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Analog-and-Algorithm-Assisted Ultra-low Power Biosignal Acquisition Systems pp 33–53Cite as

Introduction to Compressive Sampling (CS)

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Part of the book series: Analog Circuits and Signal Processing ((ACSP))

Abstract

This chapter provides an overview of compressive sampling (CS), introducing both the signal acquisition and reconstruction protocols. A novel, computationally light, overlapped window reconstruction algorithm is introduced to circumvent the problem of edge artifacts in conventional CS reconstruction. The proposed approach is shown to reduce the central processing unit (CPU) execution time by a factor of 2.4 without degradation of reconstruction accuracy compared to a traditional longer window reconstruction approach for photoplethysmogram (PPG) signals. Finally, this chapter also presents the state-of-the-art CS implementations for biosignal acquisition and processing.

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Notes

  1. 1.

    Strictly speaking restricted isometry property (RIP) of Φ Ψ−1.

  2. 2.

    This is true for analog implementations of CS. Digital implementations acquire signal at Nyquist rate (f s,N).

  3. 3.

    For perfect reconstruction, X′ = X and S′ = S.

  4. 4.

    In analog implementations of CS, only M samples are acquired.

  5. 5.

    Assuming Bernoulli measurement matrix.

  6. 6.

    The overlapping window overlaps the original window by 50%.

  7. 7.

    Random sampling is equivalent to multiplying the signal with a reduced order identity matrix.

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Authors and Affiliations

  1. imec, Leuven, Belgium

    Venkata Rajesh Pamula & Chris Van Hoof

  2. KU Leuven ESAT-MICAS, Leuven, Belgium

    Marian Verhelst

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  1. Venkata Rajesh Pamula
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  2. Chris Van Hoof
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Pamula, V.R., Van Hoof, C., Verhelst, M. (2019). Introduction to Compressive Sampling (CS). In: Analog-and-Algorithm-Assisted Ultra-low Power Biosignal Acquisition Systems. Analog Circuits and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-030-05870-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-05870-8_3

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