True linear prediction by use of a theoretical impulse response

A functional form is derived for an impulse response in a time-domain linear prediction based on an autoregressive model. For any impulse-response length, this theoretical impulse response allows us to predict correctly a given time-domain signal consisting of discrete cosine waves. A method is also given for finding the wave frequencies, which are needed in the construction of the impulse response. The properties of this theoretical impulse response are compared with those of the impulse responses computed by Burg’s algorithm or by fitting of the autocorrelation function of the original time-domain signal.