1. If I had a SACD player that can output DSD and it is hooked up via analog output to the input of an amplifier would I be getting the full quality of DSD?
1. If you are using the analog output, you are not getting DSD output.
2. Not necessarily. Just as the analog output can convey DSD after decoding to analog, HDMI can also output DSD as PCM. This is more common than sending DSD.
The long answer: it depends...
If the player's DAC is DSD capable (which can accept DSD signal) then a direct DSD to analogue conversion should normally retain the full quality of the DSD. This is in essence the reverse of a direct analogue-DSD recording in the simplest form.
Note many SACDs aren't original DSD recordings and you can't do bass management with direct DSD-analogue conversion. Even if you send DSD to the processor it often goes through PCM intermediate steps (and you rarely know what happens inside). And DSD recordings are edited via PCM (high sample rate) so very rarely you're getting a pure untouched DSD 'as is'.
If DSD is converted to PCM it needs decimation filter which might result in downsampling. Then PCM usually goes through an oversampling filter in the DAC. Whether you can hear any difference between DSD and PCM is debatable.
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