In this work, band structure, density of states and wave propagation inside one-dimensional photonic crystal is numerically computed using both the transfer matrix method and plane wave expansion method. Rigorous mathematical computation is carried out and simulated results are given for conventional SiO2-air composition as well as for novel semiconductor heterostructure also. Group theoretic approach is used to study photonic crystal structure which will help for better modelling of the devices based on 1D PC. Density of states analysis provides insight about the possible red/blueshift by tuning the material composition or dimension along the electromagnetic wave propagation; which forecasts the use of possible photonic filter design using proposed semiconductor composition supported by reflectivity calculation in optical communication wavelength. Though the work in this study is quite in its elementary stage, but this trivial work will definitely help the future research students to progress.