Parametrically Enabled Relaxation FIlters with Double and multiple Inversion (PERFIDI) is an experimental NMR/MRI technique devised to analyze samples/voxels characterized by multi-exponential longitudinal relaxation. It is based on a linear combination of NMR sequences with suitable preambles composed of inversion pulses. Given any standard NMR/MRI sequence, it permits one to modify it in a way which will attenuate, in a predictable manner and before data acquisition, signals arising from components with different r rates (r=1/T1). Consequently, it is possible to define relatively simple protocols to suppress and/or to quantify signals of different components. This article describes a simple way to construct low-pass, high-pass and band-pass PERFIDI filters. Experimental data are presented in which the method has been used to separate fat and water proton signals. We also present a novel protocol for very fast determination of the ratio between the fat signal and the total signal which avoids any time-consuming magnetization recovery multi-array data acquisition. The method has been validated also for MRI, producing well T1-contrasted images.