computer or microcontroller, we
have to use a discrete technique.
As you read through this article,
be aware that this is not a leisurely
read. If this is your first time
experimenting with the DFT, you
will need to have your sleeves rolled
up and your brain focused. Our
discussion will be about DFT theory
and the Excel spreadsheets that you
will be using to experiment with
Also keep in mind that my
purpose here is to provide only a
general introduction to the DFT and
to provide the boilerplate tools necessary to launch into an independent
detailed study or microcontroller
implementation (see suggestions for
First, we’ll discuss correlation —
the basic building block of the DFT.
Then we’ll extend correlation to
sampled signals, which is necessary
for microcontroller and computer
applications. Next, a functional DFT
program will be demonstrated in Excel
with a simple application. Finally, I’ll
wrap up with a quick overview of
aliasing, a nasty phenomenon you’ll
want to avoid.
Loosely speaking, this is a number
that represents how well two signals
are matched. The higher the correlation (or greater the value), the better
they match. Correlation is found by
multiplying the respective elements
of two sampled signals together
and adding each product together.
To make this clearer, see Figure sets
2a and 2b.
Figures 2a3 and 2b3 are the products of the other two related signals.
They contains points both above and
below zero. So in summing the correlation, some points will be added and
others subtracted. In Figure set 2b, the
input and correlation signals are the
same (2a1 and 2a2), so all of the
FIGURE Set 2b. These three graps
show signals with excellent correlation.