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Legendre Filters

The Legendre filter is a monotonic all-pole filter: the passband slope is always zero or downward, never upward. The response is optimized for the greatest slope at the passband edge.  Legendre filters are useful in applications which require a steep cutoff at the passband edge without passband ripple; or in cases where a Chebyshev I filter produces too much group delay at the passband edge.

The following are examples of Legendre low-pass and step responses: