Signed-digit-based multiplier-free realizations for multirate converters

We propose multiplier-free realizations for FIR multirate converters. Radix-r signed-digit number representation and periodically time-varying (PTV) coefficients are used to obtain multiplier-free realizations. The PTV coefficients, together with one hold-and-scale unit at the input and one scale-add-downsample unit at the output, are utilized effectively to distribute the required computations to the extent that coefficients are highly simplified. The coefficients in the realizations are designed to take values from either the ternary set (0, ±1) or the quinary set (0, ±1, ±2). Their values can be easily obtained by mapping from the target filter coefficients using a radix-r signed-digit number representation. We show that fairly high precision can be achieved by these realizations