Texas Instruments TMS320C64X manual LogN

DSP_fft16x16t

Special Requirements

-In-place computation is not allowed.

-The size of the FFT, nx, must be power of 2 or 4, and 16 ≤ nx ≤ 32768.

-The arrays for the complex input data x[ ], complex output data y[ ], and twiddle factors w[ ] must be double-word aligned.

-The input and output data are complex, with the real/imaginary components stored in adjacent locations in the array. The real components are stored at even array indices, and the imaginary components are stored at odd array indices. All data are in short precision or Q.15 format.

-The FFT coefficients (twiddle factors) are generated using the program tw_fft16x16 provided in the directory ‘support\fft’. The scale factor must be 32767.5. No scaling is done with the function; thus, the input data must be scaled by 2log2(nx) to completely prevent overflow.

Implementation Notes

-Bank Conflicts: nx/8 bank conflicts occur.

-Interruptibility: The code is interrupt-tolerant but not interruptible.

The routine uses log4(nx) − 1 stages of radix-4 transform and performs either a radix-2 or radix-4 transform on the last stage depending on nx. If nx is a power of 4, then this last stage is also a radix-4 transform, otherwise it is a radix-2 transform. The conventional Cooley Tukey FFT is written using three loops. The outermost loop “k” cycles through the stages. There are log N to the base 4 stages in all. The loop “j” cycles through the groups of butterflies with different twiddle factors, and loop “i” reuses the twiddle factors for the different butterflies within a stage. Note the following:

		Butterflies With Common
Stage	Groups	Twiddle Factors	Groups*Butterflies
1	N/4	1	N/4
2	N/16	4	N/4
..	..	..	..
logN	1	N/4	N/4

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