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[edit] How to use the DFT, with Matlab examples
DFT quick reference
| What is it? |
DFT element |
matlab example and comments |
| How often do you want to sample? |
sampling frequency fs |
| fsample=100; |
| sample at 100Hz |
| psample=1/fsample; |
| sample period |
|
| For how long do you want to sample? |
time range  |
| tmax=10; |
| run from 0 to 10 sec. inclusive |
|
| How many samples does that give you? |
N |
| nsamples=tmax/psample+1; |
| +1 because we include t=0 and t=tmax. |
| nsamples=2^ceil(log2(nsamples)); |
| round up to a power of 2 in length so FFT will work. |
| times=(0:psample:(nsamples-1)*psample)'; |
| Create a column vector of sample times. |
|
| How far apart are each of the frequency-domain result points? |
 |
| delf=fsample/nsamples; |
| frequencies=(0:delf:(nsamples-1)*delf)'; |
| Column vector of result frequencies |
|
| What signal do you want to sample? |
input x(t) |
| x=sin(2*pi*10*times)+sin(2*pi*3*times); |
| Make a 10Hz sine wave plus a 3Hz sine wave |
|
| What are the results? |
Fourier transform  |
fft_x=fft(x, length(x)); |
| What frequencies does the signal have? |
Xm(f) = | X(f) | |
fft_x_mag=abs(fft_x); |
| What phase relationships? |
 |
fft_x_phase=unwrap(angle(fft_x)); |
| How do you view the results? |
|
| plot(frequencies, fft_x_mag); |
| Or, to match the amplitude of the magnitude peak to the amplitude of the sine wave, |
| plot(frequencies, (2/nsamples)*fft_x_mag); |
|
| What about the power spectrum? |
Xp(f) = | X(f) | 2 |
| fft_x_power=fft_x_mag.^2; |
| plot(frequencies, fft_x_power); |
|
[edit] References
Lyons, Richard G. Understanding digital signal processing. Upper Saddle River: Prentice Hall PTR, 2001. ISBN 0-201-63467-8. Chapter 3 discusses the DFT.
