Fourier Problem
Problem Freq4P08
Name_______________________________________
        Here is the lab data.  Notice the large negative spikes in the oscilloscope trace.

For the record, you need to know this about the signal.         The FFT of the signal is shown below.  (It's a magnitude plot.)  (This in Mathcad, so the smallest index is 0 - not 1 like in Matlab.)

The only thing you see in the FFT is the spike at DC (frequency = 0).  However, enlarging the scale, you can see that there is something else.

There are spikes at 18 (although that one "slops over" a little bit into the 19th point!) and at 37 (which may justify calling the first spike at 18.5).  Calling it 18.5 will get us about where we should be.  Since the record is .05 seconds long, we need to multiply 18 by (1/.05) or 20.  That gives us noise at 360 Hz (or 370 for 18.5) and at multiples after that.

        Now, here's the data for the second data set (the 9.5 inch situation).  The noise spikes seem to occur a little less frequently.

Now, if we take the FFT and operate on it as above, we get this plot.

Here the strong components of this signal (except for the DC term!) seem to occur at 7, 14, 21 and 27 (whoops!).  Probably, the fact is that the first one isn't exactly at 7, but may be a little spread out.  Anyhow, the same computations as before will give frequencies of 140, 280, 420, etc.

        To reduce the lowest component by a factor of 10, we would need to have: