Example of symbol of generalized Toeplitz operators

Question

I am looking for the example to the sybol of generalized Toeplitz operators. For example if Toeplitz operator is matrix (S* O // 0 S) we have the symbol is matrix Y= (M_{\pH} 0 // 0 0). I do not know how we know that this Y is symbole for T? What is when we take T as matrix (S* 0 // 0 S*) or T as matrix (I 0// 0 S*) . How look symbol for this T. And what I sholud do to obtain this symbol Where S i shift, an I is identity