This is in essence how convolutional neural networks work- most often, looking at small patches of an image with many overlapping windows and the same core model looking at each. Then the same can be done for the output of the very small patches to get summarization of slightly larger patches of the image, and so on. At the end, the output is coming from many different analyses of different, overlapping segments of the data considered together.

I'd be wary of creating explicit synthetic examples that contain e.g. exactly one cycle of interest or whatever unless you know for a fact that it's how the model will be evaluated. You can imagine how snipping out a cycle from beginning to end could give an easier problem than taking segments of the same length but with random phase, for example. It may be simpler and more robust to do this in the model directly with convolution and feed in the whole series at once.