On the dynamic range of coefficients generated in transform processing of digitised image data

It is well known that the transform operation results in a large expansion of the numerical range of values encountered when input data is subjected to a one- or more dimensional transformation. It is usually assumed that the dynamic range expansion factor is Nc, where N is the transform order and c its dimension, but it is demonstrated here that this result is only true under very restricted conditions, and that, in general, coefficient dynamic range expansion is not only transform dependent, but is often significantly greater than the above value. It is suggested that this effect may influence the transform processing operation in feature extraction and coding applications to a greater degree than has previously been realised.