Design of Hilbert transformer using the L1-method

In this paper, a novel L
₁
-error approximation method for the design of finite impulse response (FIR) Hilbert transformer (HT) is introduced. The mathematical framework for the L
₁
-method is explained for the design of HT and the problem of differentiability of L
₁
-norm is exploited. The optimal coefficients for HT are computed using the proposed L
₁
-method. The use of L
₁
-approximation is advantageous in terms of obtaining a flat passband along with a small overshoot at the discontinuities. The effectiveness of the proposed HT is presented using two design examples and the results are compared with the different existing design techniques. The proposed HT using the L
₁
-method is demonstrated in terms of magnitude response (dB), impulse response, pole-zero plot, group delay and magnitude of error function.