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Accurate exon prediction in a genome is extremely important for understanding of life processes. Researchers use various techniques for detecting accurate location of exons. A digital filter model has been proposed in this paper for the prediction of exons in DNA sequence. The technique involves conversion of DNA character string into a numerical sequence using weak-strong bonding of nucleotides and filtering the transformed sequence using Narrow Band Pass FIR filter whose passband is centered at 2π/3. The filtered signal power of Narrow band pass FIR filter is then used as a measure parameter for both exons and introns. A plot of signal power versus nucleotide location is used to distinguish exons from introns of a DNA sequence. The simulation plots show very distinct peaks in exon regions indicating its presence where as such peaks are absent in intron regions. The design model is tested for several databases of Homo sapiens Beta-globin chromosome which have been downloaded from National Center for Biotechnology Information (NCBI) homepage.