Difference Between Butterworth and Chebyshev Filter
Difference Between Butterworth and Chebyshev Filter
The Chebyshev filter has a steeper roll-off than the Butterworth filter. But it consists of ripples in the passband (type-1) or stopband (type-2). Type-1 Chebyshev filter is commonly used and sometimes it is known as only “Chebyshev filter”. Type-2 filter is also known as “Inverse Chebyshev filter”.
The difference between the Butterworth filter and Chebyshev filter is as shown in the below table.
| Butterworth Filter | Chebyshev Filter | |
| Order of Filter | The order of the Butterworth filter is higher than the Chebyshev filter for the same desired specifications. | The order of the Chebyshev filter is less compared to the Butterworth filter for the same desired specifications. |
| Hardware | It requires more hardware. | It requires less hardware. |
| Ripple | There is no ripple in passband and stopband of frequency response. | There is either ripple in passband or stopband. |
| Poles | All poles lie on a circle having a radius of the cutoff frequency. | All poles lie on ellipse having major axis R, ξ, minor axis r. |
| Transition band | The Butterworth filter has a wider transition band compared to the Chebyshev filter. | The Chebyshev filter has a narrow transition band compared to the Butterworth filter. |
| Types | It doesn’t have any types. | It has two types; type-1 and type-2. |
| Cutoff Frequency | The cutoff frequency of this filter is not equal to the passband frequency. | The cutoff frequency of this filter is equal to the passband frequency. |
Butterworth Filter Applications
The applications of a Butterworth filter are listed below:
- Because of the maximal flat frequency response in the passband, it is used as an anti-aliasing filter in data converter applications.
- The Butterworth filter is used in the audio processing application. An efficient audio noise reduction tool can be developed using a Butterworth filter.
- It is also used in various communication and control systems.
- It is used in radar to design the display of radar target tracking.
- It is used for motion analysis.
