A signal processor for processing a receiving signal having a first usable frequency band and a second usable frequency band includes a first mixer for mixing the receiving signal with a first local oscillator signal, wherein a frequency of the first local oscillator signal is asymmetrical between the first usable frequency band and the second usable frequency band. The first mixer is implemented to obtain an in-phase signal and a quadrature signal, having a first signal portion representing a mixed image of the first usable frequency band, and having a second signal portion representing a mixed image of the second usable frequency band. The signal processor comprises a second mixer) for mixing the in-phase signal and the quadrature signal by using the second local oscillator signal. A frequency of the second local oscillator signal is selected such that the mixed image of the first usable frequency band and the mixed image of the second usable frequency band are at least partly image bands of each other with regard to the second local oscillator signal. The second mixer is implemented to separately provide information content of the first usable frequency band and the second usable frequency band at its output, for obtaining a first output signal, which substantially comprises information content of the first usable frequency band, and for obtaining a second output signal which substantially comprises information content of the second usable frequency band.