he transitions in the data become progressively less sharp as the level of filtering is increased and the bandwidth reduced. To overcome this a form of modulation known as Gaussian filtered minimum shift keying (GMSK) is widely used, and has, for example, been adopted for the GSM standard for mobile telecommunications It is derived from a modulation scheme known as minimum shift keying (MSK) which is what is known as a continuous phase scheme. Here there are no phase discontinuities because the frequency changes occur at the carrier zero crossing points. To illustrate this take the example shown in Figure 3.11. Here it can be seen that the modulating data signal changes the frequency of the signal and there are no phase discontinuities. This arises as a result of the unique factor of MSK that the frequency difference between the logical one and logical zero states is always equal to half the data rate. This can be expressed in terms of the modulation index, and it is always equal to 0.5. signal Figure 3.11 An example of an MSK signal While this method appears to be fine, it is found that the bandwidth occupied by an MSK signal is too wide for many systems where a maximum bandwidth equal to the data rate is required. A plot of the spectrum of an MSK signal shows sidebands extending well beyond a bandwidth equal to the data rate. This can be reduced by passing the modulating signal through a low-pass filter prior to applying it to the carrier. The requirements for the filter are that it should have a sharp cutoff, narrow bandwidth and its impulse response should show no overshoot. The ideal filter is known as a Gaussian filter which has a Gaussian-shaped response to an impulse and no ringing. 66 Newnes Guide to Radio and Communications Technology GMSK (BT=0.5) Frequency/Bit rate offset from carrier Figure 3.12 Graph of the spectral density for MSK and GMSK signals There are two main ways in which GMSK can be generated. The most obvious is to apply the digital modulating signal filtered by a Gaussian filter and then