FFT IP Core: User Guide

ID 683374
Date 11/06/2017
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3.4.2.3. I/O Order

The input order allows you to select the order in which you feed the samples to the FFT.
Table 7.  Input Order
Order Description
Natural order The FFT requires the order of the input samples to be sequential (1, 2 …, n – 1, n) where n is the size of the current transform.
Digit Reverse Order The FFT requires the input samples to be in digit-reversed order.
–N/2 to N/2 The FFT requires the input samples to be in the order –N/2 to (N/2) – 1 (also known as DC-centered order)

Similarly the output order specifies the order in which the FFT generates the output. Whether you can select Bit Reverse Order or Digit Reverse Order depends on your Data Representation (Fixed Point or Floating Point). If you select Fixed Point, the FFT variation implements the radix-22 algorithm and the reverse I/O order option is Bit Reverse Order. If you select Floating Point, the FFT variation implements the mixed radix-4/2 algorithm and the reverse I/O order option is Digit Reverse Order.

For sample digit-reversed order, if n is a power of four, the order is radix-4 digit-reversed order, in which two-bit digits in the sample number are units in the reverse ordering. For example, if n = 16, sample number 4 becomes the second sample in the sample stream (by reversal of the digits in 0001, the location in the sample stream, to 0100). However, in mixed radix-4/2 algorithm, n need not be a power of four. If n is not a power of four, the two-bit digits are grouped from the least significant bit, and the most significant bit becomes the least significant bit in the digit-reversed order. For example, if n = 32, the sample number 18 (10010) in the natural ordering becomes sample number 17 (10001) in the digit-reversed order.