Automated cattle activity classification allows herders to continuously monitor the health and well-being of livestock, resulting in increased quality and quantity of beef and dairy products. In this paper, a sequential deep neural network is used to develop a behavioural model and to classify cattle behaviour and activities. The key focus of this paper is the exploration of a joint time-frequency domain representation of the sensor data, which is provided as the input to the neural network classifier. Our exploration is based on a real-world data set with over 3 million samples, collected from sensors with a tri-axial accelerometer, magnetometer and gyroscope, attached to collar tags of 10 dairy cows and collected over a one month period. The key results of this paper is that the joint time-frequency data representation, even when used in conjunction with a relatively basic neural network classifier, can outperform the best cattle activity classifiers reported in the literature. With a more systematic exploration of neural network classifier architectures and hyper-parameters, there is potential for even further improvements. Finally, we demonstrate that the time-frequency domain data representation allows us to efficiently trade-off a large reduction of model size and computational complexity for a very minor reduction in classification accuracy. This shows the potential for our classification approach to run on resource-constrained embedded and IoT devices.