The spectral observation coding scheme based on compressed sensing and deep learning theory has some problems, such as the complex process of filter design and spectral reconstruction, and the difficulty of hardware implementation of the designed spectral transmittance. Therefore, in order to simplify the spectral observation system, considering the manufacturing difficulty of common interference filters, a spectral transmittance observation coding scheme based on symmetrical tridiagonal Toeplitz matrix is proposed. The well-posedness of spectral observation matrix is discussed by matrix theory, and its tolerance is studied by numerical simulation. The theoretical analysis results show that with the increase of the size of the spectral observation matrix, the condition number of the symmetric tridiagonal matrix increases slowly and the upper limit can be controlled. The numerical simulation results show that the non-negative least squares algorithm is used for spectral reconstruction, and under certain constraints, increasing the size of the observation matrix has little influence on the suitability of the spectral observation coding scheme of the symmetric tridiagonal matrix, which can still guarantee the high accuracy of spectral measurement reconstruction.