Fast Fourier Transform - Signal Processing of Random Physiological Signals - page 152

0 0

It should be noted that only W → W needs to be calculated for the first

8 8

stage.

13.6.2 Second-Stage Calculations

H

G

1

H

G 2

H

G 3

H

G 4

0

G 1 = H 1 + W

8 H 3 =

(0 + j × 0) + (1 + j × 0)(0 + j × 0) = 0 + j × 0

0

G 2 = H 2 + W H 4 = (2 + j × 0) + (1 + j × 0)(0 + j × 0) = 2 + j × 0

8

0

G 3 = H 1 − W H 3 = (0 + j × 0) − (1 + j × 0)(0 + j × 0) = 0 + j × 0

8

0

G 4 = H 2 − W H 4 = (2 + j × 0) − (1 + j × 0)(0 + j × 0) = 2 + j × 0

8

H G

H G

H G

H G

0

G 5 = H 5 + W

8 H 7

= (0 + j × 0) + (1 + j × 0)(0 + j × 0) = 0 + j × 0

0

= + = (1 . 414 + × 0) + (1 + × 0)( − 1 . 414 + × 0)

G 6 H 6 W

8 H 8

j j j

= 1 . 414 − j × 1 . 414

0

G 7 = H 5 − W

8 H 7 =

(0 + j × 0) − (1 + j × 0)(0 + j × 0) = 0 + j × 0

0

G 8 = H 6 − W

8 H 8 =

(1 . 414 + j × 0) − (1 + j × 0)( − 1 . 414 + j × 0)

= 1 . 414 + j × 1 . 414