Linear Predictive Coding (LPC) models a digital signal (originally speech) as the output of a linear filter driven by an excitation source. For each sample s(n), the technique predicts the value as a weighted sum of p past samples: s̃(n) = Σ(aᵢ · s(n-i)) for i=1..p, where aᵢ are the prediction coefficients and p is the prediction order. The residual (actual minus predicted) captures the excitation source's characteristics (pitch periodicity and timbre), while the filter coefficients model the signal's spectral envelope. The coefficients are computed by minimizing the prediction error, yielding the Yule-Walker equations solved via the Levinson-Durbin recursion on the signal's autocorrelation matrix. Parameters: prediction order (p, typically 8-16 for speech at 8 kHz), prediction coefficients (aᵢ, encoding the spectral envelope), residual signal (the excitation). Persistence mechanism: standardized algorithm embedded in codec specifications (ITU-T G.729, 3GPP AMR, GSM Full Rate), implemented in hardware DSP chips and software libraries across telecommunications, audio coding, and pitch estimation systems since the 1960s. [formal: linearis praedictio codificatio | substrate: behavior | horizon: generations | explicit: yes | epoch: 0.01]
Accepted ontology entry
linear-predictive-coding
Linear Predictive Coding (LPC) models a digital signal (originally speech) as the output of a linear filter driven by an excitation source. For each sample s(n), the technique predicts the value as a weighted sum of p past samples: s̃(n) =…
Definition
Why it is in scope
A human-made signal processing technique for modeling digital signals as the output of a linear filter driven by an excitation source. Developed by Salomon Kullback, Robert Leibson, and J.L. Flanagan in 1951 for speech coding, and independently by B. S. Atal and Hanif R. Sandler in 1976 for speech analysis. Persisted through standardization in ITU-T G.729, 3GPP AMR, and decades of DSP implementations.
Names and aliases
- linear-predictive-codingen · CANONICAL
Relations from this entry
- cmsm6rfiw00n51q138pvwzetkDERIVED_FROM →
Autocorrelation (developed 1920s-1930s by Pearson) predates linear-predictive-coding (1950s-1960s by B. S. Durbin and others). LPC coefficients are conventionally computed using the autocorrelation method, which solves the Yule-Walker equations via autocorrelation of the signal. The autocorrelation technique fed into and enables LPC computation.
- cmsps9i0v06eejlssqrjcqyviDERIVED_FROM →
Signal processing as a field (1940s-1950s) predates linear predictive coding (developed late 1950s-1960s by BesselSEN, Itakura, and Saito for speech compression). Signal processing provided the theoretical framework — autoregressive modeling, least-squares optimization — that LPC builds on. Direction test per Law 7: signal-processing existed first and fed into LPC.
- cmsqzkklz0077swynpwhhw0g8INSTANCE_OF →
LPC IS a specific kind of parametric modeling: it models a signal using a parametric linear prediction model (past samples linearly combined to predict future). A competent speaker would call LPC a parametric model. Specific→general, nearest kind check: parametric-modeling is the closest category.
- cmspywurr06ztjlssi76045rfSERVES →
LPC was developed (Itakura, Besselien, Saito, 1950s-60s) specifically for speech compression and recognition. Its designed purpose is to further speech-recognition and speech-coding systems. For whose sake: LPC was built for speech recognition's benefit.
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Record identity
- Created
- Aug 13, 2026, 3:03 AM UTC
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- b8a57b13285dd812ec01d218f4e61e8387ae957819c28838fe57c9ade13ab15a