FFT IP Core: User Guide

ID 683374
Date 11/06/2017
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4.1. Possible Exponent Values

Depending on the length of the FFT/IFFT, the number of passes through the radix engine is known and therefore the range of the exponent is known. The possible values of the exponent are determined by the following equations:

P = ceil{log4N}, where N is the transform length

R = 0 if log2N is even, otherwise R = 1

Single output range = (–3P+R, P+R–4)

Quad output range = (–3P+R+1, P+R–7)

These equations translate to the values in Table A–1.

Table 13.  Exponent Scaling Values for FFT / IFFT      (1)
N P Single Output Engine Quad Output Engine
Max  (2) Min  (2) Max  (2) Min  (2)
64 3 –9 –1 –8 –4
128 4 –11 1 –10 –2
256 4 –12 0 –11 –3
512 5 –14 2 –13 –1
1,024 5 –15 1 –14 –2
2,048 6 –17 3 –16 0
4,096 6 –18 2 –17 –1
8,192 7 –20 4 –19 1
16,384 7 –21 3 –20 0
Note to Table A–1 :
  1. This table lists the range of exponents, which is the number of scale events that occurred internally. For IFFT, the output must be divided by N externally. If more arithmetic operations are performed after this step, the division by N must be performed at the end to prevent loss of precision.
  2. The maximum and minimum values show the number of times the data is shifted. A negative value indicates shifts to the left, while a positive value indicates shifts to the right.