Recently I have done an experiment in matlab where I have tried to calculate DFT of a sine wave with different phase shifting. I have figured out that it fails to detect 90 degree and 270 degree phase shift sine waves which should not be happen. Those missing information can be detected in imaginary part of DFT but I want to know how this problem is solved usually. In matlab we can only plot() or stem() real part of fft() outcome. Let me know if I am missing something in DFT basics.
I have attached the matlab code so that you can check the issue.
"Usually", you would work in the complex plane, then there is just one set of functions exp(i*k*x) with appropriate (signed) values of k.
If you insist on sticking to real numbers, you quickly find that you cannot represent a sine with cosines (the former is an odd function, the latter are even). Hence, if you want to represent a general signal as a sum of oscillations, you need to sum cosines _and_ sines. So the result that you get is perfectly fine. I am not sure if talking about the real and imaginary part is fruitful if you stay strictly in the domain of real numbers.
Hi Kazi,
the DFT does not fail.
For a sine, the spectrum is purely imaginary and if you plot only the real part you get nothing.
Plotting only the real part is the default option in matlab when you try to plot a complex function or vector.
You can plot separately the real and imaginary parts of the spectrum with different colors or you can plot the absolute value or both.
I have figured out what wrong I had done with my experiment. I was strictly considered the real part of discrete Fourier transform only, where the information that I was looking for is in the imaginary part. So I have to take absolute value of the fft() or dft() output which calculated both the real and imaginary parts magnitude in case of calculating discrete Fourier transform.
Thanks Jacques B Sombrin and Ulf Lorenz to make it more clear which helps me to understand the basics.
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