Discussion Overview
The discussion revolves around the attenuation characteristics of a high-pass 2nd order Butterworth filter, specifically focusing on the definitions and calculations related to the cutoff frequency (fc), pass-band frequency (fp), and stop-band frequency (fs). Participants are exploring the confusion regarding the attenuation values at these frequencies.
Discussion Character
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant expresses confusion about the attenuation values at fc and fp, noting unexpected results where the passband shows more loss than the stop band.
- Another participant seeks clarification on the definitions of fc, fp, and fs for a 2nd order Butterworth high-pass filter.
- Several participants reiterate the definitions: fp as the pass-band frequency, fs as the stop-band frequency, and fc as the -3dB frequency.
- There is mention of a normalized loss function for the filter, represented as H(s) = 1/{s^2 + sqrt(2)s + 1}, with a note on the challenges of converting high-pass to low-pass filters.
- One participant raises a point about the potential variability in defining fp and fs, suggesting that these definitions might depend on the context or specific textbook references.
- Concerns are expressed about needing explicit definitions or guidance from textbooks to determine appropriate values for fp and fs in relation to the filter's polynomial.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the definitions and implications of fp, fs, and fc, indicating that multiple competing views and uncertainties remain regarding their application in the context of the filter's performance.
Contextual Notes
There are unresolved questions regarding the definitions of pass-band and stop-band frequencies, as well as the implications of the normalized loss function on the calculations. The discussion highlights the need for clarity on how these terms are defined in different contexts.
