In real-world applications, audio surveillance is often performed by large models that can detect many types of anomalies. However, typical approaches are based on centralized solutions characterized by significant issues related to privacy and data transport costs. In addition, the large size of these models prevented a shift to contexts with limited resources, such as edge devices computing. In this work we propose conv-SPAD, a method for convolutional SPectral audio-based Anomaly Detection that takes advantage of common tools for spectral analysis and a simple autoencoder to learn the underlying condition of normality of real scenarios. Using audio data collected from real scenarios and artificially corrupted with anomalous sound events, we test the ability of the proposed model to learn normal conditions and detect anomalous events. It shows performances in line with larger models, often outperforming them. Moreover, the model's small size makes it usable in contexts with limited resources, such as edge devices hardware.