ruwan2
Member level 5
Hi,
I am reading an article on FFT implementation in FPGA. I do not understand its description on roots factorization. The paragraph is:
"Figure 13.14 shows how the roots to the left and right of the imaginary (Im) axis and the roots above and below the real (Re) axis are mirrored. The angle q of roots 1, -j -1 and j follow as 2pi/(N/4). Factoring out -j, -1 and j from the roots in the third, second and first quadrants, respectively, means that the remaining factors of these roots lie solely in the fourth 1 quadrant. If the roots are then grouped with a periodicity of sita=2pi/(N/4), an extremely efficient factorization of the transform matrix is obtained."
Figure 13.14 shows 16 roots on unit circle. Thus, N=16 for this example. I don't understand the last part, which is italic and underscored. What is "the fourth 1 quadrant"?
"If the roots are then grouped with a periodicity of sita=2pi/(N/4)," means the (16-3=13) roots (after removing -j, -1, j)? It is not periodic for a number 13. Could you explain it to me?
Thanks
I am reading an article on FFT implementation in FPGA. I do not understand its description on roots factorization. The paragraph is:
"Figure 13.14 shows how the roots to the left and right of the imaginary (Im) axis and the roots above and below the real (Re) axis are mirrored. The angle q of roots 1, -j -1 and j follow as 2pi/(N/4). Factoring out -j, -1 and j from the roots in the third, second and first quadrants, respectively, means that the remaining factors of these roots lie solely in the fourth 1 quadrant. If the roots are then grouped with a periodicity of sita=2pi/(N/4), an extremely efficient factorization of the transform matrix is obtained."
Figure 13.14 shows 16 roots on unit circle. Thus, N=16 for this example. I don't understand the last part, which is italic and underscored. What is "the fourth 1 quadrant"?
"If the roots are then grouped with a periodicity of sita=2pi/(N/4)," means the (16-3=13) roots (after removing -j, -1, j)? It is not periodic for a number 13. Could you explain it to me?
Thanks