FILTER DESIGN
Question 1: Design an anti-aliasing CT filter
This filter can be realized from the classical approach, where the Transfer function is explicitly defined in the MATLAB script. This forms the basis on which the Filter Response can be derived, and the Analog functions of Butterworth, elliptical, Chebyshev 1, and Chebyshev 2 can be invoked to realize the filters.
Figure 1: Script for Designing Filters for Question 1
By running the filtord command, we end up with the following results.
>> FilterOrders = [filtord(butterworth_Filter) filtord(chebychev_1_Filter) filtord(chebychev_2_Filter) filtord(elliptical_Filter)]
%Butterworth Highest FilterOrders, elliptic lowest
FilterOrders =
27 13 13 9
Figure 2: Comparison of the filter’s behavior in the transition Band
Butterworth Filter exhibits the highest order while the Chebychevs are at median order. Elliptical Filters are seen to be of the lowest order.
Figure 3: Ripples in the Passband Region
Butterworth Filter has an excellent Passband Response, due to the Linearity in the phase. This is exhibited in the Transition band as shown below;
Figure 4: Linearity in the Transition Region
In General, Elliptic Filters exhibit the lowest order in the Magnitude response while Butterworth has excellent Linearity in the Transition band.
Question 2: Design a digital noise-reducing IIR filter:
This is designed from the Sampling techniques previously discussed in class. We seek to design a filter with the given Parameters of Frequencies and Passband Restrictions.
Therefore we load the Parameters into the Matlab and Invoke the corresponding Filter design tools from the Signal Processing toolbox.
Script
Figure 5: Script for Question 2
On running the above script, the output.is as follows. Each filter family is accessible from the fvtool command, but the Four filter families’ main Comparison is shown below;-
Figure 6: Observing Linearity Differences in the Transition Band
On inspecting the ripples at Passband, we realize that some of the filters allow ripples while the others reject them entirely. In the Passband Region, where the Filter Specifications are set to operate, there are no ripples, which is a good indicator of the Filters’s performance.
Figure 7: Inspecting the PassBand Region
Only non-linearity is exhibited in the Transition Region.
The degrees or Filter Order for the above filters are as below;
FilterOrders =
27 13 13 9
With Butterworth still taking the lead and the Elliptical having the least order. Higher-order of a filter translates to a higher fabrication cost and an improved performance of filters.