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!
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.
Thanks! Clarifies things for me.
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