I am looking to ways to store data points in the format $\left( x, y \right)$ where $x$ goes from $0$ to $255$, while $y$ can be either $0$ or $1$: (e.g. $\left[ 0, 1 \right]$ $\left[ 1, 1 \right]$ $\left[ 2, 0 \right]$ etc...). See graph below.

This is basically a clock (each "$x$" value is one clock cycle) recording when a button was pressed ($y = 0$ is button open, $y = 1$ is button pressed).

This would be a uC and EEPROM work, but I would like to investigate the possibility of making it simpler.

I recall that a set of point can be represented by a Discrete Fourier Transform (DFT).

Would it be possible to have:

  1. an Integrated Circuit (IC) that specifically just calculates DFT coefficients
  2. Points $\left( x, y \right)$ to be recorded and fed to the IC.
  3. IC calculates the DFT Coefficients and stores them in a memory (assuming said coefficient occupy way less than a full data set)
  4. When a new point is fed to the IC, this IC "updates" the DFT coefficients so this last point is also represented by the DFT.

I imagine this is impossible/impractical for two reasons:

  1. You cannot simply "update" a DFT: you have N points and calculates a DFT from these N points. It would not be possible to have one point and a DFT and just "include" this last point in an already calculated DFT.
  2. A dedicated IC for DFT probably is just a uC, so I may as well use any commercial board out there and store data in an EEPROM.

However I would appreciate more details on why this would be impractical.


Data set example

  • $\begingroup$ Regarding the second 1) in your question, you can have a look at the sliding DFT formula (one of the many links here: dsprelated.com/showarticle/776.php) which could be of help. It does exactly you suggest that cannot be done, adds the new data point and gets rid of the oldest one in a sliding manner. $\endgroup$
    – ZaellixA
    Oct 26, 2022 at 22:47
  • 3
    $\begingroup$ Why do you want to do this? If you store the data "as is" you just need 1 bit per sample. It doesn't get much better than that. What do you hope to gain from the DFT ? $\endgroup$
    – Hilmar
    Oct 26, 2022 at 23:41

1 Answer 1


Granted I've never heard about using the DFT as a data compression tool, I don’t see how it would benefit you:

If you need to retrieve the data somehow, you need a DFT (at least) the size of your input data.
An $N$ point DFT takes $N$ input samples and produces $N$ output samples… you won’t be saving any memory.

Arguably you will even add to the load since your input data is binary and the DFT output won’t be.


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