Take an example IMD term from the sinusoidal version: a1*a2*a2*cos[ (-2w2+w1)*t]. The generalization for rectangular spectra is to have a1 and a2 be (baseband) time functions rather than constants. They may have rectangular spectra or any shape.
Define the spectral bandwidth of a1(t) and a2(t) to be bw1 and bw2. Multiplying functions in time corresponds to convolution in freq. domain. Thus the sample term above has a bandwidth defined by the convolution [ a1(t) convolve a2(t) convolve a2(t) ]. The spectral bandwidths add when spectra are convolved. Therefore, this example term has a spectral bandwidth of bw1+2*bw2 centered at f = -2*f2+f1 . Each term in the expansion is treated similarly. Clearly, the maximum spectral width of the third order terms is 3*bw1 or 3*bw2 , whichever is larger.
The same principles apply to higher order IMD.
In the sheet, the attempt to create rectangular spectra is wrong. See comments in attached.
Lou
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