Suppose one observes a constant star each night at exactly the same time (i.e., a 1 day period), then the data analysis should display a period with a peak at 1 day. This is logical, as the peak is a direct result of the sampling frequency itself. The period is not the true period, but results from observing a (constant) object at exactly the same moment in time. See also Aliasing.

The Spectral Window in Peranso calculates the pattern caused by the structure of gaps in the observations. It is not a true Fourier spectrum for a star, but indicates what peaks in a Period Window are artifacts of your sampling. It is typically used in combination with any of the above period analysis methods, and is calculated to demonstrate that the period found by one of the above methods can not be the result of the data sampling.  

Tutorial 2 presents an example.