Frequencies within a filter's stopband are, by contrast, highly attenuated. The transition band represents frequencies in the middle, which may receive some attenuation but are not removed completely from the output signal.
In Figure 1, which shows the frequency response of a lowpass filter, ωp is the passband ending frequency, ωs is the stopband beginning frequency, and As is the amount of attenuation in the stopband. Frequencies between ωp and ωs fall within the transition band and are attenuated to some lesser degree.
Given these individual filter parameters, one of numerous filter design software packages can generate the required signal processing equations and coefficients for implementation on a DSP. Before we can talk about specific implementations, however, some additional terms need to be introduced.
Ripple is usually specified as a peak-to-peak level in decibels. It describes how little or how much the filter's amplitude varies within a band. Smaller amounts of ripple represent more consistent response and are generally preferable.
Transition bandwidth describes how quickly a filter transitions from a passband to a stopband, or vice versa. The more rapid this transition, the higher the transition bandwidth; and the more difficult the filter is to achieve. Though an almost instantaneous transition to full attenuation is typically desired, real-world filters don't often have such ideal frequency response curves.
There is, however, a tradeoff between ripple and transition bandwidth, so that decreasing either will only serve to increase the other.
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