  Many fluctuating systems consist of macroscopic structures in addition to
noisy signals. Thus, for this class of fluctuating systems, the scaling
behaviors are very complicated. Such phenomena are quite commonly observed in
Nature, ranging from physics, chemistry, geophysics, even to molecular biology
and physiology. In this paper, we take an extensive analytical study on the
``generalized detrended fluctuation analysis'' method. For continuous
fluctuating systems in arbitrary dimensions, we not only derive the explicit
and exact expression of macroscopic structures, but also obtain the exact
relations between the detrended variance functions and the correlation
function. Besides, we undertake a general scaling analysis, applicable for this
class of fluctuating systems in any dimensions. Finally, as an application, we
discuss some important examples in interfacial superroughening phenomena.
