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
Time-Frequency 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 Parseval's 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
