1. A fixed codebook searching apparatus, comprising: a convolution operator that convolves an impulse response of a perceptually weighted synthesis filter with an impulse response vector that has values at negative times, to generate a second impulse response vector that has values at negative times; a matrix generator that generates a Toeplitz-type convolution matrix using the second impulse response vector generated by the convolution operator; and a searcher that performs a fixed codebook search by maximizing a term using the Toeplitz-type convolution matrix.