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Digital Signals Theory
Time-domain signals
1. Signals
1.1. Preliminaries
1.2. Periodicity and waves
1.3. Units and dimensional analysis
1.4. Audio and signals
1.5. Exercises
2. Digital sampling
2.1. Sampling period and rate
2.2. Aliasing
2.3. The Nyquist-Shannon sampling theorem
2.4. Quantization
2.5. Exercises
3. Convolution
3.1. Delay, gain, and mix
3.2. Defining convolution
3.3. Impulse Response
3.4. Convolution modes
3.5. Properties of convolution
3.6. Linearity and Shift-invariance
3.7. Exercises
The frequency domain
4. Complex numbers
4.1. Defining complex numbers
4.2. Basic operations
4.3. Complex exponentials
4.4. Multiplication and division
4.5. Powers and waves
4.6. Exercises
5. The Discrete Fourier Transform
5.1. Similarity
5.2. Comparing to sinusoids
5.3. Analysis frequencies
5.4. Phase
5.5. The Discrete Fourier Transform
5.6. Examples
5.7. Summing sinusoids
5.8. Exercises
6. Properties of the DFT
6.1. Linearity
6.2. The DFT shifting theorem
6.3. Conjugate Symmetry
6.4. Spectral leakage and windowing
6.5. Exercises
7. DFT Invertibility
7.1. Warm-up: a single sinusoid
7.2. The Inverse DFT
7.3. Synthesis
7.4. Exercises
8. Fast Fourier Transform
8.1. Time-analysis of the DFT
8.2. Radix-2 Cooley-Tukey
8.3. Exercises
9. The Short-time Fourier Transform
9.1. Framing
9.2. Defining the STFT
9.3. Exercises
Filtering
10. Frequency domain convolution
10.1. The Convolution Theorem
10.2. Convolutional Filtering
10.3. Filter Design and Analysis
10.4. Phase and group delay
10.5. Exercises
11. Infinite impulse response filters
11.1. Feedback filters
11.2. Using IIR filters
11.3. Common IIR filters
11.4. Exercises
12. Analyzing IIR filters
12.1. The z-transform
12.2. Properties of the z-transform
12.3. Transfer functions
12.4. Stability, poles, and zeros
12.5. Exercises
Appendix
Mathematical fundamentals
Sets
Sequences
Modular arithmetic
Exponentials
References
Index
E
|
F
E
Exponential
function
Exponentials
rules
F
Fast Fourier Transform
