# Noise floor offset

This is from an FFT of a signal. The thick bands are supposed to be the noise floor. But why does it seem to have offset? What caused noise floor offset? Do you consider the peak at the left for example as signal? If it is a signal. What kind of signal where the noise floor also rises up around that frequency?

• Are you calling that apparent little peak, about 1/5 in from the left, an "offset"? Commented Apr 25 at 1:28
• what i mean is, the area below the peak is white or empty..it shifted up
– Jtl
Commented Apr 25 at 1:31
• Well, that's because something got added to it. This is very noisy, but there is clearly a small sinusoid at that frequency. And the broadband noise, that is everywhere, got added to it. Commented Apr 25 at 1:49
• It is an FFT plot, not a waveform plot. how can FFT plot have sinusoid?
– Jtl
Commented Apr 25 at 2:48

The FFT plot as shown is a plot of magnitude versus frequency. The magnitude itself is random (due to noise) so will vary from sample to sample.

We see very similar results in the time domain, and perhaps that would be more intuitive to see so I will show that:

Below is the results for the magnitude of 1000 samples of additive white Gaussian noise in the time domain with a standard deviation of 1:

Zooming in closer on this plot, we see how some of the samples are closer to 0 and some are further away, in all cases we have a distribution of magnitude.

The fact that there is white space under the samples, as in the FFT plot, indicates magnitudes that are further away from 0.

We also see distinct areas that are elevated in the OP's plot, indicating the presence of more energy at those frequency locations. This indicates a very low level, and noisy oscillation. As an example of this, I created a pure sinusoid and then added to that phase noise as demonstrated in the plot below:

The blue curve is a pure cosine exactly on a bin center with no added noise; the actual noise floor would be due to numerical precision, much lower than any typical range of magnitudes that we would plot. The orange curve has an added phase noise, and we can see how there is variation in the zero crossings. Any modulation of a pure tone (whether it be phase, frequency or amplitude) results in additional frequencies appearing in the spectrum adjacent to the "carrier". In this case the modulation is noise, so the additional frequencies that appear will also be presented as noise in the FFT adjacent to what would have otherwise been our pure tone.

The dB magnitude of the FFT of the time domain signal in this case, with and without the phase noise, is shown below.

What we see here, to interpret this, is the energy present at all the FFT bins in the case when phase noise was present, and that energy varies from bin to bin but also gets larger as we approach the carrier frequency. Refer to this link on Wikipedia if it still not clear how those "sidebands" are created.

Zooming in on the carrier frequency so that we see the specific bin to bin variation, we see the same behavior that was first introduced: the level is generally higher, but also varies from bin to bin due to the noise characteristic of what in this case was phase noise. Phase noise will be present in all typical sources of oscillations: when the source is of very high quality, generated with high-Q resonators, the phase noise will be very low. But any arbitrary oscillation that is picked up in a measurement will typically look very much like what the OP has shown here, indicating an oscillation with a lot of additional noise that could be phase modulation as I demonstrated and/or amplitude modulation.

• If the frequency of the peak is say 150Hz. How come in the FFT. the frequency nearby like 145Hz, 155Hz and adjacent also rises up. see green arrow in this sample figure. a4.pbase.com/o12/95/7576595/1/174501453.AbYKuJCZ.fftrisesup.jpg Using time domain plot. How do you explain why the adjacent frequencies rises up in the FFT?
– Jtl
Commented Apr 25 at 6:27
• Because it is not just a frequency at 150 Hz. Typically it is described as phase noise, but all frequency sources will have some sort of noise modulation on it-- the frequency cannot be exactly 150 Hz for all time but varies due to the noise that is present. So in the FFT you are seeing the amount of energy present at all frequencies. Also there is an effect called "spectral leakage" where a single tone in the FFT leaks into other bins, but that isn't what you are seeing here since there is so much noise (the noise is much stronger than the typical leakage we would see) Commented Apr 25 at 10:50
• @Jtl I updated to answer your question in more detail. Commented Apr 25 at 12:21
• Hi im confused about how the entire noise floor can rise up. pls give comment or answer here if you have time many tnx dsp.stackexchange.com/questions/93884/…
– Jtl
Commented May 7 at 11:44
• Hi im quite confused how the entire noise floor can rise up. pls comment or reply on the following if you have time. many tnx dsp.stackexchange.com/questions/93884/…
– Jtl
Commented May 7 at 11:45