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We propose a novel algorithm for the compression of ECG signals, in particular QRS complexes. The algorithm is based on the expansion of signals with compact support into a basis of discrete Hermite functions. These functions can be constructed by sampling continuous Hermite functions at specific sampling points. They form an orthogonal basis in the underlying signal space. The proposed algorithm relies on the theory of signal models based on orthogonal polynomials. We demonstrate that the constructed discrete Hermite functions have important ad- vantages compared to continuous Hermite functions, which have previously been suggested for the compression of QRS complexes. Our algorithm achieves higher compression ratios compared with previously reported algorithms based on continuous Hermite functions, discrete Fourier, cosine, or wavelet transforms.