>> Given 1983 technology, it was very difficult to implement digital audio filters, which require millions of multiplication/accumulation operations a second.

> This seems high? A second-order digital filter requires what, about 4 stores, recalls, and multiplies per sample? This would seem to be in the same level of complexity as six carrier/modulator interactions; you have to do a multiply to do a lookup after all. Or is the issue that the multiplies had to be 12-16 bit?

For microprocessors in 1983, multiply instructions, if they existed at all, involved a lot of shift and add cycles. That took a long time.

A simple filter might need 4 multiplies and accumulates. Times 44,000 times a second, for each sample. Times the number of voices; 16 in the case of the DX7.

Now you are easily over a million multiplies a second.

And even though the original DX7 is 12 bits, I think you'd need those multiplies to be 16x16 bits for accumulated error issues.

So the DX7 was an alternative to having to implement digital filters in 1983 technology. They could introduce a digital synth at a very reasonable price.