Frame Reconstruction with Noise Reduction in Hilbert space and Application in Communication Systems

In this work, classification for Frame and Fourier coefficient has been discussed. We provided the relation between hidden code coefficients and signal coefficients on L2[−T,T] and introduced a theorem that has been proved for recovering the original signal. We provided Key exchange algorithms to store or transmit the information. After decoding, we recovered the filter signal that is less than or equal to original signal with negligible amount of errors. In the last theorem of this paper, we provided a technique to obtain the error to recover the exact information. The application in communication systems for speech signal with low and high frequencies has been discussed at the end.