Output gain adjuster of digital filters

I haven't heard this myself. I would think that any error is simply quantization (round-off error), i.e. it wouldn't exist if implemented with infinite-precision arithmetic and isn't intrinsic to the DF I. But some filter forms do fair better than others in terms of numerical issues such as round-off, so it is possible that one implementation might be "better" than another, even though they are theoretically equivalent. (In actuality, they are only equivalent if implemented with infinite-precision arithmetic.)

Is your FPGA filter doing floating-point? I'm curious, as that seems pretty uncommon in the FPGA world.

"In theory, theory and practice are identical. But in practice, they are not!"

Seems to be tough demands. You are playing with deviations in the 7th-9th significant digit, which is on the order of the numerical accuracy of single precision floating-point numbers.

Assuming you use single precision floats: No, this is not true. Numerical inaccuracies on this scale occur, no matter what filter structure you use.

One difference between type i and type 2 filters, is that one is more robust with respect to numerical noise than the other. However, I find it hard to believe that a gain adjustement is used in order to correct for deviations on the scale indicated above.

It may be that the magnitudes of internal variables are different, so that the gain needs to be adjusted in order to prevent overflow in fixed-point arithmetics implementations.

Rune

...

How many dB error is that? Do you care? How many significant bits in your calculation?

Jerry

Steve

A meter was originally defined as 1/10,000,000th of the length of the quadrant between the North Pole and the equator passing through Paris. The currently defined meter is very close to that. Roger Bourne's error is the same as a one-meter error in the measured circumference of our planet. Pretty good mensuration, by most standards.

Jerry