There is a growing research interest in proposing new techniques to detect and exploit signals/systems sparsity. Recently, the idea of hidden sparsity has been proposed, and it has been shown that, in many cases, sparsity is not explicit, and some tools are required to expose hidden sparsity. In this paper, we propose the Feature Affine Projection (F-AP) algorithm to reveal hidden sparsity in unknown systems. Indeed, first, the hidden sparsity is revealed using the feature matrix, then it is exploited using some sparsity-promoting penalty function. Also, the step-size parameter and the weight given to the penalty function are analyzed. Furthermore, two examples of the F-AP algorithm for lowpass and highpass systems are introduced. Finally, numerical results indicate that the F-AP algorithm provides several performance improvements when the hidden sparsity of coefficients is revealed.