E-grāmata: Digital Signal Processing First, Global Edition

Introduction    1-1 Mathematical Representation of Signals   1-2 Mathematical Representation of Systems 1-3 Systems as Building Blocks 1-4 The Next Step Sinusoids 2-1 Tuning Fork Experiment    2-2 Review of Sine and Cosine Functions 2-3 Sinusoidal Signals 2-3.1 Relation of Frequency to Period 2-3.2   Phase and Time Shift 2-4 Sampling and Plotting Sinusoids 2-5 Complex Exponentials and Phasors 2-5.1 Review of Complex Numbers 2-5.2 Complex Exponential Signals 2-5.3   The Rotating Phasor Interpretation 2-5.4   Inverse Euler Formulas Phasor Addition 2-6 Phasor Addition 2-6.1   Addition of Complex Numbers 2-6.2   Phasor Addition Rule 2-6.3   Phasor Addition Rule: Example 2-6.4   MATLAB Demo of Phasors 2-6.5   Summary of the Phasor Addition Rule Physics of the Tuning Fork 2-7.1   Equations from Laws of Physics 2-7.2   General Solution to the Differential Equation 2-7.3   Listening to Tones 2-8 Time Signals: More Than Formulas Summary and Links Problems Spectrum Representation   3-1 The Spectrum of a Sum of Sinusoids 3-1.1   Notation Change 3-1.2   Graphical Plot of the Spectrum 3-1.3   Analysis vs. Synthesis Sinusoidal Amplitude Modulation 3-2.1   Multiplication of Sinusoids 3-2.2   Beat Note Waveform 3-2.3   Amplitude Modulation 3-2.4   AM Spectrum 3-2.5   The Concept of Bandwidth Operations on the Spectrum 3-3.1   Scaling or Adding a Constant 3-3.2   Adding Signals 3-3.3   Time-Shifting x.t/ Multiplies ak by a Complex Exponential 3-3.4   Differentiating x.t/ Multiplies ak by .j 2nfk/ 3-3.5   Frequency Shifting Periodic Waveforms 3-4.1   Synthetic Vowel 3-4.3   Example of a Non-periodic Signal Fourier Series 3-5.1   Fourier Series: Analysis 3-5.2   Analysis of a Full-Wave Rectified Sine Wave 3-5.3   Spectrum of the FWRS Fourier Series 3-5.3.1  DC Value of Fourier Series 3-5.3.2  Finite Synthesis of a Full-Wave Rectified Sine TimeFrequency Spectrum 3-6.1   Stepped Frequency 3-6.2   Spectrogram Analysis Frequency Modulation: Chirp Signals 3-7.1   Chirp or Linearly Swept Frequency 3-7.2   A Closer Look at Instantaneous Frequency Summary and Links Problems Fourier Series Fourier Series Derivation 4-1.1   Fourier Integral Derivation Examples of Fourier Analysis 4-2.1   The Pulse Wave 4-2.1.1  Spectrum of a Pulse Wave 4-2.1.2  Finite Synthesis of a Pulse Wave 4-2.2   Triangle Wave 4-2.2.1  Spectrum of a Triangle Wave 4-2.2.2  Finite Synthesis of a Triangle Wave 4-2.3   Half-Wave Rectified Sine 4-2.3.1  Finite Synthesis of a Half-Wave Rectified Sine Operations on Fourier Series 4-3.1   Scaling or Adding a Constant 4-3.2   Adding Signals 4-3.3   Time-Scaling 4-3.4   Time-Shifting x.t/ Multiplies ak by a Complex Exponential 4-3.5   Differentiating x.t/ Multiplies ak by .j!0k/ 4-3.6   Multiply x.t/ by Sinusoid Average Power, Convergence, and Optimality 4-4.1   Derivation of Parsevals Theorem 4-4.2   Convergence of Fourier Synthesis 4-4.3   Minimum Mean-Square Approximation Pulsed-Doppler Radar Waveform 4-5.1   Measuring Range and Velocity Problems