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A detailed explanation of butterworth filters, often referred to as maximally flat filters. It covers key characteristics, including the butterworth polynomial, damping coefficients, and filter order determination. The document also explores the relationship between the resonant frequency, passband edge frequency, and filter order. Additionally, it delves into the high-pass butterworth filter characterization, highlighting the interchange of quantities for high-pass applications.
Typology: Lecture notes
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with half-power frequency, here ωo, is also commonly called the 3 dB frequency: 20 log (^) ( 2 ) = 3. 01030 dB ≈ 3 dB. (9.3-4)
(^45) 0.1 1 10
40
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5
0
5
ω
n = 1 n = 2
n = 3 n = n = 6 n = 5
Figure 9.3-1 Butterworth Filter Frequency Response.
Here polynomials is: ωc is the edge frequency of the passband. At ω = ωc, the magnitude of all Butterworth
High-pass Butterworth Characterization:
where (9.3-11)