Recursive Delay Calculation Unit for Parametric Beamformer

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    This paper presents a recursive approach for parametric delay calculations for a beamformer. The suggested calculation procedure is capable of calculating the delays for any image line defined by an origin and arbitrary direction. It involves only add and shift operations making it suitable for hardware implementation. One delaycalculation unit (DCU) needs 4 parameters, and all operations can be implemented using fixed-point arithmetics. An N -channel system needs N + 1 DCUs per line - one for the distance from the transmit origin to the image point and N for the distances from the image point to each of the receivers. Each DCU recursively calculates the square of the distance between a transducer element and a point on the beamformed line. Then it finds the approximate square root. The distance to point i is used as an initial guess for point i + 1. Using fixed-point calculations with 36-bit precision gives an error in the delay calculations on the order of 1/64 samples, at a sampling frequency of f s = 40 MHz. The circuit has been synthesized for a Virtex II Pro device speed grade 6 in two versions - a pipelined and a non-pipelined producing 150 and 30 million delays per second, respectively. The non-pipelined circuit occupies about 0.5 % of the FPGA resources and the pipelined one about 1 %. When the square root is found with a pipelined CORDIC processor, 2 % of the FPGA slices are used to deliver 150 million delays per second.
    © (2006) COPYRIGHT SPIE--The International Society for Optical Engineering.
    Original languageEnglish
    Title of host publicationMedical Imaging 2006 : Ultrasonic Imaging and Signal Processing
    Number of pages12
    PublisherSPIE - International Society for Optical Engineering
    Publication date2006
    PagesArticle Number: 61470D
    ISBN (Print) 0-8194-6190-3
    Publication statusPublished - 2006
    EventSPIE Medical Imaging 2006: Ultrasonic Imaging and Signal Processing - San Diego, United States
    Duration: 12 Feb 200614 Feb 2006
    Conference number: 6147


    ConferenceSPIE Medical Imaging 2006
    Country/TerritoryUnited States
    CitySan Diego
    SeriesProceedings of SPIE - The International Society for Optical Engineering


    • Directional flow estimation
    • Synthetic aperture imaging
    • Parametric delay calculation
    • Medical ultrasound


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