Wordlength Optimization of Linear Time-Invariant Systems With Multiple Outputs Using Geometric Programming

This paper proposes two new methods for optimizing hardware resources in finite wordlength implementation of multiple-output (MO) linear time-invariant (LTI) systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first method relaxes the wordlength from integer to real-value and formulates the design problem as a geometric programming, from which an optimal solution of the relaxed problem can be determined. The second method is based on a discrete optimization method called the marginal analysis method, and it yields the desired wordlengths in integer values. By combining these two methods, a hybrid method is also proposed, which is found to be very effective for large scale MO LTI systems. To illustrate the effectiveness of the proposed methods, wordlength optimization problems of two-channel structural perfect reconstruction filter banks and multiplier-less fast Fourier transforms are studied in detail. Design results show that the proposed algorithms offer better results and a lower design complexity than conventional methods