We present the design of a spin-wave-based microwave signal processing device. The microwave signal is first converted into spin-wave excitations, which propagate in a patterned magnetic thin-film. An interference pattern is formed in the film and its intensity distribution at appropriate read-out locations gives the spectral decomposition of the signal. We use analytic calculations and micromagnetic simulations to verify and to analyze the operation of the device. The results suggest that all performance figures of this magnetoelectric device at room temperature (speed, area, power consumption) may be significantly better than what is achievable in a purely electrical system. We envision that a new class of low-power, high-speed, special-purpose signal processors can be realized by spin-waves.