Engineering Acoustics. Malcolm J. Crocker

Figure 1.10 Typical frequency response of a filter of center frequency f_C and upper and lower cutoff frequencies, f_U and f_L.

      In constant bandwidth filters, the bandwidth Δf = f_U − f_L is kept constant regardless of the setting of the filter center frequency.

      The constant percentage filter (usually one‐octave or one‐third‐octave band types) most parallels the way the human auditory system analyzes sound and, although digital processing has mostly overtaken analog processing of signals, it is still frequently used. The human audible range is spanned by just a few octaves, so octave analysis produces a relatively coarse classification. Resolution can be improved by breaking each octave band into fractional‐octave bands, which preserves the logarithmic band spacing. Thus, if the frequency scale is divided into contiguous frequency bands, the ratio f_U/f_L is the same for each band. The center frequency f_C for each band is defined as the geometric mean which is in the middle between f_L and f_U on a logarithmic frequency scale and is always less than the arithmetic average. Thus, the ratio of center frequencies of contiguous bands is the same as f_U/f_L for any one band. Octave and third‐octave band filters are widely used, in particular for acoustical measurements [12].

       a) One‐Octave Bands

      For one‐octave bands, the cutoff frequencies f_L and f_U are defined as follows:

      The center frequency (or geometric mean) is . Thus f_U/f_L = 2.

      The bandwidth Δf is given by

      so Δf ≈ 70% (f_C).

       b) One‐Third‐Octave Bands

      For one‐third‐octave bands, the cutoff frequencies, f_L and f_U, are defined as follows:

      The center frequency (geometric mean) is given by . Thus f_U/f_L = 2^1/3.

      The bandwidth Δf is given by

      so Δf ≈ 23% (f_C).

We thus see clearly why the filter bands we have just discussed are called constant percentage. This is because the bandwidth is a constant percentage of the filter center frequency f_C. Of course, the filter bandwidth does not have to be defined in terms of a fraction of an octave but can be defined simply in terms of the percentage of the center frequency. Since it is impracticable to make measurements at a large number of fixed frequencies, noise measurements are made at a selected number of standardized frequencies called preferred center frequencies. Standard one-octave and one-third-octave band specifications take advantage of the fact that 2^10/3 ≈ 10. The ISO recommendation values for preferred center frequencies are given in Table 1.1 [15]. Specifications for octave‐band and fractional‐octave‐band filters are defined by the IEC 1260:1995 and the ANSI S1.11:2004 standards [16, 17].

Table 1.1 Preferred center frequencies for noise measurements according to ISO R 266 [15].

Preferredfrequencies, Hz	1/1oct.	1/3oct.	Preferredfrequencies, Hz	1/1oct.	1/3oct.	Preferredfrequencies, Hz	1/1oct.	1/3oct.
16	×	×	200		×	2500		×
20		×	250	×	×	3150		×
25		×	315		×	4000	×	×
31.5	×	×	400		×	5000		×
40		×	500	×	×	6300		×
50		×	630		×	8000	×	×
63	×	×	800		×	10 000		×
80		×	1000	×	Скачать книгу В начало < 20 21 22 23 24 25 26 27 28 29 > В конец e-mail: [email protected]