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This theoretical modeling and simulation paper presents designs and projected performance of an on-chip digital Fourier transform spectrometer using a thermo-optical (TO) Michelson grating interferometer operating at∼1550 and 2000 nm for silicon-on-insulator and for germanium-on-silicon technological platforms, respectively. The Michelson interferometer arms consist of two unbalanced tunable optical delay lines operating in the reflection mode. They are comprised of a cascade connection of waveguide Bragg grating resonators (WBGRs) separated by a piece of straight waveguide with lengths designed according to the spectrometer resolution requirements. The length of eachWBGRis chosen according to the Butterworth filter technique to provide one resonant spectral profile with a bandwidth twice that of the spectrometer bandwidth. A selectable optical path difference (OPD) between the arms is obtained by shifting the notch in the reflectivity spectrum along the wavelength axis by means of a low-power TO heater stripe atop the WBGR, inducing an OPD that depends on the line position of the WBGR affected by TO switching.We examined the device performances in terms of signal recostruction in the radio-frequency (RF) spectrum analysis application at 1 GHz and at 1.5 GHz of spectrometer resolution. The investigation demonstrated that high-quality spectrum reconstruction is obtained for both Lorentzian and arbitrary input signals with a bandwidth up to 40 GHz. We also show that spectrum reconstruction of 100–200 GHz RF band input signals is feasible in the Ge-on-Si chips.