Signal Processing
1.1
1. Systems and Signals
1.1. Systems
1.2. Signals
1.2.1. Plotting Signals
1.2.1.1. Plotting Real Valued Signals
1.2.1.2. Plotting Complex Valued Signals
1.2.2. Signal Properties
1.2.3. Signal Transformations
1.2.4. Basic Signals
1.2.4.1. Constant Signal
1.2.4.2. Step Function
1.2.4.3. Pulse Function
1.2.4.4. Complex Exponential Functions
1.2.4.5. Chirp Signal
1.3. Decibels
1.4. Exercises
2. Linear Time Invariant Systems
2.1. Definition and Properties
2.1.1. Linearity and Time Invariance
2.1.2. Stable Systems
2.1.3. Causal Systems
2.2. Convolutions
2.2.1. Linearity + Translation Invariance = Convolution
2.2.2. Properties and Recipe
2.3. Linear Discrete Time Systems
2.4. Eigenfunctions
2.5. Exercises
3. The Frequency Domain
3.1. Continuous Time Fourier Series
3.1.1. The Complex Exponential Functions
3.1.2. The Fourier Series
3.1.3. Properties of the CT Fourier Series
3.1.3.1. Real Valued Signal
3.1.3.2. Even Signal
3.1.3.3. Odd Signal
3.1.3.4. Differentiation
3.1.3.5. Convolution
3.1.3.6. Fourier Series Examples
3.1.4. Exercises
3.2. Continuous Time Fourier Transform
3.2.1. The Fourier Transform
3.2.2. Properties of the CT Fourier Transform
3.2.2.1. Real Signals
3.2.2.2. Even and Odd Signals
3.2.2.3. Derivatives
3.2.2.4. Pulse Function
3.2.2.5. Time Shifts
3.2.2.6. Complex Exponential
3.2.2.7. Periodic Signal
3.2.2.8. Pulse Train
3.2.2.9. Convolution
3.2.2.10. Duality
3.2.3. Fourier Transform Pairs
3.2.3.1. Complex Exponential
\(\FTright\)
Pulse
3.2.3.2. Pulse
\(\FTright\)
Complex Exponential
3.2.4. Bode Plots
3.2.5. Exercises
3.3. The Discrete Time Fourier Transform
3.3.1. DTFT and IDTFT
3.3.2. Properties of the DTFT
3.3.3. Fourier Transform Pairs
3.3.4. Introducing Time
3.3.5. Exercises
3.4. Discrete Time Fourier Series
3.4.1. Synthesis and Analysis Equations
3.4.2. Properties of Discrete Time Fourier Series
3.4.3. Time and Frequency
3.4.4. DTFS in Numpy
3.4.5. DTFS in Linear Algebra Disguise
3.4.6. The Fast Fourier Transform
3.4.7. Exercises
4. The Complex Domain
4.1. The S-Domain
4.1.1. The Laplace Transform
4.1.1.1. Definition
4.1.1.2. Eigenfunctions of an LTI system
4.1.1.3. The Laplace Transform and the Fourier Transform
4.1.2. Properties of the Unilateral Laplace transform
4.1.3. Pairs of the (Unilateral) Laplace Transform
4.1.4. Differential Equations and the Laplace Transform
4.1.4.1. Poles and Zeros in the S-plane
4.1.4.2. An Electronic Example
4.1.4.3. A Mechanical Example
4.1.5. Exercises
4.2. The Z-Domain
4.2.1. The
\(\ZT\)
-Transform
4.2.1.1. Definition
4.2.1.2. Eigenfunctions of an LTI System
4.2.1.3. Finite and Infinite Signals
4.2.1.4. The Z-Transform and the Fourier Transform
4.2.2.
\(\ZT\)
-Transform Properties
4.2.3. Pairs of Z-Transforms
4.2.4. Difference Equations in the Z-domain
4.2.4.1. From Difference Equation to Transfer Function
4.2.4.2. Poles and Zeros
4.2.5. The Z-Operator
4.2.6. Exercises
5. Applications
5.1. Sound and Sound Processing
5.1.1. What is sound?
5.1.2. Human Perception of Sound
5.1.2.1. High Frequency Limit
5.1.2.2. Absolute Threshold of Hearing
5.1.2.3. Simultaneous Masking
5.1.2.4. Temporal Masking
5.1.3. Sound Level Measurement
5.1.4. A word of warning
5.1.5. Sound Recording
5.1.6. Sound Compression
5.2. Analog Electronics
5.2.1. Ohm’s Law
5.2.2. Serial Circuits / Voltage Divider
5.2.3. Parallel Circuits
5.2.4. Kirchhoffs Laws
5.2.4.1. Kirchhoff’s Current Law
5.2.4.2. Kirchhoff Voltage Law
5.2.5. Highway to Hell
5.2.6. Power
5.2.7. Inductors
5.2.8. Capacitors
5.2.9. Low Pass Filter
5.2.10. High Pass Filter
5.2.11. Operational Amplifiers
5.2.12. Active Analog Filters
5.2.13. Measurements
5.2.13.1. Multi-meter
5.2.13.2. Oscilloscope
5.2.14. Excercises
5.2.14.1. Equivalent Circuits
5.2.14.2. Complex Impedance
5.2.14.3. Control Sound Level
5.2.14.4. Bode Diagram
5.2.14.5. Design 2-way X-over
5.2.14.6. RIAA Correction
5.2.14.7. Non Inverting OpAmp
5.2.14.8. Sallen Key opamp filter
5.2.14.9. Audio Equalizer
5.3. Sampling
5.3.1. The Sampling Theorem
5.3.2. Interpolation
5.3.2.1. Sinc Interpolation
5.3.3. Exercises
5.4. Transforming Analog Filters into Digital Filters
5.4.1. Analog Filters
5.4.1.1. Ideal Filters
5.4.1.2. The Canonical (Low Pass) First Order Filter and its Transformations
5.4.1.3. Second Order Filters
5.4.1.4. Higher Order Filters
5.4.2. From Analog to Digital through the Bilinear Transform
5.4.2.1. The Bilinear Transform
5.4.2.2. Pre-Warping
5.4.3. IIR Filters in Python
5.4.4. Exercises
5.5. Classical Control Theory
5.5.1. Physical Modelling of Dynamic Systems
5.5.1.1. Warming Up
5.5.1.2. A Bumpy Road
5.5.1.3. The Inverted Pendulum
5.5.2. Block Diagrams
5.5.2.1. Cascade of Systems
5.5.2.2. Addition of System outputs
5.5.2.3. Feedback Systems
5.5.3. Canonical Systems
5.5.3.1. First Order Systems
5.5.3.2. Second Order Systems
5.5.4. Control Systems
5.5.4.1. Feedback Control System
5.5.4.2. Stability
5.5.4.3. PID Controller
5.5.4.4. Root Locus Analysis
6. Mathematical Tools
6.1. Geometric Sequences
6.2. Complex Numbers and Complex Functions
6.2.1. Algebra
6.2.2. Complex Functions
6.2.3. Geometrical Interpretation
6.2.4. Complex Numbers in Python/Numpy
6.2.5. Exercises
7. Python for Sound Signal Processing
7.1. Read, Write and Play Sound
7.2. Visualize Sound Signals
7.3. Real Time Processing Sound Signals
7.4. Exercises
Signal Processing
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Lecture Notes Digital Signal Processing
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Lecture Notes Digital Signal Processing
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