APPENDIX
B
TABLE OF SINUSOIDAL-INPUT
DESCRIBING FUNCTIONS (DFs)
The DF is given by (cf. Sec. 2.2)
N(A,w) = n,(A,w)
+ jn,(A,w)
=
-
7rA
j %
y(A sin y, Aw cos y)e-'p dy
In this table we employ the "saturation function" (cf. Sec. 2.3) denoted by
fW
=-
1
2
=-(sin-'y+ydl-y3
y < - 1
lylS1
7r
=
1
This function is plotted in Fig. C.1.
Y
TABLE O F S I N U S O I D A L - I N P U T DESCRIBING F U N C T I O N S (DFs) (Continued)
Nonlinearity
Comments
See Fig. B.3 and Sec. 2.3
See Fig. B.3 and Sec. 2.3
25.
y
=
"X
(x 2 0 )
=
-4-x
(x
< 0)
26. Odd square root
y
See Fig. B.3
= x"3
27. Cube root characteristic
b > -2
r(arg.) is the gamma function.
See Sec. 2.3
534
S I N U S O I D A L - I N P U T DESCRIBING F U N C T I O N S
1.4
1.3
1.2
1.1
1 .o
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
Figure B.1
I
2
Quantizer DF.
3
4
5
6
7
8
9
A
-
h
S I N U S O I D A L - I N P U T DESCRIBING F U N C T I O N S
535 6
Figure B.2
DFs for limiter and threshold characteristics.