Exploring Signal Interpolation: A Comparative Study of Convolution, Regression, and SVM Methods

Abstract

Signal interpolation plays a critical role in various signal processing applications, including wireless communications, image processing, and radar systems. Accurately reconstructing signals from decimated samples is essential for maintaining data integrity and improving transmission efficiency. To this extent, this paper presents a comparative study of five signal interpolation methods: convolution with three types of deterministic signals (triangular, rectangular and sinc signal), statistical linear regression and support vector machine (SVM). All these methods were applied on a sinusoidal signal corrupted by noise at different signal to noise ratio (SNR) values and on a QPSK (Quadrature Phase Shift Keying) modulated signal with 25 different decimation factors. The comparison between the investigated methods was made based on the inter-correlation coefficient, Euclidean distance and determinism for sinusoidal signal corrupted by noise. Two additional parameters, namely Euclidean letter distance and Bit Error Rate (BER), were defined and used for the QPSK modulated signal. Our findings suggest that for the sinusoidal signal corrupted by noise convolution with sinc function outperforms the other methods in terms of Euclidian distance in at least 98.57% of the cases and at least 95.71% of the cases in terms of inter-correlation coefficient. In the case of QPSK modulated signal it is the SVM method which surpasses all the other methods in terms of intercorrelation coefficient and Euclidean distance, in 80% and 88% of the cases respectively. If the Euclidean letter distance and the Bit Error Rate are considered for comparison, in the case of the QPSK modulated signal, convolution with sinc function was found to outperform the other investigated methods for at least 80% and 60% of the decimation factors respectively.