Sinusoids and Exponentials

This chapter provides an introduction to sinusoids, exponentials, complex sinusoids, and various associated terminology, such as exponential decay-time ``'', in-phase and quadrature sinusoidal components, analytic signals, positive and negative frequencies, and constructive and destructive interference. The fundamental importance of sinusoids in the analysis of linear time-invariant systems is introduced. We also look at circular motion expressed as the vector sum of in-phase and quadrature sinusoidal motions. Both continuous and discrete-time sinusoids are considered. In particular, a sampled complex sinusoid is generated by successive powers of any complex number .

- Sinusoids
- Example Sinusoids
- Why Sinusoids are Important
- In-Phase & Quadrature Sinusoidal Components
- Sinusoids at the Same Frequency
- Constructive and Destructive Interference
- Sinusoid Magnitude Spectra

- Exponentials

- Complex Sinusoids
- Circular Motion
- Projection of Circular Motion
- Positive and Negative Frequencies
- Plotting Complex Sinusoids versus Frequency
- Sinusoidal Amplitude Modulation (AM)
- Sinusoidal Frequency Modulation (FM)
- Analytic Signals and Hilbert Transform Filters
- Generalized Complex Sinusoids
- Sampled Sinusoids
- Powers of
*z* - Phasors and Carriers
- Importance of Generalized Complex Sinusoids
- Comparing Analog and Digital Complex Planes

- Sinusoid Problems

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