- #1
4ierTrans4m3
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Hey guys,
I was imagining that I have a sine function: y = sin(x) where x represents a distance in meters for instance. Now let us say that I sample the function at x = 0,1,2,3...,10 (meters) producing a list of values: {sin(1), sin(2), sin(3),...,sin(10)} = {0.000, 0.841, 0.909, 0.141, -0.756, -0.958, -0.279, 0.656, 0.989, 0.412, -0.544}. Obviously I know that the "spacing" between each of these consecutive points would be 1 meter.
Now I take the DFT using Mathematica (using standard Fourier parameters), to get:
Fourier[{sin(1), sin(2), sin(3),...,sin(10)}] = {0.425 + 0.000*I, 0.570 - 0.270*I, -0.860 + 1.098*I, -0.034 + 0.218*I, 0.045 + 0.095*I, 0.066 + 0.028*I, 0.066 - 0.028*I,
0.045 - 0.095*I, -0.034 - 0.218*I, -0.860 - 1.098*I, 0.570 + 0.270*I}
Which is now a list of 11 complex numbers. It is my understanding that the independent variable will now have units of (1/meter)? Which would be a wavenumber? Let us just call this new independent variable k. Here is my real question. Imagine that now I plot the absolute value of this list of complex values on one axis vs k on the other axis. What would be the "spacing" (along the k axis) between each consecutive point in my transformed list?
Thanks for any help
I was imagining that I have a sine function: y = sin(x) where x represents a distance in meters for instance. Now let us say that I sample the function at x = 0,1,2,3...,10 (meters) producing a list of values: {sin(1), sin(2), sin(3),...,sin(10)} = {0.000, 0.841, 0.909, 0.141, -0.756, -0.958, -0.279, 0.656, 0.989, 0.412, -0.544}. Obviously I know that the "spacing" between each of these consecutive points would be 1 meter.
Now I take the DFT using Mathematica (using standard Fourier parameters), to get:
Fourier[{sin(1), sin(2), sin(3),...,sin(10)}] = {0.425 + 0.000*I, 0.570 - 0.270*I, -0.860 + 1.098*I, -0.034 + 0.218*I, 0.045 + 0.095*I, 0.066 + 0.028*I, 0.066 - 0.028*I,
0.045 - 0.095*I, -0.034 - 0.218*I, -0.860 - 1.098*I, 0.570 + 0.270*I}
Which is now a list of 11 complex numbers. It is my understanding that the independent variable will now have units of (1/meter)? Which would be a wavenumber? Let us just call this new independent variable k. Here is my real question. Imagine that now I plot the absolute value of this list of complex values on one axis vs k on the other axis. What would be the "spacing" (along the k axis) between each consecutive point in my transformed list?
Thanks for any help