[newhouseb]

You don't need to sample at the Nyquist rate (i.e. 2x the intended measured frequency) to detect the presence of a particular signal but instead can just measure the overall power within a narrow frequency band of interest. Practically speaking this is done by mixing the sweep frequency down to at or around DC and then either directly measuring the power or sampling at a much lower rate and computing the power digitally.

[genewitch]

I don't think this is true, otherwise I could see the power on wifi bands with my 2.4ghz rtl-sdr device, instead of only up to 1200mhz.

[CamperBob2]

If you remove the front-end RF filter from your SDR, you can indeed pick up 2.4 GHz with it using harmonics of the ADC clock frequency. But the rest of the signal processing pipeline may be too narrow to receive much energy from a broadband WiFi signal, and what you do receive will probably just look like noise in any event.

You could probably observe the leakage from a nearby microwave oven without much difficulty, though -- in fact, that is likely to be possible even without modifying the RF filter.

Basically, Nyquist applies to the modulation bandwidth, not the carrier frequency.

[genewitch]

I'm having a hard time with this. Let's say i have an audio file in audacity at 8000hz samplerate. Can i mix in a 15khz sine wave? is there any way to represent a 15khz sine wave with 8000hz of spectrum?

I understand harmonics, but those generally don't work backward, do they? The phrase "subharmonic" comes to mind but i don't know when that actually applies. Does anyone have a link of an explanation?

If this were the case i could tune any of my radios to a subharmonic of an FMBC station and see/hear something, but i generally do not. I have a pure ADC laying around somewhere (for o-scoping), how can i prove this to myself experimentally?

[CamperBob2]

Here's one way to think about it, using an audio example. Let's say you are recording with a sound card whose ADC is clocked at 8K samples/second. You play a 15 kHz tone into the input jack. What gets recorded?

The answer is normally nothing at all. To satisfy Nyquist, your sound card uses a lowpass filter in front of its ADC with a cutoff frequency of 4 kHz. (In reality it has to be designed to cut off a bit lower since perfect filters don't exist, but never mind that.) The 15 kHz tone is so far out of band that it doesn't show up in the recording at all.

Now assume you grab a soldering iron and remove the lowpass filter from your sound card (again oversimplifying somewhat.) The line-in jack is now connected directly to the ADC input. What happens now? The 15 kHz tone will show up as an alias near some multiple of the clock frequency.

The TL;DR explanation is that each multiple of the clock frequency including the 0th has two so-called "Nyquist zones" associated with it, one above the clock and the other below it. The zone below DC is inaccessible when working with real signals, so we call the upper half of the DC zone from 0-4 kHz the "first Nyquist zone." This is where audio recording normally has to take place, since the frequency response of an audio signal chain (or an oscilloscope for that matter) needs to approach DC.

The second Nyquist zone runs from 4 kHz to 8 kHz, the third from 8 kHz to 12 kHz, the fourth from 12 kHz to 16 kHz, and so on. The latter zone is where the 15 kHz input will show up. It is 1 kHz below that clock multiple, so a 1 kHz tone is what will be recorded. When this happens accidentally, it's called "aliasing," and when done on purpose it's called "undersampling."

The key point behind the Nyquist theorem is that given an 8 ks/s recording made without an antialiasing filter in front of the ADC, there is no way to distinguish a 15 kHz input tone from a 1 kHz one. This can be awesome if you are building radios or test equipment, since it means you don't have to spend thousands of dollars on exotic ADCs and deal with the resulting firehose of data when all you wanted was to receive a narrowband signal at a high carrier frequency. It is not so awesome if you are trying to record audio from a mic or other source that isn't band-limited, though, because the higher frequencies will sound awful when they undergo aliasing.

I understand harmonics, but those generally don't work backward, do they? The phrase "subharmonic" comes to mind but i don't know when that actually applies. Does anyone have a link of an explanation?

A subharmonic is not an alias, and vice versa. It's a vaguely-defined term that doesn't correspond to any aspect of sampling theory. Subharmonics don't usually show up in audio contexts, but you run into the term in RF work where a frequency multiplier stage exhibits some leakage of the fundamental signal.

[genewitch]

Thanks, i didn't know that about aliasing.

[newhouseb]

Your rtl-sdr is _sampling_ at a mere ~3Mhz.

Much like a VNA, your rtl-sdr is down-converting from (say) 1.2Mhz to somewhere around DC. This is limited not by your sample rate but by the oscillator your rtl-sdr is mixing into your received signal and the general frequency profile of all the analogue bits in between.

[stagger87]

Who you're responding to is correct.