A novel compact on-chip Fourier transform (FT) spectrometer has been proposed based on the silicon-on-insulator (SOI) platform with wide operating bandwidth and high resolution. The spectrometer consists of a 16-channel power splitter and a Mach-Zehnder interferometer (MZI) array of 16 MZIs with linearly increasing optical path length (OPL) difference. We have also developed a spectral retrieval algorithm based on the pattern-coupled sparse Bayesian learning (PCSBL) algorithm and artificial neural network (ANN). The experimental results show that the designed spectrometer has a flat transmission characteristic in the wavelength range between 1500 nm and 1600 nm, indicating that the device has a wide operating bandwidth of 100 nm. In addition, with the assistance of the spectral retrieval algorithm, our spectrometer has the ability to reconstruct narrowband signals with full width at half maximum (FWHM) of 0.5 nm and a triple-peaked signal separated by a 3-nm distance.