Analog Fourier Transform

When embarking for this project, we were not trying to create a method that is superior to a software performed DFT. Instead, we wanted to better understand the inner mechanisms that make a DFT work and see if it could be done through a pure analog approach. Current DFT techniques rely on using a processor to perform hundreds of calculations, but multiplication and integration could be augmented by an analog circuit. With recent research and efforts in analog circuitry for application specific we thought an analog approach to the computations would be just as accurate and fast. We quickly realized the fourier transform is quite optimized already and works extremely well in software.

The value of this approach is twofold: it allows us to explicitly understand a DFT instead of treating it as a magic black box, and it assesses whether the ubiquitous software approach to DFTs is the best approach. By recreating a DFT through circuitry, we had to first understand the math that makes a DFT possible, making use of the dot product and integration that fits a known frequency to unknown data. However, this approach made plain the complexity of these circuit implementations and how software makes these calculations far more accessible. As for efficiency and performance, the analog approach was susceptible to noise and component frequency response characteristics that muddled out data. Within a digital environment, no inherent noise is introduced to the calculations and performing a DFT function is far easier than building your own circuitry. This affirmed to us that the current approach of software defined DFTs was ideal when compared to an analog approach, but it did suffer from augmenting away the fundamental math that allows this wondrous algorithm to function. We hope that by approaching the DFT this way, we were able to highlight both why the digital approach to DFTs is so prevalent as well as the concepts that work together to make DFTs possible.

We also want this page to be accessible to others, so if more students and fascinated people want to make their own analog fourier transform we can give them a good foundation to do so. This project will hopefully give readers an understanding of fourier transforms and spark their interests and apply the fourier transform to projects they are interested in.

Application

Our project is intended to analyze any alternating electric signal. Instead of mechanical vibrations, our circuit could be used to understand the frequencies received by an antenna or the varying pulsations of an electrocardiogram circuit. For time limitations and testing purposes, all of the waves analyzed within the scope of this project were generated within LTSpice, but our circuit was made to be electrical signal agnostic, meaning any signal within the acceptable range of the physical components should work. Of course, electrical components such as capacitors and ICs are somewhat frequency dependent so their behavior shifts and this would have to be accounted for if we wanted to apply this concept further.