Convolution and LTI Systems
An aid to getting started with Digital Signal Processing
Authors: Snigdha Suresh, Savitha Sthawarmath, Rajeev Rajkumar, Mohit P Tahiliani, Stephen Vadakkan
Convolution and LTI Systems are the heart and soul of Digital Signal Processing (DSP). Yet the CONVOLUTION operation has neither been defined nor explained clearly. This pedagogical gem redeems this deficiency. The flow is smooth. The presentation is lucid, precise and concise.
Contents
- Two Guitars Example
- Asymmetric versus Symmetric
- Distance Measurement using Convolution
- Long Multiplication without Carry
- Convolution Sum
- Definition of Terms
- A Simple Example
- Padding with Zeros
- Super-position Curve
- Convolution Sums and Convolution Curve
- Convolution Interval
- Example from Communication Systems
- Convolution Interval and Convolution Index
- General Form of Convolution Sum
- Convolution Integral
- Linear Convolution
- Circular Convolution
- Linear Convolution of sin(ω0t) and cos(ω0t)
- Periodic Convolution of sin(ω0t) and cos(ω0t)
- Circular Convolution of Two Guitars Example
- LTI Systems
- Shift Invariant
- Time Invariant
- Frequency Fidelity
- Complex Representation of an LTI System
- Deconvolution
- Linear
- Harmonics
- Linear Decomposition
- Unit Impulse Function
- Filtering
- Linear Constant Coefficient Difference Equations
- Infinite Impulse Response (IIR)
- Control Systems