Teaching the concept of convolution and correlation using Fourier transform

TL;DR

This paper proposes a visual and hands-on teaching method for convolution and correlation using Fourier transforms on 2D spatial signals, enhancing student understanding through simulations and experiments.

Contribution

It introduces a novel teaching approach that combines simulations and optical experiments to clarify convolution and correlation concepts using 2D signals.

Findings

Student feedback was very positive.

The method effectively demonstrates differences between convolution and correlation.

Enhances understanding of signal processing concepts.

Abstract

Convolution operation is indispensable in studying analog optical and digital signal processing. Equally important is the correlation operation. The time domain community often teaches convolution and correlation only with one dimensional time signals. That does not clearly demonstrate the effect of convolution and correlation between two signals. Instead if we consider two dimensional spatial signals, the convolution and correlation operations can be very clearly explained. In this paper, we propose a lecture demonstration of convolution and correlation between two spatial signals using the Fourier transform tool. Both simulation and optical experiments are possible using a variety of object transparencies. The demonstration experiments help to clearly explain the similarity and the difference between convolution and correlation operations. This method of teaching using simulation and hands-on experiments can stimulate the curiosity of the students. The feedback of the students, in my class teaching, has been quite encouraging.