Digital Signal Processing First, Global Edition

• Introduction    1-1 Mathematical Representation of Signals  1-2 Mathematical Representation of Systems 1-3 Systems as Building Blocks1-4 The Next Step Sinusoids 2-1 Tuning Fork Experiment   2-2 Review of Sine and Cosine Functions2-3 Sinusoidal Signals2-3.1 Relation of Frequency to Period2-3.2   Phase and Time Shift2-4 Sampling and Plotting Sinusoids2-5 Complex Exponentials and Phasors2-5.1 Review of Complex Numbers 2-5.2 Complex Exponential Signals2-5.3   The Rotating Phasor Interpretation2-5.4   Inverse Euler Formulas Phasor Addition2-6 Phasor Addition2-6.1   Addition of Complex Numbers2-6.2   Phasor Addition Rule2-6.3   Phasor Addition Rule: Example2-6.4   MATLAB Demo of Phasors2-6.5   Summary of the Phasor Addition Rule Physics of the Tuning Fork2-7.1   Equations from Laws of Physics2-7.2   General Solution to the Differential Equation2-7.3   Listening to Tones2-8 Time Signals: More Than FormulasSummary and LinksProblems Spectrum Representation  3-1 The Spectrum of a Sum of Sinusoids3-1.1   Notation Change3-1.2   Graphical Plot of the Spectrum3-1.3   Analysis vs. SynthesisSinusoidal Amplitude Modulation3-2.1   Multiplication of Sinusoids3-2.2   Beat Note Waveform3-2.3   Amplitude Modulation3-2.4   AM Spectrum3-2.5   The Concept of BandwidthOperations on the Spectrum3-3.1   Scaling or Adding a Constant3-3.2   Adding Signals3-3.3   Time-Shifting x.t/ Multiplies ak by a Complex Exponential3-3.4   Differentiating x.t/ Multiplies ak by .j 2nfk/3-3.5   Frequency ShiftingPeriodic Waveforms3-4.1   Synthetic Vowel3-4.3   Example of a Non-periodic SignalFourier Series3-5.1   Fourier Series: Analysis3-5.2   Analysis of a Full-Wave Rectified Sine Wave3-5.3   Spectrum of the FWRS Fourier Series3-5.3.1  DC Value of Fourier Series3-5.3.2  Finite Synthesis of a Full-Wave Rectified SineTime–Frequency Spectrum3-6.1   Stepped Frequency3-6.2   Spectrogram AnalysisFrequency Modulation: Chirp Signals3-7.1   Chirp or Linearly Swept Frequency3-7.2   A Closer Look at Instantaneous FrequencySummary and LinksProblems Fourier Series Fourier Series Derivation 4-1.1   Fourier Integral DerivationExamples of Fourier Analysis4-2.1   The Pulse Wave4-2.1.1  Spectrum of a Pulse Wave4-2.1.2  Finite Synthesis of a Pulse Wave4-2.2   Triangle Wave4-2.2.1  Spectrum of a Triangle Wave4-2.2.2  Finite Synthesis of a Triangle Wave4-2.3   Half-Wave Rectified Sine4-2.3.1  Finite Synthesis of a Half-Wave Rectified SineOperations on Fourier Series4-3.1   Scaling or Adding a Constant4-3.2   Adding Signals4-3.3   Time-Scaling4-3.4   Time-Shifting x.t/ Multiplies ak by a Complex Exponential4-3.5   Differentiating x.t/ Multiplies ak by .j!0k/4-3.6   Multiply x.t/ by SinusoidAverage Power, Convergence, and Optimality4-4.1   Derivation of Parseval’s Theorem4-4.2   Convergence of Fourier Synthesis4-4.3   Minimum Mean-Square ApproximationPulsed-Doppler Radar Waveform4-5.1   Measuring Range and VelocityProblems </

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