Comparing IIR Filter Types: Butterworth, Chebysheff and Elliptic

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In summary, the three types of IIR filters mentioned (Butterworth, Chebyshev, and Elliptic) are commonly used for filtering in communication systems due to their ability to control the bandwidth of a signal. Low-pass filters are particularly suited for telephony, cellular phones, and television applications because they ensure that the signal does not exceed the fixed bandwidth of each channel. The difference between the three filters lies in how they handle ripple in the passband and stopband, with the Butterworth filter providing the flattest passband response but poor roll-off, the Chebyshev filter having more ripple but a faster roll-off, and the elliptic filter being a balanced option. These filters are selected for their specific applications based
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phiska
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Hello

I'm researching IIR filters: Butterworth, Chebyscheff 1 and Elliptic types.

I've been using MatLab to model them and analyse the responses. However, I'd like to know what these three filters are particularly suited to... i understand that Low-Pass filters are typically suited to telephony, cellular phones and television, but why?

Are any of them specifically suited to any other applications?

Why would you select these filters for these applications?

Any hints/tips/suggestions would be gratefully recieved!

Thanks

Phiska
 
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Low-pass filters are used in many communications systems, because each channel in a communication system has a fixed (defined) bandwidth. Your signal cannot exceed that bandwidth, or it will interfere with neighboring channels.

For common radio transmission, you begin with a baseband signal, and use it to modulate a high-frequency carrier. For video applications, baseband might be 0 Hz to 6 MHz. You can play a baseband signal directly on your TV. If the TV channels each have a bandwidth of 6 MHz, you have to ensure that no baseband energy above 6 MHz gets through to the final broadcast signal, so you low-pass filter it at 6 MHz before using it to modulate the carrier.

The difference between the three kinds of filters you mention is how they handle ripple in the passband and stopband. In some applications, you must have as flat a response in the passband as possible, and the Butterworth filter provides a passband as flat as possible. The disadvantage is that the Butterworth filter has poor roll-off; the delineation between the passband and stopband is not sharp.

The Chebyshev filter has more passband ripple, but a faster roll-off. It also has very poor phase linearity. The elliptical filter is a sort of jack-of-all-trades.

- Warren
 
  • #3
Thanks! Clarifies things for me.

Phiska
 

What is an IIR filter?

An IIR (infinite impulse response) filter is a type of digital filter that uses feedback to achieve its filtering effect. It is designed to pass certain frequencies while attenuating others.

What are the differences between Butterworth, Chebyshev, and Elliptic filters?

Butterworth, Chebyshev, and Elliptic filters are all types of IIR filters, but they differ in their frequency response characteristics. Butterworth filters have a maximally flat response in the passband, Chebyshev filters have a steeper roll-off and can have either a maximally flat or an equiripple response, and Elliptic filters have a steeper roll-off and an equiripple response in both the passband and stopband.

Which filter type is best for my application?

The best filter type for your application depends on your specific filtering requirements. If you need a filter with a flat passband and a gradual roll-off, a Butterworth filter may be suitable. If you need a filter with a steeper roll-off and can tolerate some ripple in the passband, a Chebyshev filter may be a better choice. If you need a filter with a very steep roll-off and can tolerate ripple in both the passband and stopband, an Elliptic filter may be the most appropriate.

How do I choose the order of my IIR filter?

The order of an IIR filter refers to the number of poles and zeros in its transfer function. Higher order filters have a steeper roll-off, but they may also introduce more phase distortion and require more computation. The order of your IIR filter should be chosen based on your desired frequency response and the processing capabilities of your system.

Can I design my own custom IIR filter?

Yes, it is possible to design your own custom IIR filter using software or programming languages such as MATLAB or Python. However, it requires a good understanding of signal processing and filter design techniques. It is recommended to use established filter design tools or consult with an expert for complex filtering applications.

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