Designing of Low Pass Butterworth Filter and High Pass Butterworth Filter using Scilab is performed. Here the Input Specifications were specified by the user
(1) Pass band Attenuation (Ap< 3 dB) (2) Stop band Attenuation (As> 40 dB )
(3) Pass band Frequency (Fp) in Hz (4) Stop band Frequency (Fs) in Hz
(5) Sampling Frequency (F) in Hz
The poles for both the filters lie inside the unit circle, hence they are stable.
In the magnitude there are no ripples observed in either of the bands. A smooth magnitude curve determines a Butterworth Filter.
The order of the filter can always be increaesed for greater accuracy.
The observed and calculated values of Ap and As were found approximately same.
https://drive.google.com/open?id=0Bzfvoo_rjoa8Nm0yVGlJaWFFQkU
(1) Pass band Attenuation (Ap< 3 dB) (2) Stop band Attenuation (As> 40 dB )
(3) Pass band Frequency (Fp) in Hz (4) Stop band Frequency (Fs) in Hz
(5) Sampling Frequency (F) in Hz
The poles for both the filters lie inside the unit circle, hence they are stable.
In the magnitude there are no ripples observed in either of the bands. A smooth magnitude curve determines a Butterworth Filter.
The order of the filter can always be increaesed for greater accuracy.
The observed and calculated values of Ap and As were found approximately same.
https://drive.google.com/open?id=0Bzfvoo_rjoa8Nm0yVGlJaWFFQkU
Try using "buttmag" function in scilab code..
ReplyDeleteThe explanation is helpful. But you can also explain the design procedure.
ReplyDeleteAnalog Butterworth LPF has only poles and no zeros.
ReplyDeleteyes in butterworth the transfer function is 1 upon the equation
ReplyDeleteThe magnitude response |H(jw)| of the butterworth filter decreases with increase in frequency from 0 to infinity, while the magnitude response of the Chebyshev filter fluctuates or show ripples in the passband and stopband depending on the type of the filter.
ReplyDeleteFrequency response of butterworth filter was more smooth(monotonic) in pass band as well as in stop band. As the order of filter increases the response becomes sharper and more close to the ideal frequency response.
ReplyDeleteyes, but higher the order, the more complex the calculations
ReplyDelete