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This paper gives the analysis of Toeplitz Approximation Method (TAM) for direction finding problem. There are essentially two steps in TAM. The first step is the apporximation procedure of a parameter set and the second step consists of extracting the information (angular direction and amplitude) from parameter set. We will show how the structure of a toeplitz matrix formed from a set of Markov parameters can be exploited to efficiently solve the approximation problems. By employing the Singular Value Decomposition (SVD) technique we obtain an approximation state-space realization. We will give many desirable features of our approach. These include a good numerical performance, stability of the realization, robustness and flexibility in determining model order.