8. Synopsis
**LECTURES:**

1. Introduction to embedded systems: sensing the
environment, processing data. Investigating a typical signal path: sensors, perception
and signal conditioning, sampling, data processing. Typical embedded signal
processing architectures: microcontroller, DSP, FPGA, GPU.

2.
Temperature sensors: e.g.,
thermocouple, NTC/PTC, infra, semiconductor. Measurement of light intensity,
e.g. photodiode, phototransistor, photo resistor, photovoltaic. Specific
properties and applications of sensors.

3.
Vibroacoustic
sensors: MEMS and conventional analog sensors (piezo, electret, geophone).
Charge and voltage output devices, signal conditioning issues, typical
specifications.

4.
Measurement of
position, displacement, rotation: incremental transducers, LVDT, optical
sensors, time-of-flight sensors, Hall-sensors and magneto-resistive sensors,
inductive sensors. Force and torque measurement: strain gauges, piezo,
force-sensitive resistor.

5.
Measurement of
current: shunt resistance (bottom and top), current transformer/Rogowski coil,
magnetic field based (Hall sensor, fluxgate, magneto-resistive) sensors.
Measurement of ECG and photoplethysmographic signals.

6. Interpretation of DFT for periodic and stochastic
signals. Calculation of equivalent noise bandwidth, signal to noise ratio.
Coherent/non-coherent sampling, distortion effects. Alternative interpretations
of the discrete Fourier transform (DFT): matrix transform, filter bank, LS
estimation (generalization to sine components of arbitrary frequency).

7. DFT applications: convolution acceleration, real DFT
computation using complex DFT, cepstrum computation. Wavelet transform,
description of wavelets, implementation. Discrete cosine transform.

8.
Classification of
digital filters. Overview of the properties of IIR and FIR filters. Amplitude
and phase characteristics. Types of filters: FIR: LS and smooth wave; IIR:
Butterworth, Chebyshev, elliptic, Bessel-Thomson.

9.
Filter design
procedures for FIR and IIR filters (LS, Parks-McClellan, windowing, bilinear
transform, pulse invariant transform). Realization forms of digital filters,
biquad implementation.

10.
Specialties of fixed
point fractional representation, performing operations with fixed point
fractional numbers, design difficulties. Nonlinear filters and outlier
detection: median filter and variants, Hampel filter.

11.
An overview of
problems stemming from different sampling frequencies. Implementation of
decimation and interpolation in time and frequency domains. Decimation and
interpolation filter design, polyphase filter. Polynomial interpolation.

12.
Numerical
optimization problems: root locus search, extreme value search. Formulating a
mathematical problem, types of cost function, interpretation. One and
multi-parameter problems, conditional search for extreme values. Methods using
first and second order derivatives.

13.
Optimization methods
based on different heuristics. The problem of local extrema. Convergence
problems, ill-conditioned cases. Illustration of numerical optimization using
the Least-Mean Square (LMS) algorithm as a data-invariant filter for real-time
embedded systems.

14.
Consultation, extra
space for missing lessons due to holidays, examples of applications.

**PRACTICES:**

1.
Characterization of systematic
and random static errors: error analysis of complex circuits, contribution of
different passive and active components to the error and non-linearity of the
signal path. Reducing the errors with special components and designs.

2.
Noise analysis: noise
of circuit components (amplifiers, passive components, power supplies), noise
suppression/immunity, ambient noise/disturbance, shielding, design solutions.
Jitter and its effects.

3.
Introduction to some
basic signal processing steps through a real application. Block and sample processing: difference between
real-time embedded processing and offline processing. Interpretation of
timings. Implementing simple signal processing algorithms, e.g. measuring
signal parameters (frequency, amplitude...).

4. Introduction of filter design software packages,
design and test FIR and IIR filters with different specifications on real
signals.

5. Spectrum analysis examples. Fault detection in embedded systems based on
spectral imagery: independent periodic, modulating errors, random
errors/jitter, distortion, and their derivation from software and hardware
properties of embedded systems.

6.
Examples for
designing decimating and interpolating filters for different tasks. Synchronization
of different sampling frequencies in distributed embedded systems.