In an ideal design, a digital filter has a target gain in the passband and a zero gain (−∞ dB) in the stopband. In a real implementation, a finite transition region between the passband and the stopband, which is known as the transition band, always exists. The gain of the filter in the transition band is unspecified. The gain usually changes gradually through the transition band from 1 (0 dB) in the passband to 0 (−∞ dB) in the stopband http://zone.ni.com/reference/en-XX/help/371325F-01/lvdfdtconcepts/dfd_filter_spec/.

Question: If an ideal design, a digital filter has a target gain in the passband and a zero gain (−∞ dB) in the stopband. It has a role in the appearance of the ripples in some way in the stopband and passband?

Why the transition band always exists? does this is because the gradually through the transition band from the passband to the stopband?

In electronics, gain is a measure of the ability of a two-port circuit (often an amplifier) to increase the power or amplitude of a signal from the input to the output port.by adding energy converted from some power supply to the signal https://en.wikipedia.org/wiki/Gain_(electronics). I want to know how this definition is applied in the design of digital filters.

  • $\begingroup$ I'm not sure what your question is. Do you want to know why transition bands in real-life filter exist? $\endgroup$ – Tendero Jan 16 '18 at 17:07
  • $\begingroup$ @Tendero :yes i want to know why transition bands in real-life? $\endgroup$ – K.n90 Jan 16 '18 at 17:29

In an actual design you need to allow for a smooth transition from the passband to the stopband because the magnitude response of a realizable (i.e., causal and stable) filter is smooth; it can't jump. Of course you can try to approximate a jump in the magnitude, but you'll always get a smooth magnitude response (cf. Gibbs phenomenon). Defining a "don't care" transition band with no specification will decrease the approximation error in the bands of interest.

I don't understand your question about the ripples in the passband and stopband. Maybe you can clarify this and I'll edit my answer.

The passband gain of a filter is simply the amplification factor for signal components that are in the filter's passband.

  • $\begingroup$ if equi-ripple response in the pass band results in the amplitude distortion being distributed across the whole passband. on the other hand the gain :it is usually defined as the mean ratio of the signal amplitude . There is relation between the amplitude in the gain and the amplitude in the passband. $\endgroup$ – K.n90 Jan 16 '18 at 20:50
  • $\begingroup$ @K.n90: Yes, equi-ripple means the ripple size (and the corresponding amplitude distortion) is constant in the passband (and also in the stopband). $\endgroup$ – Matt L. Jan 16 '18 at 20:56

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