Sequences and a new code with spectral nulls at rational submultiples of the symbol frequency

Auxiliary pilot tone insertion, used for positioning the servo of magnetic or optical disk recorders, requires codes that give rise to a spectral null at an arbitrary frequency. Sequences with asymetrical runlength constraints containing spectral nulls at rational submultiples of the symbol frequency are investigated. A sufficient condition for spectral nulls at rational submultiples of the symbol frequency is given in terms of a simple runlength requirement. A new code with rate=1/3 is presented with spectral nulls at the normalized symbol frequencies 1/4, 1/2, and 3/4.<>