A method and an apparatus are provided for mitigating spectral lines in a wireless signal. First a code word is generated that is made up of a plurality of binary or ternary encoded pulses. Then a plurality of code-word-modulated wavelets are generated in response to the code word. These wavelets can be Gaussian monopulses, repeated cycles of a sine wave, or other shaped impulse signals. The plurality of code-word-modulated wavelets are then modulated with a bit of transmit data to form a plurality of data-modulated wavelets. This modulation serves to whiten the signals since the transmit data is effectively random. Finally, the plurality of data-modulated wavelets are transmitted to a remote device.