A method for implementing a digital filter is provided. The method includes (a) determining a bit-width of an incoming data sample of an incoming signal by measuring a distance between a leading zero or one of the incoming data sample and a trailing zero of the incoming data sample. The incoming data sample is obtained by sampling the incoming signal at a pre-defined time interval, (b) obtaining bit-width multipliers with variable bit-widths based on a first probability distribution function (PDF) of bit-widths of incoming data samples, (c) allocating the incoming data sample and a filter coefficient based on the bit-width of the incoming data sample and a bit-width of the filter coefficient to one bit-width multiplier of the bit-width multipliers, and (d) performing a multiply operation of a Multiply and Accumulate (MAC) operation on the one bit-width multiplier to generate an output of the digital filter.