1.1  To Learn in This Chapter
1.2  Analog, Digital and Discrete-Time Signals
1.2.1  Advanced: Ambiguous notation: whole signal or single sample
1.2.2  Digitizing Signals
1.2.3  Discrete-time signals
1.3  Basic Signal Manipulation and Representation
1.3.1  Manipulating the independent variable
1.3.2  When the independent variable is not an integer
1.3.3  Frequently used manipulations of the independent variable
1.3.4  Using impulses to represent signals
1.3.5  Using step functions to help representing signals
1.3.6  The rect function
1.4  Block or Window Processing
1.4.1  Advanced: Block processing with overlapped windows
1.5  Advanced: Complex-Valued and Sampled Signals
1.5.1  Complex-valued signals
1.5.2  Sampled signals
1.6  Signal Categorization
1.6.1  Even and odd signals
1.6.2  Random signals and their generation
1.6.3  Periodic and aperiodic signals
1.6.4  Power and energy signals
1.7  Modeling the Stages in A/D and D/A Processes
1.7.1  Modeling the sampling stage in A/D
1.7.2  Oversampling
1.7.3  Mathematically modeling the whole A/D process
1.7.4  Sampled to discrete-time (S/D) conversion
1.7.5  Continuous-time to discrete-time (C/D) conversion
1.7.6  Discrete-time to sampled (D/S) conversion
1.7.7  Reconstruction
1.7.8  Discrete-time to continuous-time (D/C) conversion
1.7.9  Analog to digital (A/D) and digital to analog (D/A) conversions
1.7.10  Sampling theorem
1.7.11  Different notations for S/D conversion
1.8  Relating Frequencies of Continuous and Discrete-Time Signals
1.8.1  Units of continuous-time and discrete-time angular frequencies
1.8.2  Mapping frequencies in continuous and discrete-time domains
1.8.3  Nyquist frequency
1.8.4  Frequency normalization in Python and Matlab/Octave
1.9  An Introduction to Quantization
1.9.1  Quantization definitions
1.9.2  Implementation of a generic quantizer
1.9.3  Uniform quantization
1.9.4  Granular and overload regions
1.9.5  Design of uniform quantizers
1.9.6  Design of optimum non-uniform quantizers
1.9.7  Quantization stages: classification and decoding
1.9.8  Binary numbering schemes for quantization decoding
1.9.9  Quantization examples
1.10  Correlation: Finding Trends
1.10.1  Autocorrelation function
1.10.2  Cross-correlation
1.11  Advanced: A Linear Model for Quantization
1.12  Advanced: Power and Energy in Discrete-Time
1.12.1  Power and energy of discrete-time signals
1.12.2  Power and energy of signals represented as vectors
1.12.3  Advanced: Power and energy of vectors whose elements are not time-ordered
1.12.4  Power and energy of discrete-time random signals
1.12.5  Advanced: Relating Power in Continuous and Discrete-Time
1.13  Applications
1.14  Comments and Further Reading
1.15  Review Exercises
1.16  Exercises