dbdf3ff7-f698-4f3c-a2a9-e06251298473 21 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

N 15 :

k 1 N range p k el π 2 k * 1 - (* 2 N * / sin - i π 2 k * 1 - (* 2 N * / cos * + : for

The analog XFR s H 1 s p k el + / k 1 N product 11 line :

x 02 0.01 range : y i x * H abs vectorize eval : Butterworth x y augment : 31 line

Butterworth 1 2 sqrt / 1 1 1 0 2 2 mat 3 1 sys

sampling interval (s) T 0.001 :

... implies aband limit (Hz) fmax 12 T * / : 500

passband edge fp 90 :

stopband edge fs 100 :

Attenuation for frequencies
above stopband edge G 2 :

Butterworth Filter Design:

To prepare for analog filter design, prewrap the passband & stopband frequencies and normalise the frequency range so that the passband edge is @ 1 [Parks & Burrus]

ωπ 2 π * fp * : ωσ 2 π * fs * : 21 mat 565.4867 628.3185 21 mat

up 2 T / ωπ T 2 / * tan * : us 2 T / ωσ T 2 / * tan * : 21 mat 581.0537 649.8394 21 mat

Frequency normalisation u us up / : 1.1184

N 1 G / (2^1 - log10 2 u log10 * / Ceil Im : 15

q 1 ωπ T 2 / * tan / : 3.442

z H q z 1 - z 1 + / * H :

f 018 T * / 0.001 T / range :

Y i 2 * π * f * T * exp H abs vectorize eval :

DRF: DigitalFrequencyResponse DRF f Y augment :

plot DRF fp 1 fp 022 mat fs 1 fs 022 mat 12 sqrt / 0.2 51 sys :

plot

a q p + q p - / vectorize :

f 012 T * / 0.001 T / range :

x y XY x y / - :

poles a Re vectorize a Im vectorize augment :

Zero 1 - 012 mat :

UnitCircle i 4 * π * f * T * exp Re vectorize i 4 * π * f * T * exp Im vectorize augment :

UnitCircle poles XY Zero 4 1 sys