I use a white-noise generator in an rf bridge to measure antenna impedance.
The receiver is an ordinary AM/CW/SSB communications type, nothing fancy, nothing 'coherent'.

As I approach the null of the bridge the signal is masked by receiver noise. To make it stand out I 'modulate' the noise with a 1kHz square wave (the noise source is switched on/off at about 1kHz.) I 'null' on the 1kHz audio, not the received noise power.

The question: What is the spectrum of the modulated noise and how is it different from that of the 'raw' noise?


Short answer: most likely white noise.

Long answer:

Amplitude modulation using a sinusoidal wave shifts the original spectrum in frequency by the sinusoids frequency. For instance, if there is a source with a square spectrum spanning -100Hz to 100Hz, and it is modulated by a 1000Hz sinusoid, it will have shifted the spectrum in both positive and negative frequency. Thew new spectrums will show two sources of energy from -1100Hz to -900Hz and 900Hz to 1100Hz. Effect of amplitude modulation with sinusoid

To answer your question, we also should consider that their source signal is white-noise, and the carrier signal is a square wave rather than a sinusoid. A square wave, rather than having a single peak in the frequency domain (such as a sinusoid does), has multiple harmonics of descending strength. Modulating with a square wave will create multiple images of your source signal to appear, each centered around the square wave's harmonics and scaled by the half the strength of the harmonic. Square wave spectrum

If your input signal is true white noise (really only observed mathematically), the shifted noise signals would only add up to more white noise. But, if you have band-limited noise, then you will see copies of the noise spectrum shifted to the square wave's harmonics.

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  • $\begingroup$ Ok, I understand how modulation produces sidebands. I'm familiar with the harmonics of a square wave. (I use square-wave modulation only because it's easier to turn the noise on/off than modulate it linearly.) $\endgroup$ – Pete Singleton Aug 13 '15 at 19:40
  • $\begingroup$ What still puzzles me is "If your input signal is true white noise the shifted noise signals would only add up to more white noise. " That is my picture of the spectrum. Given the receiver bandwidth is a few kHz and the noise source is from below 100kHz to above 30MHz, I don't see how the band-limiting of the source affects the received spectrum. Can you clarify? $\endgroup$ – Pete Singleton Aug 13 '15 at 19:54
  • $\begingroup$ BTW, the noise source is an avalanche diode, reputed to be a pretty good white noise source. It is followed by a wide-band amplifier, which does limit the bandwidth but not significantly for my purpose. $\endgroup$ – Pete Singleton Aug 13 '15 at 20:03
  • $\begingroup$ @PeteSingleton To clarify, "true white noise" in my description might be better described as white noise with infinite bandwidth. Mathematically, it's useful to describe noises as having infinite bandwidth, but practically all analog noises sources and analog systems have frequency limitations. $\endgroup$ – planetSunshine Aug 20 '15 at 10:37
  • $\begingroup$ @PeteSingleton, it is true that because the noise source bandwidth is much greater than the receiver bandwidth that it is unlikely that the band-limiting in the noise source will affect the output. What are the frequency ranges of the receiver? Since the modulating frequency is 1KHz, the modulated signal will have most of it's energy in the 99kHz to 30.001 MHz range. $\endgroup$ – planetSunshine Aug 20 '15 at 11:04

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