{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT2_017JF09_p43

MIT2_017JF09_p43 - 43 SPECTRAL ANALYSIS TO FIND A HIDDEN...

This preview shows pages 1–2. Sign up to view the full content.

43 SPECTRAL ANALYSIS TO FIND A HIDDEN MESSAGE 180 43 Spectral Analysis to Find a Hidden Message As you know, the fast Fourier transform ( fft() in MATLAB), turns time-domain signals x into frequency-domain equivalents X . Here you will analyze a given signal from the site and apply several of the common treatments so as to get clean power spectral densities. 1. First, download the x data file from the site; it is called computeSpectra.dat . This signal x looks like a mess at first because of the noise, but we will tease out some specific information about X . Make a plot of the data versus time, assuming the time step is 0.0001 seconds. What features do you see if you zoom in on x , if any? It’s an evidently narrowband signal with content around 1.6kHz (10krad/s), but prob- ably with a lot of noise. Overall it is very hard to see anything beyond this. 2. Use the FFT to make the transformed signal X . Plot the magnitude of X versus frequency; recall that the frequency vector corresponding to X goes from zero to the roughly the sampling rate (use the instructions from your previous homework). In your plot, only show the frequency range near 10000 rad/s where there is significant energy, and remember the 2 /n scaling that is needed to put FFT peaks into the same units as x . What do you see? See the top plot of the psd’s. There are about fifteen peaks at frequencies slightly above 10 krad/s. 3. Treatment 1: Windowing. The Fourier transform operation on a finite-length signal x assumes periodicity, and so any discontinuity between the last and the first points in x is a feature that will be accounted for in X . In general we don’t want this effect, because it muddies up the water and makes it harder to see the details in X that we are interested in. For this and some other reasons, it is common to multiply x by a windowing function, before taking the transform.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern