A Generalised Transform Methodology Using Quantum Computation and Its Application for Electrocardiogram (ECG) Classification

Transforms play a pivotal role in the study of signals and images. With the advent of quantum systems, analysing signals in the quantum domain is of particular interest. In this work, we aim to build a generalised transform circuit in the quantum domain. We have shown the working of this circuit for Wavelet transform, Fourier transform, and Discrete Cosine Transform (DCT) on $1-D$ vector, $2-D$ matrix, and an image respectively. We also take inverse transforms in each of the cases to match with the given initial input. We use simulators for this work, and the results obtained are favourable. We further use this circuit for classification of heart beats as it is an essential task in detection of cardiac diseases. We utilise both classical and quantum computation to classify beats of Electrocardiogram (ECG, hereafter) signals into normal and not-normal beats (non-beats and abnormal beats). This novel architecture to carry out transform is quite general and can be used for any arbitrary transform.