Oscillation-based testing of analogue electronic filters removes the need for test signal synthesis. Parametric faults in the presence of normal component tolerance variation are challenging to detect and diagnose. This study demonstrates the suitability of statistical learning and deep learning techniques for parametric fault diagnosis and detection by investigating several time-series classification techniques. Traditional harmonic analysis is used as a baseline for an in-depth comparison. Eight standard classification techniques are applied and compared. Deep learning approaches, which classify the time-series signals directly, are shown to benefit from the oscillator start-up region for feature extraction. Global average pooling in the convolutional neural networks (CNN) allows for Class Activation Maps (CAM). This enables interpreting the time-series signal’s discriminative regions and confirming the importance of the start-up oscillation signal. The deep learning approach outperforms the harmonic analysis approach on simulated data by an average of 11.77% in classification accuracy for the three parametric fault magnitudes considered in this work.