Continuous-Time Chebyshev and Elliptic Filters

[@louisdavies5367]

Great video :)

[@prajwolgyawali6770]

Timestamp: 1:55 Can anyone help me with the fact how does Chebyshev's polynomial oscillate between +- 1?

[@carstenmeyer7786]

First, define the Chebyshev polynomials by recursion:
*Tn(x) := 2x * T_{n-1}(x) - T_{n-2}(x) // T0(x) = 1, T1(x) = x*
Then prove via induction:
*Tn(x) = / cos(n * arccos(x)) for |x| < 1*
*\ sign(x)^n * ch( n * arch|x|) else*
The representation for *|x| < 1* should answer your question.

[@MOHAMMEDRUSH]

thanks