Transfer functions and mobility filters

The effect a filter exerts on a signal is represented by the filter transfer function. For linear systems, the filter output is the product of the transfer function and the filter input (cf. eqn (4.2.14), where Xi( u) is the transfer function). The output signal is high for those parameters for which the transfer function is high and vice versa. For a qualitative 

Although the timescale and the principle of mobility filters are readily outlined in this way, the validity of the representation is limited, because relaxation times depend on the spectral densities of molecular motion at more than one frequency, which is neglected in Fig. 7.1.3. In addition, the spectral densities relevant to NMR of condensed matter 

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