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Bandwidth Filters

Instruments used to analyze noise have either constant bandwidth or proportional band- width devices. The constant bandwidth is essentially a tunable narrow band ¯lter with constant bandwidth, w=fu¡f`, wherefuandf`are the upper and lower half-power frequencies. The center frequency of the ¯lter, de¯ned in general as f c=q f uf`(1) is usually variable so that the ¯lter can be swept over the desired frequency range. Band- widths range from a few tens of a hertz to less than a few hundredths of a hertz. The proportional bandwidth instrument consists of a series of relatively broadband ¯lters with upper and lower half-power frequencies satisfying the relationshipfu=f`= constant. Each bandwidth, being proportional to the center frequency, increases with increasing fre- quencies with contiguous bands. Common instruments of this type are theoctave-band¯lter withfu=f`= 2, the1/3-octave-band¯lter withfu=f`= 21=3, and the1/10-octave-band¯lter withfu=f`= 21=10. As an example, let us derive the1/3-octave-band¯lter width in terms of the center frequency. w= (q 2 1 3 ¡1 q 2 1 3 )fc;(2) which gives w= 0:232fc:(3) In many problems, we deal with the power spectral density normalized with respect to != 2¼fc. In this case,

¢!= 0:232(2¼)fc= 0:232!c:(4)

In decibels, this implies that we add

10log10!c¡6:353:

1 Table 2-l Center, lower, and upper frequencies for *-octave bands

Frequency, Hz

Band no.LowerCenterUpper l2 l3 t4 r5 l6 t7 l8 l9 20 2r 22
23
24
25
26
27
28
29
30
3r 32
33
34
35
36
37
38
39
40
4t 42
43
44
45
l6t 20 25
31.5t
40
50
63t
80
100
t25t 160
200
250t
315
400
5001
630
800

1,0001

1,250 1,600

2,0001

2,500

3, 150

4,0001

5,000 6,300

8,0001

10,000

12,500

16,000t

20,000

25,000

3 I,5001

14.0 18.0 22.4I
28.0
35.5
4st 56
7t e0t n2 140
I 80t 224
280
355t
450
560
7 lOt 900
1,120

1,400f

1,800 2,240

2,800f

3,550 4,500

5,6001

7,100 9,000

I 1,200f

14,000

18,000

22,400t

28,000

18.0 22.4t
28.0
35.5
4st 56
7t

90tlt2

r40 I 80t 224
280
3 55t 450
560
7lOt 900
I,120

1,400t

1,800 2,240

2, g00t

3 ,550

4,500

5,6001

7,100 9,000

I 1.200t

14,000

18,000

22,400t

28,000

35,500

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