Using the orthogonality property of the Chebyshev polynomials, show that the criterion J FI [ ( f ) ] can be expressed as Where Show that the filters defined in XXXXXXXXXXpreserve the nulls of 𝐡′ ( f...

Using the orthogonality property of the Chebyshev polynomials, show that the criterion J_FI
[ ( f ) ] can be expressed as

Where

Show that the filters defined in (10.60) preserve the nulls of 𝐡′ ( f ) = 𝐡_NR( f ); that is, if 𝜃₀
is a null of 𝐡′ ( f ), then

Where