Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based Introduction
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Table of contents
- PREFACEvii
- CONTENTSix
- 1. BIOENGINEERING SIGNALS AND SYSTEMS1
- 1.1 Biological Systems1
- 1.2 Biosignals3
- 1.2.1 Signal Encoding6
- 1.3 Linear Signal Analysis: Overview9
- 1.3.1 Analysis of Linear Systems11
- 1.3.2 Analog Analysis and Analog Models11
- 1.3.3 Systems Analysis and Systems Models15
- 1.3.4 Systems and Analog Analysis: Summary22
- 1.4 Noise and Variability23
- 1.4.1 Electronic Noise24
- 1.4.2 Signal-to-Noise Ratio27
- 1.5 Summary27
- Problems29
- 2. BASIC SIGNAL PROCESSING31
- 2.1 Basic Signals: The Sinusoidal Waveform31
- 2.1.1 Sinusoidal Arithmetic34
- 2.1.2 Complex Representation36
- 2.2 Signal Properties: Basic Measurements38
- 2.2.1 Decibels42
- 2.3 Advanced Measurements: Correlations and Covariances44
- 2.3.1 Standard Correlation and Covariance45
- 2.3.2 Autocorrelation and Cross-Correlation48
- 2.4 MATLAB Implementation54
- 2.4.1 Mean, Variance, and Standard Deviation54
- 2.4.2 Ensemble Averaging57
- 2.4.3 Covariance and Correlation58
- 2.4.4 Autocorrelation and Cross-Correlation61
- 2.5 Summary65
- Problems66
- 3. FREQUENCY TRANSFORMATIONS69
- 3.1 Useful Properties of the Sinusoidal Signal72
- 3.2 Fourier Series Analysis75
- 3.2.1 Symmetry79
- 3.3 Frequency Representation80
- 3.4 Complex Representation82
- 3.5 The Continuous Fourier Transform85
- 3.6 Discrete Data: The Discrete Fourier Transform87
- 3.6.1 Data Sampling: Sampling Theorem88
- 3.6.2 Amplitude Slicing: Quantization (Optional)93
- 3.6.3 Data Length: Truncation95
- 3.7 Power Spectrum97
- 3.7.1 Spectral Averaging99
- 3.8 Signal Bandwidth101
- 3.9 MATLAB Implementation102
- 3.10 Summary115
- Problems116
- 4. CIRCUIT AND ANALOG ANALYSIS IN SINUSOIDAL STEADY STATE121
- 4.1 Circuits and Analog Systems121
- 4.2 System Variables and Elements123
- 4.2.1 Electrical Variables125
- 4.2.2 Electrical Elements127
- 4.2.3 Active Elements135
- 4.2.4 The Fluid Analogy137
- 4.3 Phasor Analysis139
- 4.3.1 Phasor Representation: Electrical Elements144
- 4.4 Mechanical Elements147
- 4.4.1 Passive Elements148
- 4.4.2 Elasticity151
- 4.4.3 Sources153
- 4.5 Summary157
- Problems158
- 5. ANALYSIS OF ANALOG MODELS AND PROCESSES161
- 5.1 Conservation Laws: Kirchhoff’s Voltage Law161
- 5.1.1 Mesh Analysis: Single Loops162
- 5.1.2 Mesh Analysis: Multiple Loops168
- 5.1.3 Mesh Analysis: MATLAB Implementation171
- 5.2 Conservation Laws: Kirchhoffs Current Law„Nodal Analysis173
- 5.3 Conservation Laws: Newtons Law„Mechanical Systems178
- 5.4 Summary186
- Problems187
- 6. FREQUENCY CHARACTERISTICS OF CIRCUITS AND ANALOG PROCESSES: THE TRANSFER FUNCTION193
- 6.1 The Circuit or Mechanical System as a Process193
- 6.1.1 Superposition195
- 6.1.2 The Transfer Function196
- 6.1.3 Transfer Function Characteristics197
- 6.2 Transfer Function Frequency Plots: The Bode Plot198
- 6.2.1 Frequency Characteristics of Bode Plot Primitives201
- 6.3 Filters213
- 6.3.1 Filter Types214
- 6.3.2 Filter Bandwidth215
- 6.3.3 Filter Order216
- 6.3.4 Filter Initial Sharpness217
- 6.3.5 Evaluating Filter Frequency Characteritics217
- 6.3.6 Filter Design219
- 6.4 MATLAB Implementation221
- 6.4.1 Transfer Function221
- 6.4.2 System Identification227
- 6.4.3 The Transfer Function and Fourier Series Decomposition230
- 6.5 Summary234
- Problems234
- 7. RELATIONSHIPS BETWEEN ANALOG ELEMENTS239
- 7.1 System Simplifications: Passive Network Reduction239
- 7.1.1 Series Electrical Elements240
- 7.1.2 Parallel Elements242
- 7.1.3 Network Reduction: Passive Networks244
- 7.2 Ideal and Real Sources252
- 7.2.1 The Voltage–Current or v-i Plot252
- 7.2.2 Real Voltage Sources: The Thévenin Source255
- 7.2.3 Real Current Sources: The Norton Source258
- 7.2.4 Thévenin and Norton Circuit Conversion261
- 7.3 Thévenin and Norton Theorems: Network Reduction with Sources264
- 7.4 Measurement Loading269
- 7.4.1 Ideal and Real Measurement Devices270
- 7.4.2 Maximum Power Transfer273
- 7.5 Mechanical Systems275
- 7.6 Multiple Sources: Revisited281
- 7.7 Summary283
- Problems283
- 8. THE ANALYSIS OF TRANSIENTS: THE LAPLACE TRANSFORM289
- 8.1 The Laplace Transform289
- 8.1.1 Definition of the Laplace Transform290
- 8.1.2 Laplace Representation of Elements: Calculus Operations in the Laplace Domain292
- 8.1.3 Initial Conditions293
- 8.1.4 Voltage–Current and Force–Velocity Relationships in the Laplace Domain294
- 8.1.5 Sources: Common Signals in the Laplace Domain296
- 8.1.6 Converting the Laplace Transform to the Frequency Domain298
- 8.1.7 The Time-Delay Element299
- 8.1.8 The Inverse Laplace Transform300
- 8.2 Laplace Analysis: The Laplace Transfer Function300
- 8.2.1 First-Order Processes302
- 8.2.2 Second-Order Processes306
- 8.3 Nonzero Initial Conditions316
- 8.4 Initial and Final Value Theorems320
- 8.5 The Laplace Domain and the Frequency Domain321
- 8.6 Summary330
- Problems330
- 9. SYSTEM MODELS AND BEHAVIOR335
- 9.1 The System Model335
- 9.1.1 Feedback337
- 9.2 The Convolution Integral340
- 9.2.1 MATLAB Implementation343
- 9.3 Resonance354
- 9.3.1 Resonant Frequency355
- 9.3.2 Resonant Bandwidth, Q355
- 9.4 Summary365
- Problems367
- 10. BASIC ANALOG ELECTRONICS: OPERATIONAL AMPLIFIERS371
- 10.1 The Amplifier372
- 10.2 The Operational Amplifier374
- 10.3 The Noninverting Amplifier376
- 10.4 The Inverting Amplifier379
- 10.5 Practical Operational Amplifiers381
- 10.5.1 Limitations in Transfer Characteristics of Real Operational Amplifiers382
- 10.5.2 Input Characteristics389
- 10.5.3 Output Characteristics396
- 10.6 Power Supply398
- 10.7 Operational Amplifier Circuits, or 101 Things to Do with an Operational Amplifier399
- 10.7.1 The Differential Amplifier400
- 10.7.2 The Adder401
- 10.7.3 The Buffer Amplifier402
- 10.7.4 The Transconductance Amplifier403
- 10.7.5 Analog Filters405
- 10.7.6 Instrumentation Amplifier407
- 10.8 Summary411
- Problems411
- APPENDIX A:415
- A.1 Derivation of Euler’s Formula415
- A.2 Confirmation of the Fourier Series416
- A.3 Derivation of the Transfer Function of a Second-Order Op Amp Filter417
- A.4 Derivation of the Transfer Function of an Instrumentation Amplifier418
- APPENDIX B: Laplace Transforms421
- APPENDIX C: Trigonometric and Other Formulas423
- APPENDIX D: Units425
- APPENDIX E: Complex Arithmetic429
- E.1.1 Addition and Subtraction430
- E.1.2 Multiplication and Division430
- APPENDIX F: LF 356 Specifications433
- APPENDIX G: Determinants and Cramer’s Rule435
- BIBLIOGRAPHY437
- INDEX439
Approaches such as the Transfer Function and the Fourier and the Laplace transforms are important tools for bioengineers that often considered borrowed from electrical engineering. This text allows bioengineering students and bioengineers the ability to foster a sense of ownership of these tools by providing them with a solid foundation in the concepts of linear systems analysis. Circuits, Signals and Systems for Bioengineers guides readers through the basic engineering concepts that underlie biological systems, medical devices, biocontrol, and biosignal analysis. Material important to their study and traditionally taught in an electrical engineering service course can now be embraced by bioengineers. Instructive illustrations and MATLAB routines and examples are provided throughout the book.
All disc-based content for this title is now available on the Web.
· Translates important electrical engineering tools such as Fourier Transform, Laplace Transform, analog modeling, systems modeling, and other linear systems analysis techniques for bioengineering students.
· Includes MATLAB examples and problems.
· Includes companion website with PowerPoint presentations, extra examples, figures, and support routines.