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.


  1. Two Guitars Example
  2. Asymmetric versus Symmetric
  3. Distance Measurement using Convolution
  4. Long Multiplication without Carry
  5. Convolution Sum
  6. Definition of Terms
  7. A Simple Example
  8. Padding with Zeros
  9. Super-position Curve
  10. Convolution Sums and Convolution Curve
  11. Convolution Interval
  12. Example from Communication Systems
  13. Convolution Interval and Convolution Index
  14. General Form of Convolution Sum
  15. Convolution Integral
  16. Linear Convolution
  17. Circular Convolution
  18. Linear Convolution of sin(ω0t) and cos(ω0t)
  19. Periodic Convolution of sin(ω0t) and cos(ω0t)
  20. Circular Convolution of Two Guitars Example
  21. LTI Systems
  22. Shift Invariant
  23. Time Invariant
  24. Frequency Fidelity
  25. Complex Representation of an LTI System
  26. Deconvolution
  27. Linear
  28. Harmonics
  29. Linear Decomposition
  30. Unit Impulse Function
  31. Filtering
  32. Linear Constant Coefficient Difference Equations
  33. Infinite Impulse Response (IIR)
  34. Control Systems