This research focuses on frequency-based lossless new encoding technique with low computation and low memory scheme. This encoding technique doesn't require, any table similar to Huffman and Golomb Rice encoder, and doesn't take high computation time like an arithmetic encoder. For better comparative results, nearly 200 standard images were tested with the proposed encoder and their results were compared with the standard encoders. Based on the analysis of results reported in the experimental part, the proposed scheme in Discrete Cosine Transformation (DCT) achieves a high Compression Ratio (CR) of 97.68 %, Bits Per Pixel (BPP) of 0.19, Peak Signal To Noise Ratio (PSNR) of 27.62 dB for pepper image, CR of 98.65%, BPP of 0.11 and PSNR of 29.24 dB for house image, CR of 98.58 %, BPP of 0.11, PSNR of 30.59 dB for pepper image, CR of 98.37%, BPP of 0.13, PSNR of 31.37dB for house image in Discrete Wavelet Transformation (DWT) than compared to other encoders. It consumes less computation time to attain superior CR with a better quality of reconstructed picture than DCT based Huffman, Golomb-Rice (GR) coder and Low Complexity, Low memory Entropy Coder (LLEC), DWT based Arithmetic, GR code, LLEC.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.