# Jonathon Spaulding

### From Murmann Mixed-Signal Group

BSEE, Massachusetts Institute of Technology,

2009 MSEE, Massachusetts Institute of Technology,

2010 Admitted to Ph.D. Candidacy: 2010-2011

**Research**: Low Power Integrated Analog Front Ends for Portable Ultrasound Imaging

My research focuses on designing low-power systems for portable medical applications. Specifically, my work focuses on leveraging known signal properties of ultrasonic transducers to lower the sampling (and data processing rate) of the analog front end (AFE) receivers. The fundamental idea behind this work is that if we can model a received signal as a sum of time-shifted, amplitude-varying pulse wave forms with known pulse shape, the actual information rate of the signal is much lower than what Nyquist would suggest [Vetterli et al., 2002], [Tur et al., 2011]. My work is focused on implementing a Finite Rate of Innovation (FRI) algorithm to capture ultrasound signals at a rate 20-50x below the Nyquist rate, resulting in a lower power AFE for continuous ultrasonic health monitoring.

One way to demonstrate the underlying idea of such an FRI algorithm is to examine a high-bandwidth signal such as a pulse train of gaussian pulses. A traditional Nyquist-rate system would need to take many samples in the time-domain to resolve the high-frequency pulses accurately. However, by convolving the high-bandwidth signal with the known impulse response of a low-pass filter, we effectively project this information to a space where we can resolve the signal with fewer samples. By back-calculating the effect of the filter's impulse response digitally, we can resolve each of the received pulse amplitudes and times, assuming we know the general pulse shape of the input signal. Such an operation is presented in the Figure below, with the input sum of gaussian pulses in the top pane, and the filtered signal in the lower pane with samples shown.

In addition to implementing an FRI-based sub-Nyquist sampler for ultrasound imagers, we also introduce a novel subarray beamforming technique. We note that in an array, adjacent elements see only small delays relative to one another. Coupling this with the fact that the FRI system has the effect of modeling our system as narrowband in nature, we introduce a mixer-based hybridized beamforming scheme. By summing signals in the analog domain, we can further reduce both the total sample count as well as the hardware complexity of ultrasound imaging systems. A block diagram detailing our architecture, including subarray beamforming, can be found below.

**Email**: jspauld AT stanford DOT edu