an increase in Transmit Dynamic Range (TDR) when using accurate delay profiles generated by the embedded PLL method described, as opposed to using delay profiles quantized to the system clock

Plane wave imaging challenge

The plane wave imaging challenge (PICMUS) has been introduced for the first time to IUS in order to encourage participants to compete and share their knowledge in medical ultrasound plane wave imaging. To participate in this challenge, we have chosen the contrast enhanced delay and sum (CEDAS) post signal processing method. This technique have been used to improve B-mode image contrast to noise ratio (CNR) without effecting the image spatial resolution. With CEDAS the energy of every envelope signal is calculated, mapped, and clustered in order to identify the cyst and clutter location. CEDAS significantly reduces the clutter inside the cyst by attenuating it from envelope signals before the new B-Mode image is formed. This paper describes in more details the techniques and parameters we have been using for the challenge. Results obtained for CEDAS shows that it outperforms conventional DAS by 18.33% in experiment and 79.24% in simulation for CNR

Phonon transport in large scale carbon-based disordered materials: Implementation of an efficient order-N and real-space Kubo methodology

We have developed an efficient order-N real-space Kubo approach for the calculation of the phonon conductivity which outperforms state-of-the-art alternative implementations based on the Green's function formalism. The method treats efficiently the time-dependent propagation of phonon wave packets in real space, and this dynamics is related to the calculation of the thermal conductance. Without loss of generality, we validate the accuracy of the method by comparing the calculated phonon mean free paths in disordered carbon nanotubes (isotope impurities) with other approaches, and further illustrate its upscalability by exploring the thermal conductance features in large width edge-disordered graphene nanoribbons (up to ~20 nm), which is out of the reach of more conventional techniques. We show that edge-disorder is the most important scattering mechanism for phonons in graphene nanoribbons with realistic sizes and thermal conductance can be reduced by a factor of ~10.Comment: Accepted for publication in Physical Review B - Rapid Communication