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 LinksProblemsSpectrum 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 Derivation4-1.1 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