TABLE OF CONTENTS
Dedication…………………………………………………………………………...……iii
Acknowledgments………………………………………………………………………..iv
List of Tables…………………………………………………………………...……….viii
List of Figures…………………………………………………………………………….ix
Abstract of Thesis……………………………………………………………………...….x
Chapter 1 Introduction…………………..…………………………………………...1
1.1 Objective………………………………………………………………..…1
1.2 Outline of the Thesis………………………………………………………2
Chapter 2 Sampling and Quantization………………………………………………..3
2.1 Analog and Digital Signals………………………………………………..3
2.2 Introduction to Sampling………………………………………………….3
2.3 Introduction to Quantization………………………………………………4
2.4 Sampling Continuous-Time Signals………………………………………5
2.4.1 Dirac Delta Function………………………………………………………5
2.4.2 Time-Domain Impulse Sampling………………………………………….6
2.5 Nyquist Rate……………………………………………………………….7
2.6 Quantization……………………………………………………………….9
2.7 Uniform Quantization Error……………………………………………...10
2.8 Summary…………………………………………………………………12
Chapter 3 Discrete-Time Fourier Series…………………………………………….14
3.1 Introduction………………………………………………………………14
3.2 Definition of the DTFS…………………………………………………..16
3.3 Twiddle Factor…………………………………………………………...17
3.4 Properties of the DTFS………………………………………………..…20
3.4.1 Linearity………………………………………………………………….20
3.4.2 Symmetry………………………………………………………………...20
3.4.3 Time and Frequency Scaling…………………………………………….20
3.4.4 Time and Frequency Shifting…………………………………………….21
3.4.5 Parseval’s Theorem………………………………………………………22
3.4.6 Periodicity………………………………………………………………..22
3.5 Zero Padding……………………………………………………………..24
3.6 Strengths of the DTFS…………………………………………………...25
3.6.1 Analyzing Periodic Signals………………………………………………25
3.6.2 Input Flexibility………………………………………………………….25
3.6.3 Sets of Data………………………………………………………………25
3.6.4 Coherent Integration Gain……………………………………………….26
3.7 Weaknesses of the DTFS……………………………………….………..27
3.7.1 Computational Requirements……………………………….……………27
3.7.2 Quantization Noise Error…………………………………….………..…28
3.7.3 High Sidelobes………………………………………………………...…29
3.7.4 Spectral Leakage…………………………………………………………29
3.7.5 Analyzing Transient Signals……………………………………………..30
3.8 Summary…………………………………………………………………30
Chapter 4 The Fast Fourier Transform…………………………………………...…32
4.1 Introduction………………………………………………………………32
4.2 FFT Improvements to the DTFS…………………………………..…..…32
4.2.1 Computational Load……………………………………………………...32
4.2.2 Reduced Quantization Noise Error………………………………………34
4.3 Additional Weaknesses of the FFT………………………………………34
4.4 Radix-2 Decimation-in-Time FFT Algorithm…………………………...34
4.5 Summary…………………………………………………………………39
Chapter 5 Window Functions………………………………………………...……..41
5.1 Introduction………………………………………………………………41
5.2 Window Functions……………………………………………………….45
5.3 Characteristics of Window Functions……………………………………46
5.3.1 Coherent Integration Gain………………………………………………..46
5.3.2 Highest Sidelobe Level…………………………………………………..46
5.3.3 Sidelobe Rolloff Ratio…………………………………………………...46
5.3.4 Frequency Straddle Loss…………………………………………………47
5.3.5 Equivalent Noise Bandwidth…………………………………………….47
5.3.6 Three-dB Main Lobe Bandwidth………………………………………...48
5.4 Common Window Functions…………………………………………….48
5.4.1 Rectangular……………………………………………………………….48
5.4.2 Triangular………………………………………………………………...49
5.4.3 Sine Lobe………………………………………………………………...49
5.4.4 Hanning………………………………………………………………….50
5.4.5 Hamming………………………………………………………………...50
5.4.6 Blackman………………………………………………………………...50
5.5 Summary…………………………………………………………………51
Chapter 6 Data Acquisition and Spectral Analysis System…………………………53
6.1 Introduction………………………………………………………………53
6.2 NI 5112 High-Speed Digitizer…………………………………………...53
6.3 Software Functionality…………………………………………………...54
6.3.1 Data Acquisition…..……..………………………………………………55
6.3.2 Time-Domain Plot…..……………..…………………………………….57
6.3.3 Additional Time-Domain Tools………………………………………….59
6.3.4 Frequency Plots…………………………………………………………..60
6.3.5 Help……………………………………………………………………....62
Chapter 7 Conclusions and Future Work…………………………………………...63
7.1 Conclusions………………………………………………………………63
7.2 Future Work……………………………………………………………...64
References ……………………………………………………………………………66
Appendix A ……………………………………………………………………………67
Appendix B …………………………………………………………………………..131
Appendix C ………………………………………………………………………..…137
Appendix D …………………………………………………………………………..141
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