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Difference between Butterworth filter vs Chebyshev vs Bessel vs Elliptic filter

This page compares Butterworth filter vs Chebyshev filter vs Bessel filter vs Elliptic filter and mentions basic difference between Butterworth filter,Chebyshev filter,Bessel filter and Elliptic filter.

As we know filter is the module which passes certain frequencies and stops certain frequencies as designed. There are two categories in the filter viz. analog and digital. Analog filter operates on analog input frequency and digital filter operates on digital input data. Refer analog filter vs digital filter for more.

There are various types of filter in each of the above categories. They are known as Low Pass Filter(LPF), High Pass Filter(HPF), Band Pass Filter(BPF) and Band Stop Filter(BSF). The names are as per their functionalities of operation.

For example, LPF passes all the frequencies in the lower band and stops the frequencies in the higher band. These points are considered with reference to certain cutoff frequency during design. Refer filter types which describes difference between LPF, HPF, BPF and BSF.

Based on technical design specifications there are filter types such as Butterworth, Chebyshev, Bessel and Elliptic filters. They have their own unique characteristics and hence they have been choosen for different applications as desired. Following section describes difference between Butterworth filter, Chebyshev filter, Bessel filter and Elliptic filter.

Butterworth filter

Following are the major unique characteristics of the butterworth filter. • Maximally flat response within the passband of the filter.
• Moderate phase distortion.

Butterworth LPF will have all the poles and they will be located on the unit circle with equal angles.

Chebyshev filter

As the name suggests, chebyshev filter will allow ripples in the passband amplitude response. It is also known as equal ripple response filter. The amount of ripple is provided as one of the design parameter for this type of chebyshev filter.

This filter type will have steeper roll-off near cutoff frequency in comarison to butterworth filter. But this results into monotonicity in passband region along with poor transient response.

Following are the silent characteristics of chebyshev filter:
• Ripple in passband
• Sharper transition band as compared to butterworth
• Poorer group delay

This filter will have all poles and are located on an ellipse inside the unit circle.

Bessel filter

Butterworth Filter vs Bessel Filter

As shown in the figure, when non-sinusoidal waveform(such as square wave) is applied as input to the butterworth low pass filter it results into distortion. The resultant output waveform will have ringing and overshoot. This is due to the fact that component frequencies of square wave will shift in time w.r.t. each other. This is because if the phase increases linearly with frequency, it will result into delay in the output signal by certain constant time period.

The Bessel filter avoids the situation mentioned above. This filter will introduce linear phase shift with respect to frequency. Hence it will act as a delay line having low pass characteristics. In this type of filter output waveform will not have any ringing and overshoot. The same has been depicted in the figure. It will round off the input square wave at the places where high frequency harmonic components are present in the input waveform.

Elliptic filter

• In this type of elliptic filter cutoff slope is shaper compare to all other filters such as Butterworth, Chebyshev and Bessel.
• But it will have ripples in passband and stopband of amplitude response.
• It will have very non-linear phase response.

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