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fft in fpga using polar form

i understand that representing large number of twiddle factors that are req uired in a fft with large number of points is an issue when using fixed poi nt scheme. To my understanding (which could be very wrong as i am new to th is),the issue is large dynamic range that is needed to represent real and i maginary parts of the complex numbers. Would the use of polar form to repre sent them solve this problem, as for all twiddle factors, the absolute valu e will be one and the argument will change from 0 to 360? (or should the ar gument be specified in radians always?)

Reply to
jack.pett.son
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As far as I know, that isn't a problem.

No matter how you do it, you can't have a large dynamic range with the FFT. (Or, even worse usually, the non-fast DFT.) Enough addition and subtraction is done that the dynamic range is pretty much whatever precision the computation is done at.

I don't believe that helps. For the usual twiddle factors, all you need is a small (or big) lookup table. In polar coordinates, with any angular measure, you need to compute sines and cosines at each step.

Well, if all you needed to do was rotations in polar coordinates, then yes. But you also have to add and subtract values at different rotations.

More obvious to me, binary fractions of a whole rotation.

-- glen

Reply to
glen herrmannsfeldt

Which reminds me of a different question I have wondered about for a while:

Why do so few high-level languages provede trigonometric functions in degrees in their math libraries?

The only one I know of is PL/I, not so commonly used these days.

I know the reasons for doing trigonometry in radians, and have no complaint against doing it in radians, but reasonably often it is convenient to do in a unit that is a rational fraction of a whole rotation.

Now, the same arguments against degrees could be used against supplying a log10 function, but many systems do supply that one.

Usually the first thing that non-inverse trigonometric routines do is argument reduction after dividing by some multiple of pi. If one actually wants a nice fraction of a whole circle, it is extra work and precision loss to multiply by some multiple of pi just before the routine divides by a multiple of pi.

-- glen

Reply to
glen herrmannsfeldt

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