Digital Signal Processing Reference
In-Depth Information
2
0
−2
0
50
100
150
200
(a) Sample
2
0
−2
0
50
100
150
200
(b) Sample
Figure 2.14:
(a) The real part of a complex exponential series having one cycle per eight samples, growing
in amplitude by a factor of 1.5 per cycle; (b) The imaginary part of a complex exponential series having
one cycle per eight samples, growing in amplitude by a factor of 1.5 per cycle.
Figure 2.15 shows the result from making the call
LVPowerSeriesEquiv(0.9,3,32)
As a final illustration, we generate 2 cycles of a unity-amplitude cosine over 8 samples, using
complex exponentials as follows
real(exp(j*2*pi*2*(0:1:7)/8))
and then compute the same complex exponential using the Euler identity
cos
(θ)
=
(e
jθ
+
e
−
jθ
)/
2
for which a suitable call would be
(exp(j*2*pi*2*(0:1:7)/8) + exp(-j*2*pi*2*(0:1:7)/8) )/2
