THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

9.11 Noise Measurement in Selected Frequency Bands, Band Pass Filters 191Figure 9.13. (a) Circuit for a single, low-pass filter and (b) frequency response of thelow-pass filter.Equation (9.9) becomes∣ H ′ (ω) ∣ ∣ ≈−20 log 1 = 0 for (ωRC ) 2 ≪ 1that is, for relatively small frequency values the amplitude transfer function is 0 dB.In the case of large values of frequency, i.e., (ωRC) 2 ≫ 1, Equation (9.9) becomes∣∣H ′ (ω) ∣ ∣ ≈−20 log(2π fRC)The amplitude characteristic therefore exists as a slope of 20 dB per decade. Theintersection f 1 of the two asymptotes is the cutoff frequency given byf 1 = 12π RCAccording to Equation (9.9) the amplitude decreases by 1/ √ 2 at the cutoff frequency,or 3 dB. Because power is proportional to the square of the pressure amplitude,the cutoff frequency is also the half-power point. The amplitude responsesof complex filters can be obtained in a similar manner.Filters may be grouped in bands so that serial analysis is rendered possibleby switching manually or automatically from one band to the next. The octaveband analyzer constitutes an example of a commonly used serial analyzer. Thisdevice is so called because it is capable of resolving the noise-signal spectruminto frequency bands that are one octave in width. We have already seen in Chapter3 that the center frequency of an octave band is √ 2 times the lower cutofffrequency, and the upper cutoff frequency is twice the lower cutoff frequency. Theoctave bands in the audio range are designated by their center frequencies and are