Learning to See Signals Differently

I did not start with colorful brain plots or intuitive explanations.

I started with math.

In the second year of my bachelor’s, I was introduced to imaginary numbers. Like many students, I struggled with the idea at first, how could a number squared become negative? It felt abstract, almost artificial. But at the same time, it pulled me in. There was something fascinating about it.

I remember staying up late, going through different books and problems, trying to get comfortable with this idea of an “imaginary” domain. At that point, though, it felt disconnected from reality—interesting, but not obviously useful.

That changed when I took Signals and Systems course.

For the first time, I saw where those imaginary numbers actually belonged. They were not just mathematical curiosities, they were essential for understanding signals in the frequency domain. Through Fourier transforms, I learned that a signal is not just something that evolves over time; it can also be understood as a combination of frequencies.

That shift in perspective was not easy. At first, it all felt abstract again—formulas, integrals, transformations. I could follow the math, but I did not yet feel what it meant. It was like knowing the rules of a language without being able to speak it.

As a biomedical engineering student, I had spent time learning about the anatomy of the brain, how MRI machines worked, what EEG devices were measuring. The brain had always fascinated me, but it felt like a separate world from the math I was learning in Signals and Systems.

Then the two worlds collided.

I realized that those abstract concepts - the frequency domain, Fourier transforms, all of it — were not just mathematical exercises. They were the actual tools researchers used to study brain signals. The thing I found puzzling in one class was the key to understanding something I genuinely wanted to know more about.

That realization was what pushed me toward my master's. I wanted to go deeper, not just into the methods, but into the brain itself.

My master was where theory met reality. Real EEG data looks nothing like textbook examples, it is messy, noisy, and full of artifacts. Getting from that raw signal to colorful interpretable maps took months of working in MATLAB, applying Fourier transforms, building time–frequency representations, and learning to turn raw signals to beautiful visualization.

And then, those wiggly lines started to make sense.

The colorful time–frequency plots, something I had once seen as almost magical, became interpretable. I could see how different frequency components evolved over time, how certain patterns emerged in response to stimuli, and how these patterns related to underlying brain activity.

It felt like I found the tool to see the brain in a new way.

My research focused on the neural signatures of music perception. Specifically, how the brain responds to pleasant versus neutral musical excerpts. I spent more than two years working on this project, and over time, time–frequency analysis became more than just a method. It became a way of thinking.

I thought I would be satisfied with the tools I had. But I was wrong.

In seeking to go further, I was lucky to join a translational research team at Yale School of Medicine. The focus shifted to neuroimaging, computational modeling, and understanding how psychiatric disorders manifest in the brain and how patients respond to treatment. The more I learned the methods behind those colorful brain maps, the more I wanted to understand.

After two years, I moved to the Aphasia Lab, and got involved in a study combining both EEG and MRI. EEG came back into the picture.

This time, however, I was the only engineer in a team of clinicians and researchers from very different backgrounds. And that is when I realized something important: understanding a concept is very different from being able to explain it.

Time–frequency analysis, which had become intuitive to me, was anything but intuitive to others. Terms like Fourier transform, convolution, or even frequency-domain representation could easily become barriers instead of tools. I had to find ways to explain those concepts to people who were sharp, but who had not come from a mathematical background.

I could not start with equations. I had to start with figures and intuition.

I began describing signals as combinations of rhythms, like layers of musical notes playing together. The time domain shows how the signal changes moment by moment, while the frequency domain reveals the building blocks behind those changes. Time–frequency analysis, then, becomes a way to watch those building blocks evolve over time.

That shift changed how people engaged with the concept.

And interestingly, it also changed how I understood it.

What once felt like a purely mathematical framework became something more human, something that could be explained, shared, and connected to real experiences. Looking back, my path into time–frequency analysis was not a straight line. It started with abstract mathematics, moved through implementation, and only later became intuitive and meaningful.

If there is one thing I’ve learned, it is this:

Those colorful plots are not magic. And yet, the more I understood them, the more extraordinary they became.