Digital Filtering and Exact Reconstruction of Digital Audio

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SUMMARY

This discussion focuses on digital filtering and the exact reconstruction of digital audio using the Sinc function. It emphasizes the importance of two times upsampling in achieving high-quality audio reproduction, assuming infinite bit depth for calculations. The Sinc function is highlighted as a critical component in the filtering process, ensuring that audio signals are accurately represented and reconstructed without loss of quality. The insights presented build upon previous articles and provide a deeper understanding of digital audio processing techniques.

PREREQUISITES
  • Understanding of digital audio concepts
  • Familiarity with the Sinc function in signal processing
  • Knowledge of upsampling techniques
  • Basic principles of digital filtering
NEXT STEPS
  • Research the mathematical properties of the Sinc function in audio processing
  • Explore advanced upsampling techniques in digital audio
  • Learn about digital filter design and implementation
  • Investigate the impact of bit depth on audio quality
USEFUL FOR

Audio engineers, digital signal processing specialists, and anyone involved in the design and optimization of digital audio systems will benefit from this discussion.

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Table of Contents
ToggleIntroductionThe Sinc FunctionUsing the Sinc Function
Introduction
This elaborates some of the claims in my insights article on digital audio.
The Sinc Function
The first link in my insights article has a section on filters, but I will detail the most critical case. The bit depth is assumed to be so large for all practical purposes that it is infinite, and all calculations are done at that resolution. To clarify the statement above, we will start with two times upsampling and how it is done. You put the...

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