Digital Signal Processing Reference
In-Depth Information
250
1.2
(
a
)
(
b
)
200
1
ringing
150
0.8
100
0.6
50
0.4
0
0.2
-50
-100
0
412
462
512
562
612
0
0.2
0.4
0.6
0.8
1
Index,
k
Normalized Frequency,
F
Normalised Frequency,
F
10
(
c
)
0
-10
-20
-30
-40
-50
-60
-70
-80
0
0.2
0.4
0.6
0.8
1
Normalized Frequency,
F
Normalised Frequency (fc/fN)
Figure 2.1
(a) Impulse response function of (2.2) for
F
c
= 0.4,
N
= 1024. The Fourier Transform of the
impulse response of (a) is shown for (b) linear and (c) logarithmic scales.
unchanged under Fourier transformation. We can manipulate this window so that
the designed filter achieves a range of attenuation levels in the rejection band of
the filter. Moreover, it involves a single step calculation and was chosen for its
relative simplicity and performance.
The discrete Gaussian window is given by
