1. A fixed codebook searching apparatus, comprising: an impulse response modifier, implemented by at least one processor, that convolutes a first impulse response (h(n)) with an impulse response of a non-causal filter to generate a second impulse response (h (0) (n)), in a code excited linear prediction (CELP) encoder, the second impulse (h (0) (n)) having a value where an index (n) in time domain equals a negative integer; a matrix generator that generates a Toeplitz-type convolution matrix from the second impulse response (h (0) (n)); and a searcher, that performs a codebook search by maximizing a term using the Toeplitz-type convolution matrix and an input speech signal, wherein the fixed codebook searching apparatus, comprising the impulse response modifier, the matrix generator and the searcher perform a code excited linear prediction (CELP) encoding of the input speech signal.