This paper provides a review accompanied with examples regarding the usage of four basic discrete time model reduction techniques namely Balanced Truncation, Hankel Optimal Approximation, Impulse Response Gramians and Least Squares for the purpose of approximating an FIR digital filter with complex coefficients by its equivalent reduced order IIR digital filter. Simulation results indicate that stable reduced order IIR filters approximants with computational savings can be obtained using all the four techniques. However for a specified order, some model reduction techniques result in reduced order models which better approximate the original FIR digital filter compared to other techniques. The criteria used for comparison between the performances of the four model reduction algorithms were passband magnitude root mean squared error (RMSE) and computational cost. Two numerical examples are provided to demonstrate the application of model reduction techniques for complex co efficient filters and to compare the performances.