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I can assume therefore that for a signal with random values on both sides of zero the issue of dc bias is absorbed and the two algorithms become equivalent.
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They're never quite the same, since the average of the positive values and the average of the negative values would be different for the two rounding methods.
As to how you'd show that has an effect on signals, lets see if I can think of a scheme where it would have an effect ... Ah, I have one ...
Consider the power in a series of random numbers rounded using round() versus convergent(). Given samples x[n], the power is an average of x[n]^2, or the square-root of this (if you want RMS). Since round() causes a slight bias in the positive and negative values, you should get a slight bias in the power measurement.
So, round() and convergent() would give different power estimates ... but is the difference large enough to matter? It would depend on the variance of your power estimate; if you averaged for long enough (small variance), then yes the difference would matter.
Cheers,
Dave
Honored Contributor
