When choosing a window function, window duration, and/or transmission frequency (assuming sampling rate satisfies Nyquist), one may want to understand what sort of spectral leakage would occur at a frequency of interest.

It is known that a finite-duration window corresponds to a non-finite bandwidth frequency response (e.g. rect <-> sinc), and it is also known that a multiplication in the time domain corresponds to a convolution in the frequency domain.

Consider the simple case of a non-windowed, constant-frequency sinusoid in the time domain, which corresponds to a frequency response of two delta spikes centered around 0 Hz.

Applying a window function would convolve the frequency response of the window function (e.g. a sinc function) over the delta spikes.

**1.** Does this convolution of the window function extend to the negative frequencies when calculating the spectral leakage in the positive frequency components (and vice versa)?

I would say yes based on the above (time domain multiplication <-> frequency domain convolution), and the following two images ([source][1]) which I annotated in red.  But it leads me to question 2, which I find a bit concerning.

[![enter image description here][2]][2]

[![enter image description here][3]][3]


**2.** If spectral leakage does extend to opposite-sign frequencies, doesn't that imply window functions without a zero crossing at 2x of a frequency of interest would result in constructive and/or destructive interference ("spectral leakage") in the frequency response of the windowed duration at that frequency?  I.e., frequencies would interfere with themselves?

Here is an image ([source][4]) showing that even for a given window duration, some common window functions could result in a non-zero value at a frequency's negative counterpart:

[![enter image description here][5]][5]


  [1]: http://saadahmad.ca/fft-spectral-leakage-and-windowing/
  [2]: https://i.sstatic.net/mOgRE.png
  [3]: https://i.sstatic.net/DCn99.png
  [4]: https://upload.wikimedia.org/wikipedia/commons/f/f2/Window_functions_in_the_frequency_domain.png?1574635778748
  [5]: https://i.sstatic.net/nJlMX.png