Analog circuits are a critical part of industrial electronics and systems. Estimates in the literature show that, even though analog circuits comprise less than 20% of all circuits, they are responsible for more than 80% of faults. Hence, analog circuit fault diagnosis and isolation can be a valuable means of ensuring the reliability of circuits. This paper introduces a novel technique of learning time–frequency representations, using learnable wavelet scattering networks, for the fault diagnosis of circuits and rotating machinery. Wavelet scattering networks, which are fixed time–frequency representations based on existing wavelets, are modified to be learnable so that they can learn features that are optimal for fault diagnosis. The learnable wavelet scattering networks are developed using the genetic algorithm-based optimization of second-generation wavelet transform operators. The simulation and experimental results for the diagnosis of analog circuit faults demonstrates that the developed diagnosis scheme achieves greater fault diagnosis accuracy than other methods in the literature, even while considering a larger number of fault classes. The performance of the diagnosis scheme on benchmark datasets of bearing faults and gear faults shows that the developed method generalizes well to fault diagnosis in multiple domains and has good transfer learning performance, too.