Frequency occupation of a digital bitstream

We represent a digital bitstream as a serial flow of zero's and one's. The bit speed, i.e. the number of bits per second is expressed in the unit Baud.
This way of chaining zeros and ones is called Non Return to Zero (NRZ). The bandwidth of a signal like this is theoretically spoken infinity, because the sudden changes, the steep edges between zero's and one's, contain many and very high harmonics. The amplitude (strength) of these harmonics decreases just slowly when we look into the area of higher frequencies. That is the reason that we can't give a clear judgement on which is the highest frequency in such a signal.


This is changing when we suppress the quite useless higher harmonic frequencies by filtering the signal. This can be done by an analogue low-pass filter.
If we do this in the correct way we may expect a result that looks like this on an oscilloscope screen:
na low-pass filter
In principle we haven't lost any information, because everything above the dashed line represents a one and everything below it a zero. Now the steep edges are replaced by parts of a sine wave (to be precise: a cosine wave), and a sine wave has no harmonics.

Highest frequency

We see the highest frequency occuring when we see a 010101....-pattern happening.

Its frequency is 0,5 times the number of bits per second, because two bits together form one period of a sine wave. The low-pass filter has to pass this frequency unattenuated. Practically such filters are designed having a a cut-off frequency of 20% higher, so they suppress all higher frequencies. The highest frequency in the filtered signal then becomes 0,6 times the number of bits/second.

Is there then still something in between 0,5 and 0,6 times the bit-frequency? Yes indeed, because lower fundamental frequencies, generated by bit patterns like 1111111000000011111110000000 remain a square wave, although with rounded edges, and they can still have harmonics in that part of the frequency band. And we need them to ensure nice and gradual conversions from a straight line to a cosine and reverse.