# BME 130 Biomedical Signals and Systems (2012-2013)

#### BME 130 Biomedical Signals and Systems

**BME 130 Biomedical Signals and Systems (Credit Units: 4)** Analysis of analog and digital biomedical signals; Fourier Series expansions; difference and differential equations; convolutions. System models: discrete-time and continuous-time linear time-invariant systems; Laplace and Fourier transforms. Analysis of signals and systems using computer programs. Prerequisite: Mathematics 3A; Mathematics 3D. Stats 8 recommended. (Design units: 1)

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1. Understand the nature of common biomedical signals (EAC a)

2. Apply the essential techniques for analyzing analog and digital biomedical signals (EAC a, EAC k)

3. Analyze linear time invariant systems (EAC a, EAC k)

4. Develop computing skills by using MATLAB for signal analysis and system modeling (EAC k)

Understanding of infinite sequences and series, complex numbers, systems of algebraic equations, determinants, and basic linear algebra (vectors, matrices, determinants)

- Definition of Systems, Signals and Variables. Mathematical Models.
- Input-output and state-space modle.s Physiological variables and signals.
- Time domain signal characteristics. Linear systems.
- Time-invariable. Review of ordinary differential equations.
- Time domain response of linear time invariant (LTI) systems. Convolution. Causality.
- Comparative review of continuous and discrete LTI systems. Laplance transform.
- Transfer function. Equilibrium. Stability.
- Frequency response. Bode plot
- Fourier transform. Fast Fourier transform and power spectrum.
- Time-frequency analysis. The sampling theorem. Random signals and denoising.

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

Basic knowledge of MATLAB.

None.

Contributes toward the Biomedical Engineering Topics and Major Design experience.

Approach: The design skills are developed and tested through a number of homework problems such as:

* design of signal samplers so that the periodicity of a signal is preserved after discretization

* determining personalize drug injection rate that guarantees given steady-state drug concentration

* determining hormone's loss rate constant given concentration at different points in time

* design a pendulum clock so that its oscillation period matches the specifications

* design a strategy for glucose intake that will prevent pre-diabetic response

* design a feedback controller to stabilize an open-loop unstable system

* determining parameters of the transfer function given its Bode plot

* design a low-pass filter that attenuates particular high-frequencies from a signal with a specific attenuation factor

- Homework: 20%
- Midterm #1: 25%
- Midterm #2: 25%
- Final: 30%
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 3.0 credit units

Engineering Design: 1.0 credit units