Linear Predictive Coding is All-Pole Resonance Modeling

Linear predictive coding (LPC) is a widely used technique in audio signal processing, especially in speech signal processing. It has found particular use in voice signal compression, allowing for very high compression rates. As widely adopted as it is, LPC is covered in many textbooks and is taught in most advanced audio signal processing courses. So why another article on LPC? Despite covering LPC during my undergraduate coursework in electrical engineering, it wasn’t until implementing LPC for my own research project that I understood what the goals of LPC were and what it was doing mathematically to meet those goals. A great part of the confusion stemmed from the somewhat cryptic name, Linear-Predictive-Coding. “Linear” made sense, however “Predictive” and “Coding”, sounded baffling, at least to the undergraduate me. What is it trying to predict? And coding? What does that mean? As we will find in the following sections, the name LPC does make sense. However, it is one catered to a specific use, speech signal transmission, possibly obscuring other applications, such as cross-synthesis. It takes a moment to understand the exclamation, “I used linear predictive coding to cross-synthesize my voice with a creaking ship!”. Thus the purpose of this article is to explain LPC from a general perspective, one that makes sense to me and hopefully to others trying to grasp what LPC is. Another purpose is to present a complete derivation in simple linear algebra terms before mentioning other concepts and approaches. Finally, I prefer calling LPC, All-Pole Resonance Modeling.