After analyzing different algorithms for obtaining filter(system) output, it's time to design a filter. Firstly, IIR(Infinite Impulse Response i.e. on taking Inverse Z-Transform, h[n] has infinite length) filters were designed on Scilab. The first type are Butterworth filters with no ripple in passband and stopband. On substituting the input parameters As,Ap, Ws,Wp and sampling frequency, for both High Pass and Low Pass, Filters,a high order filter is designed.Here, first , an Analog and then a Digital Filter is designed. The poles of this filter lie on a circle inside the unit circle in the z-plane. As BLT method is used for design, there is one-to-one mapping of filter poles, but the frequency bands are compressed in case of digital filters.
Higher orders of the filter makes its hardware implementation difficult.
ReplyDeleteHence digital filters are used.
Deletewhat is the limitation of BLT method?
ReplyDeleteAs compared to IIM method the computations can increase.
DeleteAlso, for Band Pass and Band Stop filters, the order may increase after LPF to BPF/BSF transformation is used.
Another limitation involves the Direct Form Realization. The block in the realization increase as terms in numerator increase.
This comment has been removed by the author.
ReplyDeleteWorth explained
ReplyDeleteRefer to MATLAB's documentation for more information.
DeleteIs IIM better than BLT?
ReplyDeleteFor Low pass filters IIM can be used as it involves less computation. However, BLT is preferred as there is no aliasing effect.
DeleteIn Butterworth filter as we go on increasing order of filter, response becomes more sharper and at approaches to ideal response.
ReplyDeleteAs the order increases, the response starts appearing as an ideal filter.
DeleteCan be used where amplitude is of more importance
ReplyDeleteBecause of maximally flat passband.
DeleteButterworth does not have ripples in any band in its frequency response
ReplyDeleteit gives flatband reaponse
ReplyDeleteThis is important for critical applications.
DeleteIn Butterworth filters, the transition band becomes sharper as the order increases
ReplyDeleteAt this point the response appears as that of an ideal filter.
DeleteDigital Butterworth filters are preferred as Analog filters require more number of discrete components.
ReplyDeleteThat is the inherent advantage of digital filters.
DeleteThe frequency response of the Butterworth filter is maximally flat
ReplyDelete