Python Implementation of Real Sequence

Transform using Half-length Complex FFT

John Bryan

We want to transform a length real sequence using a length complex FFT. The input real sequence is,

| (1) |

The output complex sequence is

- For the even-indexed values:
(6) For the odd-indexed values:

(7) Form a complex sequence of length :

(8) - Calculate
(9) using a length complex FFT

- For :
(10) (11) - For , calculate:
(12) - For the single value :
(13) - For , use symmetry of real transforms:
(14)

- FFT of Pure Real Sequences.
- Hayes, Monson H., Digital Signal Processing.