Apparatus and methods for performing a Fourier transform mechanically, using an array of one or more resonators. By tuning the resonators so that their natural frequencies correspond to harmonics of an input signal, the vibration of the resonators in response to the input signal may be measured to provide phase and amplitude information that is equivalent to the Fourier coefficients of the input signal. Preferably, the resonators are microelectromechanical (MEMS) resonators. Using MEMS resonators, the Fourier transform of a signal can be determined using substantially less power than would be consumed by a digital signal processor (DSP) or microprocessor performing similar calculations. MEMS resonator-based apparatus and methods according to various embodiments may be used for applications including compression and image processing.