Can Someone please explain and clarify the following points for the General Filter Second Order Double Precision:
1. For a Bandpass Filter
a. Ideally a Band pass Filter has two cut-off frequencies which is not evident in the Sigma Studio's GUI for a bandpass filter. The Filter Frequency of the BandPass filter in Sigma Studio (say i set it to 100Hz) is that the cut-off frequency ? If yes how do I interpret the single cut-off frequency for a Bandpass Filter
b. Next what is the bandwidth in octaves and how do Interpret the range please explain with example (say for instance setting the octave to 0.90 for a 100kHz cut-off frequency) .
You can set the 2nd Order Bandpass filter's low and high cutoff frequencies by adjusting its two GUI settings. The box labeled Freq is the filter's center frequency. The -3 …
You can set the 2nd Order Bandpass filter's low and high cutoff frequencies by adjusting its two GUI settings. The box labeled Freq is the filter's center frequency. The -3 dB Low and High Cutoff frequencies are located at equal distances away from the center frequency when viewed on a log frequency scale. The Bandwidth (octaves) adjustment determines the distance between these and the center frequency.
For example, the bottom filter in this image has a BW of 2 octaves. Each octave is a doubling of frequency, so two octaves means that the high cutoff frequency H must be four times more than the low cutoff frequency L. Thus, the blue curve on the graph shows L at 50 Hz, H at 200 Hz, and the center frequency at 100 Hz. The green and red lines correspond to filters of narrower bandwidths, as shown in this table:
BW Line color Low cutoff High cutoff
0.5 red 84 Hz 119 Hz
1.0 green 71 Hz 141 Hz
2.0 blue 50 Hz 200 Hz
In general, if we call C the center frequency, L the low cutoff, H the high cutoff, and BW the bandwidth in octaves, then:
H = C * (2^(BW/2)) and L = C / (2^(BW/2))
We can work this backwards. Given the desired cutoff frequencies L and H, the two figures to enter into the 2nd Order Bandpass Filter GUI are:
C = sqrt (H*L) and BW = 3.322 * log (H / L)