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I am doing some research on low-cost air pollution sensors. I'm measuring the "ground truth" with a single low-noise sensor, and I'm trying to use it to calibrate a low-cost sensor that has high noise. My goal is to reduce the noise of the low-cost sensor so that I may better calibrate it to the low-noise one.

I want to use low-pass filters to remove the noise of low-cost sensor, because in general it has a slow response time, meaning higher frequency components are almost purely noise.

In order to analyze the performance of the filter, I want to figure out what frequency range in my signal has the highest signal to noise ratio. To do this, I calculate:

SNR

Where (Exp - Ground) is the "noise" of the sensor. The resulting plot looks like:

Magnitude(FFT(Ground)) / Magnitude(FFT(Noise))

Is it valid to call this a "signal to noise ratio" in frequency? If not, does such a thing exist? Or am I going about this wrong?

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