I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency component is present and the PHASE tells "where" the frequency component is in the image. I understood about the MAGNITUDE part but not able to understand PHASE part. Please explain what it means by "PHASE tells "where" the frequency component is in the image". Thanks
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2 Answers
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I don't think of the phase as providing information related to position or location.
A simple example might be illustrative. In 1-D, consider these two signals, x and y:
t = 0:0.001:0.1;
x = cos(2*pi*20*t) + cos(2*pi*30*t);
y = cos(2*pi*20*t + pi/4) + cos(2*pi*30*t - pi/6);
The magnitude spectrums of x and y are the same, but they're not the same signal; if you plot them, you'll see that they're different. In the frequency domain, you need both the magnitude and the phase to fully describe the signals. It doesn't make sense to refer to the harmonics as "being somewhere".
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The fourier transform decomposes a signal into basic sinusoidal waves that are phase shifted in such a way that when added together, they sum up to form the original time domain signal. The magnitude, is the energy that that particular frequency contributes to the summation.
