Spectral null codes

The servo position information of magnetic tape or disk recorders is often recorded as low-frequency components usually called pilot tracking tones. Binary codes giving rise to a spectral null at an arbitrary frequency are used to provide space for the allocation of auxiliary pilot tones. Here, encoding methods are treated in which binary data are mapped into constrained binary sequences for shaping the spectrum. The rate and power spectral density function of memoryless codes that exhibit spectral nulls are computed. The relationship between the code redundancy and spectral notch width is quantified with a parameter called the sum variance. It is found that twice the product of the spectral notch width times the sum variance is approximately unity