Digital Butterworth Design:
This was the first experiment where we used Scilab for implementing the code. Scilab is a software in Ubuntu similar to Matlab in Windows.
In this experiment, the various parameters like pass band attenuation, stop band attenuation, pass band frequency, stop band frequency and sampling frequency are passed as input and the order of the filter is calculated. Similarly, the cutoff frequency is calculated.
The normalized transfer function is evaluated according to the filter type,i.e LPF or HPF(replacing s by 1/s). From the normalized transfer function, the denormalized function is calculated by substituting the value of cut off frequency. The response in z -domain is equivalently calculated by IIM or BLT transformations.
In this experiment, the various parameters like pass band attenuation, stop band attenuation, pass band frequency, stop band frequency and sampling frequency are passed as input and the order of the filter is calculated. Similarly, the cutoff frequency is calculated.
The normalized transfer function is evaluated according to the filter type,i.e LPF or HPF(replacing s by 1/s). From the normalized transfer function, the denormalized function is calculated by substituting the value of cut off frequency. The response in z -domain is equivalently calculated by IIM or BLT transformations.
Butterworth filter is used to obtain a flat passband in the frequency response
ReplyDeleteButterworth filter can have minimum order 1
ReplyDeleteThe order of the filter increases as the transition width of the filter decreases. In butterworth filter there is no ripple in stopband as well as in passband
ReplyDeleteAs transition becomes steeper, the magnitude response of the filter approaches the magnitude response of an ideal filter.
ReplyDeleteAnalog Butterworth LPF has only poles and no zeros.
ReplyDeleteChebyshev filters have sharper frequency cut-off while butterworth filters have a wide transition band
ReplyDeleteHigher the order more is the hardware requirement.
ReplyDeleteThe complexity or filter type is defined by the filters order.
ReplyDeleteThe transition width criteria is rightly pointed out. This parameter is used for selecting the windowing function in practical applications.
ReplyDeleteMaximally flat passband is an advantage of Butterworth Filters
ReplyDelete