The n sequence is obtained by a simple modification of the PRBS. This consists of changing the sign of every other bit in the PRBS. The modifica­tion of a PRBS with Z bits (Z always odd) gives an n sequence with 2Z bits. For example, a seven-bit PRBS and the corresponding 14-bit n sequence are shown in Fig. 3.6. The power spectrum for a Z-bit n sequence is given by

7-bit PRBS

The power spectrum of the 14-bit n sequence is shown in Fig. 3.7. The n sequence may be generated by a PRBS generator with additional components added to accomplish the bit inversion.

The autocorrelation function of a general n sequence is shown in Fig. 3.8. From these results we can deduce the following:

1. The autocorrelation function has a large positive spike at 0, T, 2T,… and a large negative spike at T/2, ЗТ/2, 5T/2,… , with a string of smaller spikes between the large spikes. As the number of bits increases, the large

spikes become sharper and the small spikes become smaller. Thus the auto­correlation function looks more like a series of delta functions with alternating signs every half period as the number of bits increases.

2. The power spectrum becomes flatter as the number of bits increases, as with the PRBS.

3. The absolute magnitude of the harmonics decreases as the number of bits increases, as with the PRBS. Since the shape of the power spectrum is the same as for the PRBS, the same bandwidth relations apply (Eqs. 3.1.4-3.1.7).

4. The n sequence is antisymmetric (and thereby discriminates against nonlinear effects).