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We present jump function Kolmogorov (JFK), a novel signal representation, which is (a) additive, thus the sum of signal and noise yields the sum of their JFKs; (b) sparse, therefore the signal and noise are separable in this domain. In this paper, the proposed signal representation is used in developing a classification system under noise-mismatch conditions. In this framework, we estimate JFKs from noisy signals in wavelet domain and compare them with the templates trained in clean condition. As the JFK is additive and sparse, the noise is simply eliminated by limiting JFKs only within the confidence intervals. The experiments show that the JFK-driven method significantly outperforms the conventional ones in three different classification tasks. The proposed method is further improved by adopting a discriminative feature selection for the classification.