# What does clipping gaussian noise mean?

I found the subject at here like this "Does clipping noise colour the spectrum" When I researching for clipping noise.

But I can't understand because typically something has clipped means something has removed. But he has some different point of view about this. so I want to know what is the clipping noise and how to undertand the posing about "Does clipping noise colour the spectrum"?

# update

Especially, I want to know the meanning about clipping gaussian noise.

Especially this part IV. CLIPPING (CENSORING) A. Clipped observations model

• There were lots of these questions lately... Clipping occurs, when the amplitude is exceeding the bounds in digital domain. For example when using 16 bit data, you must fit everything between -32768:32767. You amplify to much - you clip. And that is distorting the amplitude. What is the clipping noise then? I am sure you can take it from here. – jojek Jun 2 '15 at 22:12
• Clipping is a nonlinear operation and while something is being removed by the clipping, what is removed is not what is being measured when you measure the spectrum. As a general rule, one gets an output signal with larger bandwidth when the input to the clipper is processed – Dilip Sarwate Jun 2 '15 at 22:14
• noise is an (unwanted) signal whereas clipping is a distortion. When a good signal is clipped it becomes severley (irrecoverably and nonlinearly) distorted and bad. When noise is added to a clear signal it becomes degraded and dirty. When a noise signal is clipped then possibly the clipping noise happens... :) The clipping operation, because of its very nonlinear character, has the tendency to add rich harmonics to the signal, which may be is why it is defined as a coloring opearation on the noise spectrum – Fat32 Jun 2 '15 at 22:58
• In the context of the OP's question, the concept of "clipping noise" is an aid to model and understand clipping. If the signal's allowed range is [0,255], but the actual signal is $s=-2,258,257$, we can think of the clipped signal as $s_c=s+n_c$, where the "clipping noise" $n_c=2,-3,-2$. – MBaz Jun 3 '15 at 0:46
• @Mbaz in the context of signal processing, the error resulting from clipping is considered to be a distortion and not a noise, however one is of course free to call his signals whatever way he finds appropriate as either a distortion or a noise. May be they are extending the termninology from Quantization noise model to clipping noise in a similar manner.. – Fat32 Jun 3 '15 at 7:48

If your noise has independent and identically distributed samples from a zero-mean distribution (for example Gaussian), it is white. Other definitions of white noise also require the distribution to be symmetrical, but that is not required for the spectrum to be flat. Clipping the samples of such white noise will only change the common probability distribution of the samples: This will affect the mean of the distribution, but if both sides are clipped in a way that preserves the zero mean of the distribution, then there is no "coloring" of the spectrum by a 0 Hz peak and the noise remains white.

Example in Octave (MATLAB clone):

Create random variables from a Gaussian distribution:

N = 65536;
x = normrnd(zeros(N, 1), ones(N, 1));


Clip from above:

y = min(x, 1);


Clip symmetrically from below:

z = max(y, -1);


Plot values of Gaussian random variables (blue), clipped above (green), clipped symmetrically (red). Horizontal axis = index, vertical axis = value:

plot(1:N, x, 1:N, y, 1:N, z) Plot spectrum of Gaussian random variables (blue), clipped above (green), clipped symmetrically (red). Horizontal axis = frequency, vertical axis = magnitude:

loglog(1:N/2, abs(fft(x)(1:N/2)), 1:N/2, abs(fft(y)(1:N/2)), 1:N/2, abs(fft(z)(1:N/2))); The sequence that was clipped from above has a spectral peak at 0 Hz. Otherwise, the spectral envelopes are flat. This is not very easy to see because of the increasing density of plot points in the high frequencies in the logarithmic scale plot.

• I guess from his question that OP is not talking about a white noise... May be he should make it clear... – Fat32 Jun 3 '15 at 22:23
• @Fat32 yes I am talking about a gaussian noise clipping. – gmotree Jun 3 '15 at 23:36
• Gaussian noise can be white. Yours isn't? – Olli Niemitalo Jun 4 '15 at 5:18
• I added an example. – Olli Niemitalo Jun 4 '15 at 15:18
• It depends. If you clip it so that the mean of the sample value distribution remains 0, the expected spectrum of the noise process remains flat. If you clip it so that the mean of the distribution becomes non-zero, the spectrum will no longer be flat but will have a higher peak at 0 Hz. The rest of the spectrum remains flat. – Olli Niemitalo Jun 8 '15 at 5:46