TABLE OF CONTENTS

Title Page

Abstract

Chapter 1. INTRODUCTION

Chapter 2. CONVOLUTION TECHNIQUES

• Definition of Convolution
• Time-Domain Convolution
• Frequency-Domain Convolution
• Overlap-Add Block Convolution
• Overlap-Save Block Convolution
• Zero Delay Convolution

Chapter 3. MULTIRATE FILTER BANKS

• Introduction
  • Decimation and Expansion
  • Errors in the QMF Bank
  • The Noble Identities
  • Polyphase Representation
  • M-Channel Filter Banks
• Perfect Reconstruction Filter Banks
• The QMF Lattice
• Filter Banks with Minimized Amplitude Distortion
• IIR Approximation of Linear Phase Perfect Reconstruction Filter Banks

Chapter 4. MULTIRATE CONVOLUTION

• Introduction
• Orthonormal and Biorthonormal Convolvers
  • Convolution Theorem for Orthonormal Filter Banks
  • Convolution Theorem for Biorthonormal Filter Banks
  • Coding Gain
• "Running" Convolution with Multirate Filter Banks
• Multirate Convolution with Cross-Convolved Channels
• Multirate Convolution without Cross-Convolved Channels

Chapter 5. COMPUTATIONAL COMPLEXITY

• Computational Complexity for the Convolution Methods
• Time-Domain Convolution
• Frequency-Domain Convolution
• Block Convolution
• Multirate Convolution with Biorthonormal Filter Banks
• Multirate Running Convolution
• Multirate Convolution with Cross-Convolved Channels
• Multirate Convolution without Cross-Convolved Channels
• Comparison of Convolution Methods

Chapter 6. FURTHER RESEARCH

• An Open Problem in Multirate Convolution without Cross-Convolved Channels
• Additional Qualitative Tests
• Pre- or Post-Processing
• Expansion to M Channels
• Subband Skipping
• Subband Processing

Chapter 7. CONCLUSION

REFERENCES

APPENDIX A: Qualitative Judgements for Multirate Convolution without Cross-Convolved Channels

• Procedure
• Results
• Discussion

APPENDIX B: Matlab Scripts