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DSP First (2nd Edition)
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This chapter discusses the development of the Phasor Addition Rule, a method for solving the problem of how to incorporate Euler's inequality into the discrete-time model.Abstract:
2 Sinusoids 9 2-1 Tuning-Fork Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2-2 Review of Sine and Cosine Functions . . . . . . . . . . . . . . . . . . . . 12 2-3 Sinusoidal Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2-3.1 Relation of Frequency to Period . . . . . . . . . . . . . . . . . . . 15 2-3.2 Phase and Time Shift . . . . . . . . . . . . . . . . . . . . . . . . . 17 2-4 Sampling and Plotting Sinusoids . . . . . . . . . . . . . . . . . . . . . . . 19 2-5 Complex Exponentials and Phasors . . . . . . . . . . . . . . . . . . . . . 21 2-5.1 Review of Complex Numbers . . . . . . . . . . . . . . . . . . . . 22 2-5.2 Complex Exponential Signals . . . . . . . . . . . . . . . . . . . . 23 2-5.3 The Rotating Phasor Interpretation . . . . . . . . . . . . . . . . . . 25 2-5.4 Inverse Euler Formulas . . . . . . . . . . . . . . . . . . . . . . . . 27 2-6 Phasor Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2-6.1 Addition of Complex Numbers . . . . . . . . . . . . . . . . . . . . 29 2-6.2 Phasor Addition Rule . . . . . . . . . . . . . . . . . . . . . . . . . 29 2-6.3 Phasor Addition Rule: Example . . . . . . . . . . . . . . . . . . . 31 2-6.4 MATLAB Demo of Phasors . . . . . . . . . . . . . . . . . . . . . 33 2-6.5 Summary of the Phasor Addition Rule . . . . . . . . . . . . . . . . 33 2-7 Physics of the Tuning Fork . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2-7.1 Equations from Laws of Physics . . . . . . . . . . . . . . . . . . . 34 2-7.2 General Solution to the Differential Equation . . . . . . . . . . . . 37 2-7.3 Listening to Tones . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2-8 Time Signals: More Than Formulas . . . . . . . . . . . . . . . . . . . . . 38 2-9 Summary and Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2-10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40read more
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Dissertation
Measuring seismic station timing errors from ambient noise
TL;DR: In this article, the authors applied techniques similar to those used for monitoring velocity changes in the structure, are applied on ambient seismic noise to find instrumental timing errors, and the processing procedure is divided into four main parts: preparing the data, preprocessing, cross correlation and stacking, and measuring the timing errors.
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Dissertation
Measuring seismic station timing errors from ambient noise
TL;DR: In this article, the authors applied techniques similar to those used for monitoring velocity changes in the structure, are applied on ambient seismic noise to find instrumental timing errors, and the processing procedure is divided into four main parts: preparing the data, preprocessing, cross correlation and stacking, and measuring the timing errors.