Sparsity has been a great issue in the design of FIR filter. The objective of a Sparse FIR filter design is to reduce the implementation complexity as the number of nonzero-coefficients is reduced. By increasing the number of zero-valued coefficients, the implementation of the filter becomes simple as the additions and multiplications corresponding to zero-valued coefficients are omitted. The proposed paper discusses the various techniques used earlier for designing a sparse FIR filter. This paper also presents the comparative study of several filter designing methods used by researchers for this work.