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Continuous phase modulation
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== Phase trajectory == [[Minimum-shift keying]] (MSK) is another name for CPM with an excess bandwidth of 1/2 and a linear ''phase trajectory''. Although this linear phase trajectory is continuous, it is not ''[[smoothness|smooth]]'' since the derivative of the phase is not continuous. The spectral efficiency of CPM can be further improved by using a smooth phase trajectory. This is typically accomplished by filtering the phase trajectory prior to modulation, commonly using a [[raised cosine]] or a [[Gaussian filter]]. The raised cosine filter has zero crossings offset by exactly one symbol time, and so it can yield a ''full-response'' CPM waveform that prevents [[intersymbol interference]] (ISI).
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