Understanding IFFT: Revealing Hidden Tumor Reflections

Why Frequency Data Isn't Enough

When our NanoVNA measures S21 transmission, it gives us 201 data points across frequencies from 2 GHz to 3 GHz. That's useful—but it only tells us how much signal gets through at each frequency. It doesn't directly tell us when the signal arrives.

That's a problem. Because tumors create reflections. And reflections mean delays.

The Frequency vs. Time Domain

Think of it like this:

• Frequency domain – Tells you which notes are playing in a song (pitch information)

• Time domain – Tells you when each note is played (rhythm information)

For tumor detection, both matter. The tumor changes the frequency response (attenuation), but it also creates a delayed reflection (the signal bounces off the tumor and arrives later). To see that delay, we need time-domain data.

The Fourier Transform Bridge

The Fourier Transform (and its inverse, IFFT) lets us move between these two domains:

In simple terms:

• Forward FFT – Takes a signal in time and tells you its frequency components

• IFFT (Inverse FFT) – Takes frequency components and reconstructs the time-domain signal

We use IFFT to convert our S21 frequency data into a time-domain representation.

Why IFFT Reveals Tumor Location

Here's the key insight:

When our transmitting antenna sends a microwave pulse, it travels through the chest. Most of the signal goes straight to the receiving antenna. But some of it reflects off the tumor and arrives later.

In the time-domain signal, that reflection shows up as a peak at a specific time delay. That delay tells us how far the tumor is from the antennas (time = distance / speed).

From our experiments:

• Healthy phantom – Small reflections from tissue boundaries, but no strong peak

• Tumor phantom – A distinct peak appears at a specific time delay, indicating the tumor location

The 9 Features We Extract

From each path's time-domain signal, we extract 9 features:

Feature	What It Measures	Why It Helps
Maximum amplitude	Strongest reflection	Indicates tumor size/contrast
Peak location (index)	When reflection arrives	Indicates tumor distance
Mean	Average energy	Baseline tissue properties
Standard deviation	Variation in reflections	Tissue heterogeneity
90th percentile	Strong reflections	Tumor presence
10th percentile	Weak reflections	Noise baseline
Total energy	Sum of all reflections	Overall tissue density
Range (max – min)	Dynamic range	Contrast between tumor and healthy
Squared energy	Power of reflections	Highlights strong scatterers

A Simple Example

Imagine we send a pulse at time t = 0. The direct signal arrives at t = 2 ns. If a tumor is present, a reflection might arrive at t = 4 ns.

In frequency domain, this looks like a ripple (interference pattern). But it's hard to see. In time domain (after IFFT), you see two distinct peaks: one at 2 ns (direct), one at 4 ns (reflection). That's much easier to detect.

Our Results

Adding these 9 time-domain features per path (36 total) significantly improved our microwave model's ability to detect tumors. The IFFT features helped distinguish:

• Baseline (air) – almost no reflections

• Healthy phantom – small reflections from tissue boundaries

• Tumor phantom – strong, distinct reflection peaks

Visualizing IFFT

Imagine you have a recording of an echo in a cave. The frequency spectrum tells you which pitches echo. But the IFFT tells you when the echo comes back—and that tells you how far away the wall is. Same principle with tumors.

What's Next?

Now that we have time-domain reflections, we can combine them with frequency-domain attenuation. That's exactly what our feature vector does: 804 frequency points + 36 time-domain features = 840 total features.

In the next post, we'll explore the dielectric properties that make tumors visible to microwaves in the first place.