I have a pretty basic doubt about how tuning works in spectrum analyzers. I'm reading about the topic from Keysight's AN 150.
The problem arises in this paragraph in page 11:
We need to pick an LO frequency and an IF that will create an analyzer with the desired tuning range. Let’s assume that we want a tuning range from 0 to 3.6 GHz. We then need to choose the IF. Let’s try a 1-GHz IF. Because this frequency is within our desired tuning range, we could have an input signal at 1 GHz. The output of a mixer also includes the original input signals, so an input signal at 1 GHz would give us a constant output from the mixer at the IF. The 1-GHz signal would thus pass through the system and give us a constant amplitude response on the display regardless of the tuning of the LO.
The sentence in bold is what confuses me. As far as I know, the product of two sinusoids of different frequencies returns two sinusoids at the difference and the sum of the original frequencies. So how is it possible that the original input and LO frequencies are present after the mixing?