In contrast to the previous equation, each data point has a different weighting factor (a). The sum
of these weighting factors (a0…n) will always be 1.
Characteristic of noise filters is that processing the signal results in a delay. This is inevitable; the
mathematics of digital signal processing requires a number of previous data points to process a
new data point. A filter characteristic in DSP is often named after the scientist who “invented” the
mathematics behind the signal processing routine. Well-known names in this field include Bessel,
Chebychev, Savitsky, Golay, Hamming, and many others.
7.2.3 Amplitude response plot
Figure 7–7: Amplitude response plot of an ideal low pass filter with a cutoff frequency of 1
Hz
There are several ways to describe filter characteristics. An amplitude response plot gives
important information on filter behavior. Suppose our signal of interest has a frequency between 0
Hz and 1 Hz, and all higher frequencies are noise. An ideal filter is shown in
Amplitude response plot of an ideal low pass filter with a cutoff frequency of 1 Hz (Page 68)
where signal frequencies between 0 and 1 Hz completely pass, while frequencies higher than 1
Hz are completely blocked.
In practice, filters behave a bit differently than the ideal. An amplitude response plot shows a
more gradual attenuation profile at higher frequency. The cutoff frequency is where the output
signal amplitude is 70% of the input signal, also known as the 3 dB point.
Figure 7–8: An amplitude response plot of a low pass filter with a cutoff frequency of 1 Hz;
it is a 2 (A), 4 (B), and 8 (C) pole Bessel filter
shows that the number of poles is important; a
filter behaves more ideally as the number of poles increases. In a hardware filter the number of
poles is the number of filter circuits that are placed in series.
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