Instrumentation & Measurement Magazine 23-4 - 43

Fig. 2. LTC algorithm. (a) Initialization: we consider the set of straight lines with origin in the first point and passing for the segment with center in the second
point and semi-amplitude equal to the maximum interpolation error. (b) For each new point, we consider the subset of straight lines that intersect all the segments
formed by the previous points. (c) When the intersection is nil, the interpolation terminates and the parameters of the interpolating segment are transmitted.

the smartphone level; however when acquired raw data are
transferred over a BLE wireless connection, a simple way to
reduce bandwidth requirements is to compress data before
transmission. In the following, compression algorithms wellsuited for implementation in a resource-constrained wearable
system are discussed.

Piecewise Approximation
Lightweight Temporal Compression (LTC) [13] is a well-known
algorithm that was originally proposed to compress environmental signals in WSN nodes. The monitored signal is
approximated by a piecewise linear signal by considering
the algorithm briefly explained in Fig. 2 (see [13] for more
information).
Every time a new interpolating segment is found, as illustrated in Fig. 3, its parameters are sent to the processing unit.
This allows the system to significantly decouple transmission
rate from signal variability, but it introduces random latency
that depends on signal features. Since in some applications

Fig. 3. Original signal (black) compared with a LTC-compressed signal.
Transmitted samples are marked with red squares.
June 2020

a variable latency may not be acceptable, it is possible to introduce an upper bound by setting the maximum duration
of the interpolated interval. The length of that interval does
not affect the reliability of the reconstructed signal but only
the latency in signal reconstruction. Obviously, the shorter
the duration, the worse the performance of the compression
algorithm will be since more frequent transmissions will be
required.

Compressive Sampling
Compressive sampling (CS) allows a vector x of N signal samples
to be compressed into a vector y of size M, with M << N, retaining the same information content, which allows the data rate
of the monitored signal to be uniformly reduced. The latency it
introduces is constant, known a-priori and independent of the
signal features, as it depends on the time needed to acquire N
samples.
At the local sensing node, the compressed vector y = Φx
is calculated by using a suitable M×N sensing matrix Φ that
needs to be stored within the local sensor. The use of CS in lowcost sensors requires the design to overcome the large memory
cost represented by the sensing matrix. This can be achieved
by using a binary-valued Bernoulli matrix, whose elements are
easily obtained from a pseudo-random binary sequence (PRBS).
The order of the generating polynomial should be high enough
to ensure that Φ satisfies the restricted isometry property (RIP)
[14] that is needed for unambiguous signal reconstruction.
Compressed samples can be transmitted within a single packet
to reduce overhead, or by several messages containing one or
more compressed sample in their payload.
The operation of signal reconstruction is highly resource
demanding and may affect the performances of a multi-task
system such as the smartphone. The sensor signal can be reconstructed by solving a typical sparse optimization problem,
in the form: sˆ = arg min y − Θs where Θ = ΦΨ is the product
1
between the sensing and a sparsifying matrix Ψ providing
the signal model. The vector of signal samples can be finally

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