Technical Abstract: A new adaptive time-frequency (t-f) analysis and classification procedure is applied to impact acoustic signals for detecting hazelnuts with cracked shells and three types of damaged wheat kernels. Kernels were dropped onto a steel plate, and the resulting impact acoustic signals were recorded with a PC-based data acquisition system. These signals were segmented with a flexible local discriminant bases (F-LDB) procedure in the time-frequency plane to extract discriminative patterns between damaged and undamaged food kernels. The F-LDB procedure requires no prior knowledge of the relevant time or frequency indices of the impact acoustics signals for classification. The method automatically finds all crucial time-frequency indices from the training data by combining local cosine packet analysis and a frequency axis clustering approach, which supports individual time and frequency band adaptation. Discriminant features are extracted from the adaptively segmented acoustic signal, sorted according to a Fisher class separability criterion, post-processed by principal component analysis, and fed to a linear discriminant classifier. Experimental results establish the superior performance of the proposed approach when compared to prior techniques reported in the literature or used in the field. The new approach separated damaged wheat kernels (IDK, pupal, and scab) from undamaged wheat kernels with 96%, 82%, and 94% accuracy, respectively. It also separated cracked-shell hazelnuts from those with undamaged shells with 97.1% accuracy. The adaptation capability of the algorithm to the time-frequency patterns of signals makes it a universal method for food kernel inspection that can resist the impact acoustic variability between different kernel and damage types.