米6体育平台手机版

SPRACN4 August 2019 66AK2G12 , 66AK2H06 , 66AK2H12 , 66AK2H14 , OMAP-L132 , OMAP-L138 , TMS320C6452 , TMS320C6454 , TMS320C6455 , TMS320C6457 , TMS320C6652 , TMS320C6654 , TMS320C6655 , TMS320C6657 , TMS320C6672 , TMS320C6674 , TMS320C6678 , TMS320C6742 , TMS320C6743 , TMS320C6745 , TMS320C6746 , TMS320C6747 , TMS320C6748

Using DSPLIB FFT Implementation for Real Input and Without Data Scaling

1.3 Returning to a Length N Real Sequence Using a Length N/2 Complex IFFT

Let G(k) be a N-point complex valued sequence derived from a real-valued sequence g(n). You want to get back g(n) = IFFT{G(k)}. However, you want to do this with an N/2-point IFFT. This can be accomplished using the following procedure:

X_r(k) = G_r(k)IA_r(k) – G_i(k)IA_i(k) + G_r(N/2–k)IB_r(k) + G_i(N/2–k)IB_i(k), for k = 0, 1, ..., N/2–1 and G(N/2) = G(0)
X_i(k) = G_i(k)IA_r(k) + G_r(k)IA_i(k) + G_r(N/2–k)IB_i(k) – G_i(N/2–k)IB_r(k)

Find X(k) using the above equations.
Compute the N/2-point inverse FFT of X(k) to get x(n) = x1(n) + jx2(n). Note that the IFFT should be performed with bit reversal.
Get g(n) from x(n) using the following equations:

g(2n) = x₁(n), for n = 0, 1, ..., N/2–1
g(2n+1) = x₂(n)

The above equations look similar to those used in our forward FFT computation. However, the pre-computed coefficients are slightly different. The following C code can be used to initialize IA(k) and IB(k), again, even indices contains the real part and odd indices contain the imaginary part.

for (i = 0; i < N/2; i++)
{
  IA[2 * i]     = 0.5 * (1.0 - sin (2 * PI / (double) (2 * N) * (double) i));
  IA[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * N) * (double) i));
  IB[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * N) * (double) i));
  IB[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * N) * (double) i));
}

Note that IA(k) is the complex conjugate of A(k) and IB(k) is the complex conjugate of B(k).