In this paper, we investigate novel low-dimensional and model-free representations for multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) data. We depart from the classical definition of the phasor in the complex plane to propose the extended output phasor (EOP) and extended phasor (EP) for multi-spectral information. The frequency domain properties of the EOP and EP are analytically studied based on a multiexponential model for the impulse response of the imaged tissue. For practical implementations, the EOP is more appealing since there is no need to perform deconvolution of the instrument response from the measured m- FLIM data, as in the case of EP. Our synthetic and experimental evaluations with m-FLIM datasets of human coronary atherosclerotic plaques show that low frequency indexes have to be employed for a distinctive representation of the EOP and EP, and to reduce noise distortion. The tissue classification of the m-FLIM datasets by EOP and EP also improves with low frequency indexes, and does not present significant differences by using either phasor.