Two essential elements of a seeded FEL based on the echo-enabled harmonic generation (EEHG) are the undulator-modulators, in which a laser beam modulates the beam energy. We study how the interaction of electrons in these undulators changes the noise properties of the beam. This paper is based on the method of noise analysis developed in SLAC-PUB-14225 and extends it for the case of EEHG.