Studio delle prestazioni di un sistema a fosfori per mammografia ...

space. Since Û is almost always much greater than the width of the presampling LSF, one can
usually approximate Û×�Ò ÙÛ as Æ Ù . The ÇÌ���� then simplifies to:
ÇÌ���� Ù � � ÇÌ�ÔÖ� Ù £ ÁÁÁ Ù� �
(2.20)
The MTF is defined for analog systems as �ÇÌ� �. As long as there is no aliasing from
undersampling, the same definition can also be applied to digital systems without alteration.
However, when a digital system is undersampled, two conceptual difficulties arise: the digital
MTF no longer describes the amplitude of a single frequency passed by the system (see Fig. 2.2)
and it is phase dependent, and therefore not spatially invariant as required for the stationarity
property of the linear system definition of MTF.
The difficulties arising from the first item can be explained considering that two working
definition of MTF exist. The MTF can be measured as the response of a system to a delta
function:
ÅÌ���� Ù � �ÇÌ���� Ù �
�ÇÌ����
�
(2.21)
i.e. the MTF is defined as the frequency output of a system when an input consisting of uniform
frequency content is present. On the other side the MTF can be measured as the amplitude
modification of a single sinusoid passed by a system:
ÅÌ� ��� Ù � ��Ì��� Ù �
��Ì�Ò Ù �
(2.22)
where �Ì�Ò and �Ì��� are the amplitudes of the sinusoid before and after sampling. These
two working definitions of MTF are equivalent for analog systems and for digital systems at
frequencies unaffected by aliasing (see for instance Fig. 2.2 (a) and (b)). However the two def-
initions do not agree in undersampled digital systems for frequencies where aliasing causes an
overlap of adjacent MTF replications. In summary, the amplitude response of an undersampled
digital system to a single sinusoid contains replicated but not overlapped values, and is equal to
ÅÌ�ÔÖ�. The standard definition of ÅÌ����, on the other hand, is the response of a system to a
delta function input, and contains overlapped values if undersampled. The second item relates to
the fact that ÅÌ���� depends on the phase relation of the sampling comb function with respect
to the function being digitized, when aliasing occurs [12]. This effect is described in Fig. 2.3,
where the ÅÌ�ÔÖ� response of the system to a Æ function is shown. If the sampling comb is
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