Difference between direct and indirect synthesizers?

This nomenclature (direct vs. indirect) sound "old".
almost every syntetized generators are "indirect".

Direct:
^^^^^
An array of N fixed frequecncy oscillators (i.e. 1,2,4,8,10,20,40,80,100,200,400,800MHz)
An array of N mixers.
With appropriate switch bank you may get an output freq. from 1 to 1665 MHz with 1 MHz step. Lowest phase noise but expensive and large.

Indirect:
^^^^^^
The PLL are indirect
The minimum step is smaller as the dividing factor is large. Fmax/Fmin depend on VCO and typically is 1 octave. Phase noise is moderately low, in most cases is low enough.

DDS:
^^^^
The waveform of the out signal is "syntetised" point by point.
Extremally low phase noise, but few spuriuos signal near the carrier.
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A short note about stability:
Phase noise (or FM noise) far from the carrier depend on synt. technology. But phase noise close to carrier depend to the frequency standard only (i.e. the Quartz).

In addition:

DIRECT:

Sweep speed limited by the switch speed (tipically us).
Spurious frequencies reduced up to 100 dBc.
high resolution

DDS (I think iy means DIGITAL Synthesizer):

High sweep speed
high resolution
fmax limited by reference frequency
spurious frequencies (due to D/A converter) may be high (50 - 60 dBc)