This paper focuses on the problem of data representation for feature selection and extraction of 1D electronic nose signals. While PCA signal representation is a problem dependent method, we propose a novel approach based on frame theory where an over-complete dictionary of functions is considered in order to find the near-optimal representation of any 1D signal considered. Feature selection is accomplished with an iterative methods called matching pursuit which select from the dictionary the functions that reduce the reconstruction error. In this case we can use the representation functions found for feature extraction or for signal compression purposes. Classification results of the selected features is performed with neural approach showing the high discriminatory power of the extracted feature.