Approximate Computation of DFT without Performing Any Multiplications: Applications to Radar Signal Processing

TL;DR

This paper introduces a multiplication-free algorithm for approximate DFT computation, reducing multiplications in radar signal processing, especially for correlation calculations like the ambiguity function.

Contribution

A novel multiplication-free DFT approximation method replacing multiplications with an additive operator, enhancing efficiency in radar correlation tasks.

Findings

Reduces the number of multiplications in DFT calculations.

Effective in radar ambiguity function computation.

Demonstrated through simulation examples with passive radars.

Abstract

In many practical problems it is not necessary to compute the DFT in a perfect manner including some radar problems. In this article a new multiplication free algorithm for approximate computation of the DFT is introduced. All multiplications $(a\times b)$ in DFT are replaced by an operator which computes $sign(a\times b)(|a|+|b|)$. The new transform is especially useful when the signal processing algorithm requires correlations. Ambiguity function in radar signal processing requires high number of multiplications to compute the correlations. This new additive operator is used to decrease the number of multiplications. Simulation examples involving passive radars are presented.