Known N-dimensional filters 100 and methods for N-dimensionally filtering apply noise reduction to an original image pixel. However, carrying out only noise reduction to a pixel of an image is often not enough when a good picture quality is required. Thus, additionally, sharpness enhancement (peaking) is carried out. However, noise reduction and peaking have contrasting spectral behaviors which lead to non-optimal results when both operations, noise reduction and peaking, are implemented in series. By appropriately defining coefficients .alpha.(p, n) or .beta.(p, n) of the transmission function, the transmission function is capable of applying both noise reduction and sharpness enhancement to the input signal of the N-dimensional filter 100.