Digital Signal Processing Reference
In-Depth Information
the distances from the origin along the real and imaginary axes, respectively. Let
a = 3 and b = 4:
imaginary axis
imaginary axis
z = −a + jb
z = a + jb
2
j
j
1
r
1
r
q
2
q
2
1
real axis
real axis
.
imaginary axis
imaginary axis
j
j
q
q
4
3
real axis
real axis
r
4
r
3
z = a − jb
z = −a − jb
4
3
Figure 1.2: Calculating = arctan(b=a) leads to a problem when a is negative.
p
p
r
1
=
a
2
+ b
2
=
3
2
+ 4
2
= 5
p
p
(a)
2
+ (b)
2
=
(3)
2
+ 4
2
= 5
r
2
=
p
p
r
3
=
(a)
2
+ (b)
2
=
(3)
2
+ (4)
2
= 5
p
p
(a)
2
+ (b)
2
=
(3)
2
+ (4)
2
= 5:
r
4
=
Here are the calculated angles:
