Labels:black | darkness OCR: Non-Linear Transmission This example illustrates the effects of a non-linear transmission on the frequency spectrum of a wave. It can also be regarded as another example for the Fourier transform functions. Please oad the project fileDblFred'. First of all we construct a set of x co-ordinates using/did function (variabla). Note that the table length must be a power of 2 if you want to useRhdH/FFTRfunctions. Using the x co-ordinates we define a simple sine wave (variabloud. This should be seen as the input of some non-linear transmission device. Here, this device is represented by the variable consisting of a normal linear transmission and a quadratic transmission. To see the effect of this non-linearity, please plot thinputand output functions against into one diagram (use cubic splines). Now we want to see how this transmission has changed the frequency spectrum. We define two variablesspek_inputandspek_output yielding the spectra ofput and outputrespectively (if you compare the functions with those used in the tutorialri_Ang you will note that we have used the simpler, but risky, version; this is save here, because we can rely on the oscilla- tion with the highest frequency being zero). Again, plot these functions agaitlass time us- ing a marker-type diagram. There is only one point different from zero in the original frequency spectrum (with frequency 2). However, in the output spectrum there are three points. The output wave consists of a wave of the original frequency (2), a wave of the double frequency (4) and an overall additive constant ( frequency 0). You can now experiment with your transmission functiefun as well as with your origi- nal function (apun. For example, if you add a term depending on the third power of input, you will see a portion of the triple frequency in the output spectrum. On the other side, if you add a second frequency to the input (and revert to the original, quadratic output function), you can see oscillations whose frequencies are the sum and the difference respectively of the input frequen-
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