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DISCUSSION:

The choice between a Finite Impulse Response (FIR) filter and an Infinite Impulse

Response (IIR) filter depends on the importance to the design problem of the advantages of each

type. IIR filters, for example, have the advantage that a variety of frequency-selective filters can

be designed using closed form design formulas. That is, once the problem has been specified interms appropriate for a given approximation method (e.g., Butterworth, Chebyshev, or elliptic),

then the order of the filter that will meet the specifications can be computed and the coefficients

(or poles and zeros) of the digital filter can be obtained by straightforward substitution into a set

of design equations. This kind of simplicity of the design procedure makes it feasible to design

IIR filters by manual computation if necessary and it leads to straightforward non-iterative

computer programs for IIR filter design.

There are many filter types, but the most common are lowpass, highpass, bandpass, and

bandstop. A lowpass filter allows only low frequency signals (below some specified cutoff)

through to its output, so it can be used to eliminate high frequencies. A highpass filter does just

the opposite, by rejecting only frequency components below some threshold. Bandpass filter is

designed to ensure that only output signals within its narrow range of the frequency spectrum are

transmitted. Meanwhile, bandstop filters; which pass both low and high frequencies, to block a

predefined range of frequencies in the middle. As we are assigned to remove the middle

frequencies from a given mixed signals, we need to filter it by designing the bandstop filter.

Before we find the right and suitable filter design, there are a lot of graphs have been

plotted and analyzed so we can compare which type can offer the best filtering. Firstly, we have

designed Butterworth type of 5th

and 10th

order. Notice that, 10th

order Butterworth has sharpertransition of the magnitude graph. However, the phase response of the 5 th order has better

linearity. In many applications, it is necessary to ensure that there is no phase distortion of the

frequency components of the input signal. In an ideal case, it requires a zero-phase characteristic

for the digital filter. However, it is impossible to design a causal IIR filter with zero phases. A

linear-phase characteristic represents a pure delay, so a linear-phase IIR filter is desirable in

many applications.

By analyzing of the group delay graph, the 5th order of Butterworth has flatter group

delay response compared to the 10th order. The group delay is defined as the derivative of the

phase with respect to angular frequency and is a measure of the distortion in the signal

introduced by phase differences for different frequencies. So, the good one should have more flat

and approaching zero at most of the time.

After that, we have designed the Chebyshev type of 5th

order and 10th

order. We did

similar analysis as 5th order and 10th order Butterworth filter. As the results, the comparisons of 

magnitude response, phase response and group delay characteristics are quite similar to the

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