Elliptic Filter - Properties

Properties

  • In the passband, the elliptic rational function varies between zero and unity. The passband of the gain therefore will vary between 1 and .
  • In the stopband, the elliptic rational function varies between infinity and the discrimination factor which is defined as:
The gain of the stopband therefore will vary between 0 and .
  • In the limit of the elliptic rational function becomes a Chebyshev polynomial, and therefore the filter becomes a Chebyshev type I filter, with ripple factor ε
  • Since the Butterworth filter is a limiting form of the Chebyshev filter, it follows that in the limit of, and such that the filter becomes a Butterworth filter
  • In the limit of, and such that and, the filter becomes a Chebyshev type II filter with gain


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