7.2 Lab 4: lab  (Page 4/7)

The length of the FFT is defined as a label K_FFT_SIZE and the bit-reversing algorithm assumes that theinput starts at data memory location _fft_data. To have your code assemble for anN-point FFT, you will have to include the following label definitions in your assembly code.

The FFT provided by TI requires that the input be in normal order, with alternating real and imaginary components. The output will be in bit-reversed order, so bit-reversing needs to be done after the FFT. Bit-reversed addressing is a convenient way toorder input/output $x(n)$ into a FFT so that the output/input $X(k)$ is in sequential order ( i.e. $X(0)$ , $X(1)$ , …, $X(N-1)$ for an $N$ -point FFT). The following table illustrates the bit-reversed order for an eight-point sequence.

The following routine performs the bit-reversed reordering of the FFT output data. The routine assumes that the output isstored in data memory starting at the location labeled _bit_rev_data , which must be aligned to the least power of two greater than the input buffer length, andconsists of alternating real and imaginary parts. Because our input data is going to be purely real in this lab, youwill have to make sure that you set the imaginary parts to zero by zeroing out every other memory location.

As mentioned, in the above code _fft_data is a label indicating the start of the input data and _bit_rev_data is a label indicating the start of a circular buffer where the bit-reversed data will bewritten.

In general, to have a pointer index memory in bit-reversed order, the T0 register needs to be set to one-half the length of the circular buffer; a statement suchas ARx+T0B is used to move the ARx pointer to the next location. For more information regarding the bit-reversed addressing mode, refer to Chapter 6 in the DSP Programmer's Reference Guide . Is it possible to bit-reverse a buffer in place?

C fft routine

A bit-reversing and FFT routine have also been provided in lab4fft.c , listed in Appendix C . Again, make sure you understand how the bit reversal is takingplace. In main.c , the line defining C_FFT must not be commented for use of the C FFT routine. The sine tables (twiddle factors) are located in sinetables.h . This fft requires its inputs in two buffers, the real buffer real and the imaginary buffer imag , and the output is placed in the same buffers.The length of the FFT, N , and logN are defined in lab4.h , which is also listed in Appendix C . When experimenting with the C FFT make sure you modify these length values instead of the onesin the assembly code and main.c !