Internet of Things (IoT) devices generate massive amounts of time-series data during continuous operation. These IoT time-series data are crucial for monitoring device health, predicting failures, and ensuring system security. However, the characteristics of these data, such as long- and short-term dependencies, hidden periodicity, and noise, pose considerable challenges for anomaly detection. Although unsupervised anomaly-detection methods based on deep learning have progressed, their generalisability in handling noise and complex data still needs to be improved. This study proposes a novel unsupervised anomaly-detection method that leverages multi-scale temporal convolution networks and adaptive spectral analysis collaboration to mine the time–frequency characteristics of time-series data, effectively filtering noise and enhancing feature expression. To further improve the model’s generalisation ability, we employed a gated memory mechanism to capture and reinforce the time–frequency features in the data, thereby enhancing the accuracy of anomaly detection. In addition, we introduced a radial basis function (RBF) neuron layer to enhance the detection capability of subtle anomalies. From results of experiments on five publicly available IoT time-series datasets, it was concluded that our method outperformed existing baselines in terms of detection performance, with an average F1 score improvement of 19.22%, thereby significantly improving the detection accuracy and real-time performance.