A digital signal processing apparatus comprises a wavelet transforming device that divides an input digital signal into a first low-frequency sub band and a first high-frequency sub band by wavelet transformation and further divides the first low-frequency sub band into a second low-frequency sub band and a second high-frequency sub band, a coring device that executes a coring process to data of specific coordinates of the second high-frequency sub band, a judging device that judges whether the data of the specific coordinates of the second high-frequency sub band is an edge component or not with reference to peripheral data, in the second low-frequency sub band, of coordinates corresponding to the specific coordinates, and a coring controlling device that controls the coring device not to executes the coring process to the data of the specific coordinates when the judging device judges that the data is an edge component.