vDSP_fft_zrip understanding the transformed DSPSplitComplex content

Question

Assuming "A" is a real vector packed (with vDSP_ctoz) in the proper way, doing:

vDSP_fft_zrip(setupReal, &A, 1, FFT_LENGTH_LOG2, FFT_FORWARD);

Will transform my real content to it's frequency representation.

What do then the following values represents ?:

A.realp[0];
A.imagp[0];

A.realp[i];
A.imagp[i];

A.realp[N-1];
A.imagp[N-1];

Actually I'm wondering where is the DC and Nyquist components stored. Also is the A.imagp[j] the imaginary part of A.realp[j] ?

Answer 1

Let H be the vector that is the mathematical result of the FFT, so that H_k is the k^th element of the vector. H₀ is the DC component, and H_N/2 is the Nyquist component. Then:

A.realp[0] contains H₀.

A.imagp[0] contains H_N/2.

For 0 < k < N/2, A.realp[k] and A.imagp[k] combined contain H_k. Specifically, A.realp[k] contains the real part of H_k, and A.imagp[k] contains the imaginary part of H_k. Equivalently, H_k = A.realp[k] + i • A.imagp[k].

Some documentation about the vDSP FFTs is here.