cfft

Overflow Handling Methodology If scale==1, scaling before each stage is implemented for overflow prevention

Special Requirements

-This function requires the inclusion of file “twiddle.inc” which contains the twiddle table (automatically included).

cfft

-Data memory alignment (reference cfft.cmd in examples/cfft directory):

J Alignment of input database address: (n+1) LSBs must be zeros, where n = log2(nx).

J Ensure that the entire array fits within a 64K boundary (the largest possible array addressable by the 16-bit auxiliary register).

J For best performance the data buffer has to be in a DARAM block.

J If the twiddle table and the data buffer are in the same block then the radix-2 kernal is 7 cycles and the radix-4 kernel is not affected.

Implementation Notes

-Radix-2 DIF version of the FFT algorithm is implemented. The implementation is optimized for MIPS, not for code size. The first stage is unrolled and the last two stages are implemented in radix-4, for MIPS optimization.

-This routine prevents overflow by scaling by 2 before each FFT stage, assuming that the parameter scale is set to 1.

Benchmarks (preliminary)

-5 cycles (radix-2 butterfly – used in both scaled and non-scaled versions)

-10 cycles (radix-4 butterfly – used in non-scaled version)

CFFT – SCALE

†Assumes all data is in on-chip dual-access RAM and that there is no bus conflict due to twiddle table reads and instruction fetches (provided linker command file reflects those conditions).

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cfir

cfir

dbuffer[2*nh + 2] Pointer to delay buffer of length nh =2 * nh + 2

Overflow Handling Methodology No scaling implemented for overflow prevention.

Special Requirements nh must be a minimum value of 3. For smaller filters, zero pad the h[] array.

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cfir

Implementation Notes The first element in the dbuffer array is present only for alignment purposes. The second element in this array (index=0) is the entry index for the input history. It is treated as an unsigned 16-bit value by the function even though it has been declared as signed in C. The value of the entry index is equal to the index – 1 of the oldest input entry in the array. The remaining elements make up the input history. Figure 4–1 shows the array in memory with an entry index of 2. The newest entry in the dbuffer is denoted by x(j–0), which in this case would occupy index = 3 in the array. The next newest entry is x(j–1), and so on. It is assumed that all x() entries were placed into the array by the previous invocation of the function in a multiple-buffering scheme.

Figure 4–1, Figure 4–2, and Figure 4–3 show the dbuffer, x, and r arrays as they appear in memory.

Figure 4–1. dbuffer Array in Memory at Time j

cfir

Figure 4–2. x Array in Memory

xi(0)

xr(1)

xi(1)

•

•

•

xr(nx–2)

xi(nx–2)

xr(nx–1)

Figure 4–3. r Array in Memory

†Assumes all data is in on-chip dual-access RAM and that there is no bus conflict due to twiddle table reads and instruction fetches (provided linker command file reflects those conditions).

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