Howtosignalprocessing
- What are Chebyshev polynomials used for?
- How do you approximate a function using the Chebyshev polynomial?
- Are Chebyshev polynomials Orthonormal?
What are Chebyshev polynomials used for?
Chebyshev polynomials are usually used for either approximation of continuous functions or function expansion.
How do you approximate a function using the Chebyshev polynomial?
To approximate a function by a linear combination of the first N Chebyshev polynomials (k=0 to N-1), the coefficient ck is simply equal to A(k) times the average of the products Tk(u)f(x) T k ( u ) f ( x ) evaluated at the N Chebyshev nodes, where A=1 for k=0 and A=2 for all other k.
Are Chebyshev polynomials Orthonormal?
Abstract It is known that Chebyshev polynomials are an orthogonal set associated with a certain weight function. In this paper, we present an approach for the con- struction of a special wavelet function as well as a special scaling function. Main tool of the special wavelet is a first kind Chebyshev polynomial.
