Reversed Chebyshev implementation of McClellan transform and its roundoff error

A new structure, called the reversed Chebyshev structure, for the fixed point implementation of the FIR filters designed with the McClellan transformation is presented. It shows the best roundoff noise performance among the existing ones for both rounding and truncation operations. The incremental rate of the upper bound on the variance of the roundoff noise, as the size of the 2-D filters increases, is very small. The reversed Chebyshev structure is rooted from our calculation of the upper bound on the variance of the output roundoff noise of 2-D FIR filters designed with the McClellan transformation. This upper bound is independent of the transformation filters and can be easily calculated to estimate the number of bits needed for the desired accuracy in the fixed point implementation.