OK... found what I think is the first post where I heard the 4x DSP requirement for doubling the sampling rate. It was by John Kotches after talking to Bob Stuart on AVS:

"Shawn,

In talking with JRS, he was saying at least 4x DSP horsepower. You have 2x the operations and 1/2 the window for the operations. Buffering might remain constant as you don't have to buffer as long, so maybe there's a break there and in the DACs smile There has to be a break somewhere in the process, otherwise it's just a vast undertaking.

It's going to be interesting to see what happens next year with HD optical media, I'm not expecting much to happen in 4Q2005. HD-DVD might launch but I think the real fireworks will be in early 2006.

Cheers,"

Good reply expanding on this from Andre Yew:

The computational power depends on the order of complexity of the algorithms used. For some things, there will be a linear increase in computational power, for other things, like convolution algorithms, it will be more like O(n^2) like JRS's example (he may be thinking of room EQ since Gerzon uses that exact analogy in his early room EQ papers). And some will require even more.

Precision requirements will go up by lots, too --- the number of bits in order to accurately compute something --- because the more operations you do, the more temporary accumulation space you need. For example, addition of 2 n-bit numbers requires n+1 bits to store the result. Multiplication requires 2*n. Since you don't want to truncate to the DAC's output resolution until all your computations are done in order to maintain highest accuracy and lowest noise, you need to be able to to hold the internal result accurately until truncation. If you have a 10-tap FIR filter (which is rather small by audio standards), each sample undergoes 10 additions and 10 multplications. For a naive algorithm, that requires a little more than 2*10*n, or 20*n bits. For 32-bit integers, that's over 640 bits per sample. No one does it this way, as there is always truncation at each stage, but some algorithms are highly sensitive to small precision changes, so you have to maintain some amount of extra precision. Meridian seems to do it with 48 bits, and I don't know what Lexicon does. I know audio research people, like the AAC and MP3 people, have found that sometimes many dozens of bits are necessary.

This is the secret cost of high sample rates that no one talks about. Some things become significantly more difficult to do correctly with high sample rates. Any company claiming indefinite future compatibility had better be prepared to show you how they'll significantly increase their computational power.

--Andre

Shawn

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