Digital Signal Processing Reference
In-Depth Information
(a)
0.2
h
()
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
0
5
10
15
20
n
(b)
(c)
1
1.2
H
()
ω
H
()
ω
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
200
400
600
800
1000
0
200
400
600
800
1000
ω
ω
2
π
2
π
(d)
(e)
1.2
1.2
H
()
ω
H
()
ω
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
200
400
600
800
1000
0
200
400
600
800
1000
ωπ
2
ω2
Fig. 6.12 Impulse response (a) and filter frequency characteristics for: b N = 20, f
1
= 50 Hz,
f
2
= 150 Hz, c N = 20, f
1
= 75 Hz, f
2
= 125 Hz, d N = 100, f
1
= 75 Hz, f
2
= 125 Hz, e as d,
with application of Hamming window
6.3.2 Application of Fast Fourier Transform
The method presented here is based on sampling in frequency domain that relies
on substituting for continuous frequency response its samples taken for identical
frequency distance and application to these samples inverse discrete Fourier
transform (DFT) to calculate filter coefficients. To follow the relationship between
the filter coefficients and its spectrum let us assume that the filter coefficients
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