How to calculate roll-off of a filter

The roll-off rate of the n^th-order filter is 20 × n dB/decade or 6 × n dB/octave, where “n” is the order of the filter (Figure 3). A “sharp” multistage filter may have a roll-off of 20 dB/decade, while a less-sharp single-stage one will have just a 3-dB/decade value.

1. What do you mean by roll-off rate of a filter?
2. What is the roll-off rate of a Butterworth filter?
3. What is roll-off in frequency?
4. What is the roll-off rate of first order high pass filter?

What do you mean by roll-off rate of a filter?

The steepness of the gain in the stop band is referred to as the filter's roll-off. All first-order filters have a 20 dB/decade roll-off. The same roll-off can also be specified as 6 dB/octave. An octave is a term borrowed from music and represents a doubling of frequency.

What is the roll-off rate of a Butterworth filter?

When plotted on logarithmic scales, the Butterworth filter response is flat within its pass-band and then rolls off with an ultimate linear roll off rate of -6 dB per octave (-20 dB per decade).

What is roll-off in frequency?

The roll-off frequency is defined as the frequency under which some percentage (cutoff) of the total energy of the spectrum is contained. The roll-off frequency can be used to distinguish between harmonic (below roll-off) and noisy sounds (above roll-off).

What is the roll-off rate of first order high pass filter?

It has the roll-off rate of 40dB/Decade or 12dB/octave providing more steeper gain slope. The first order filter has 20dB/Decade or 6dB/octave.