Biomedical signals and systems /

Bibliographic Details
Main Author:	Tranquillo, Joseph Vincent, 1975- (Author)
Format:	eBook
Language:	English
Published:	San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, 2014.
Series:	Synthesis lectures on biomedical engineering ; # 52.
Subjects:	Biological systems > Mathematical models. Biomedical engineering. Signal processing > Mathematics. System analysis. Laplace transform PID control biological signals biological systems convolution correlations feedback filters medical devices signal processing stability system response Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

1. Introduction
1.1 What is a system?
1.1.1 Cause and effect
1.1.2 The systems of engineering
1.2 What is a signal?
1.2.1 Signals in engineering
1.2.2 Sensors
1.3 System boundaries
1.4 Design using signals and systems
10. Time domain analysis
10.1 Basic signal processing
10.1.1 Average
10.1.2 Signal power
10.1.3 Variance and standard deviation
10.1.4 Signal to noise ratio
10.2 Correlations
10.2.1 Cross-correlation
10.2.2 Cross covariance
10.2.3 Auto correlation
10.3 Matlab
10.4 Exercises
11. Frequency domain analysis
11.1 Comparing a signal to sinusoids
11.1.1 Properties of sinusoids
11.1.2 A problem with the cross-correlation
11.2 The Fourier series
11.3 The Fourier transform
11.3.1 Power at a frequency
11.3.2 Fourier transform properties
11.3.3 The rectangle function
11.3.4 Inverse Fourier transform
11.4 The discrete Fourier transform
11.4.1 Aliasing and the Nyquist rate
11.4.2 The Nyquist rate and aliasing
11.5 Matlab
11.6 Exercises
12. Filters
12.1 Ideal filters
12.1.1 Ideal filter phase shift
12.1.2 The chirp signal
12.2 Filters in reality
12.2.1 Roll-off
12.2.2 Ripples
12.2.3 Phase shifts
12.3 First and second order filters
12.3.1 A first order filter
12.3.2 A second order filter
12.4 Higher order filters
12.4.1 Butterworth
12.4.2 Chebyshev
12.4.3 Elliptical
12.4.4 Bessel
12.4.5 Filter evaluation
12.4.6 High, bandpass and notch filter
12.4.7 Electrical implementation
12.5 Windowing in the time domain
12.6 Matlab
12.7 Exercises
2. System types
2.1 Introduction
2.2 conservative and non-conservative systems
2.3 Open and closed systems
2.4 Static and dynamic systems
2.5 Continuous and discrete signals and systems
2.6 Stable and unstable systems
2.7 Time varying and time invariant systems
2.8 Deterministic and non-deterministic systems
2.9 Finite and infinite systems
2.10 Linear and non-linear systems
2.11 Stationary and non-stationary
2.12 Memory and memoriless systems
2.13 Time constants
2.14 Conclusion
2.15 Exercises
3. System models
3.1 What is a model
3.2 Models using conservation
3.2.1 Conservation of momentum
3.2.2 Conservation of charge
3.2.3 Conservation of mass
3.2.4 Fluid mass and volume
3.2.5 Conservation of energy
3.2.6 Other models
3.3 State and compartment models
3.3.1 Volume balance
3.3.2 Models of ion channels
3.4 Reduction of a higher order equation
3.5 Exercises
4. Laplace transform
4.1 Introduction
4.2 Formal definitions
4.2.1 Laplace transform
4.2.2 Inverse Laplace transform
4.3 Transform tables
4.4 Four useful Laplace transforms
4.4.1 The impulse
4.4.The unit step
4.4.3 The sinusoid
4.4.4 The derivative
4.5 From differential to algebraic equations
4.6 From algebraic equations to a solution
4.7 Other interesting applications
4.7.1 The Fourier transform
4.7.2 Non-time mapping
4.8 The z-transform
4.9 Exercises
5. Block diagrams
5.1 Block diagram of a pacemaker-defibrilator
5.2 Parallel, series and junctions
5.3 Transfer functions
5.3.1 Reducing block diagrams
5.3.2 Series connection reduction
5.3.3 Parallel connection reduction
5.3.4 Combining series and parallel
5.4 Matlab, signals and systems
5.5 Exercises
6. Stability
6.1 Introduction
6.2 Stability and transfer function poles
6.2.1 Finding poles and zeros
6.2.2 Visualizing poles and zeros
6.2.3 Relationship to stability in time
6.3 The role of zeros
6.4 Designing systems
6.5 Matlab and stability
6.6 Exercises
7. Feedback
7.1 Open and closed loop systems
7.2 Feedback transfer functions
7.3 Block diagram reductions
7.4 Stability and feedback
7.5 Feedforward
7.6 Opening the loop
7.7 Matlab and feedback
7.8 Exercises
8. System response
8.1 Zero input and zero state response
8.2 The impulse response
8.2.1 A first order example
8.2.2 A different first order example
8.2.3 A second order example
8.3 The step response
8.3.1 The importance of the step response
8.3.2 Comparing the step and impulse responses
8.4 Quantifying a response
8.4.1 Estimating a transfer function
8.4.2 A generic second order system
8.5 The sine response
8.5.1 decibels
8.5.2 The Bode plot
8.5.3 The 3dB point
8.6 Response to an arbitrary input
8.6.1 Convolution
8.6.2 Deconvolution
8.7 Other applications
8.7.1 Other useful test signals
8.8 Matlab and system responses
8.9 Exercises
9. Control
9.1 The generic control model
9.2 Evaluating a controlled response
9.2.1 Time domain evaluation
9.2.2 Frequency domain evaluation
9.3 On-off controllers
9.4 PID controllers
9.4.1 Proportional (P) control
9.4.2 Proportional derivative (PD) controller
9.4.3 Proportional integral (PI) controller
9.4.4 Proportional integral derivative (PID) controller
9.4.5 Choosing constants
9.4.6 Alternative formulation
9.5 Example of a PID controlled system
9.6 The problem of system delays
9.7 Other controllers
9.7.1 Lag-lead controllers
9.8 Reverse engineering biological systems
9.9 Matlab
9.10 Exercises
A. Complex numbers
A.1 Introduction
A.2 The complex plane
A.3 Euler's identity
A.4 Mathematical operations
A.4.1 Addition and subtraction
A.4.2 Multiplication
A.4.3 Conjugation
B. Partial fraction expansion
C. Laplace transform table
D. Fourier transform table
Author's biography.