BRUEL & KJAER 1617 - Special Considerations in Frequency Analysis; Filter Definitions; The Ideal Filter; Bandwidth

4. SPECIAL CONSIDERATIONS IN FREQUENCY ANALYSIS
4.1. FILTER DEFINITIONS
4.1.1. The Ideal Filter
An ideal band pass filter is one which has zero attenuation within its pass band and infi-
nite attenuation at all other frequencies. The ideal filter is compared with a practical fil-
ter in Fig.4 .1 .
1,1 1,2 1,3 1,4 1,5 1,6 1,7 f
__ Fr equency
t:
161968
Fig.4. 1. Ideal and practical filters
4.1.2. Bandwidth
38
Whereas the bandwidth of an ideal filter can be precisely specified as in 4 .1 .1 , two defi-
nitions of the bandwidth of a practical filter are in common use. The -3 dB band-
width is defined by the points on the filter characteristic at which the voltage trans-
mission is 3 dB below the maximum transmission level (i.e., the point at which power
transmission is halved). This case is illustrated in Fig .4 .1 together with the ideal filter of
the same bandwidth .
The Effective
Bandwidth of the filter (sometimes referred to as the Effective Noise Band-
width) is the bandwidth of the ideal filter which would pass the same amount of white
noise power as the specified filter. This is the definit ion of bandwidth on which the oc-
tave and third-octave
filters of the Type 1617 are based. Since noise power is propor-
tional to the square of noise voltage, the area below the " Practical Filter Squared" char-