Spectral purity of direct digital frequency synthesizers

A short introduction to the problems of frequency synthesis is given. Mathematical models suitable for direct digital frequency synthesizers (DDFS) which provide quasi-periodic omission of clock pulses such as continued fraction expansion, modified Engel series expansion, and modulo-N arithmetic are investigated. It is shown that in these instances the peaks of the phase-time modulation function do not exceed one clock period. Using the Fourier series algorithm all spurious signals in the output wave can be found. However, the procedure might be lengthy. Pulse train, square wave, and sine wave outputs are discussed.<
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