How Do I Create a Complex Gaussian Joint PDF Plot?

Upload and start working with your PDF documents.
No downloads required

How To Create PDF Online?

Upload & Edit Your PDF Document
Save, Download, Print, and Share
Sign & Make It Legally Binding

Easy-to-use PDF software

review-platform review-platform review-platform review-platform review-platform

How do I create a complex Gaussian joint PDF plot (example figure)?

You are confusing the "time domain" with the "frequency domain". The term "white noise" is based on an analogy with white light. The latter term means that all optical frequency components >>within the visible range<< are present with nominally equal intensity. When we refer to "white noise", again the meaning is context dependent. In the context of acoustics, it might mean that all frequency components in a band from 20 Hz to perhaps 15 kHz are present with equal spectral density, that frequency range being what human ears typically span. All of the above instances relate to the "frequency domain." But when we are looking at, for example, noise voltages, we may be interested in the "time domain" statistics. For example, what is the probability that the instantaneous noise voltage exceeds, say, 11.5 microvolts. In the time domain, "random" noise voltages tend to have a so-called "normal" or Gaussian amplitude distribution. This is especially likely to be true if the observed voltage is some kind of summation of >many< individual random electron motions. In that situation, a statistical concept called "the central limit theorem" becomes relevant. (can be googled!)

PDF documents can be cumbersome to edit, especially when you need to change the text or sign a form. However, working with PDFs is made beyond-easy and highly productive with the right tool.

How to Create PDF with minimal effort on your side:

  1. Add the document you want to edit — choose any convenient way to do so.
  2. Type, replace, or delete text anywhere in your PDF.
  3. Improve your text’s clarity by annotating it: add sticky notes, comments, or text blogs; black out or highlight the text.
  4. Add fillable fields (name, date, signature, formulas, etc.) to collect information or signatures from the receiving parties quickly.
  5. Assign each field to a specific recipient and set the filling order as you Create PDF.
  6. Prevent third parties from claiming credit for your document by adding a watermark.
  7. Password-protect your PDF with sensitive information.
  8. Notarize documents online or submit your reports.
  9. Save the completed document in any format you need.

The solution offers a vast space for experiments. Give it a try now and see for yourself. Create PDF with ease and take advantage of the whole suite of editing features.

Customers love our service for intuitive functionality



46 votes

Create PDF: All You Need to Know

The theorem states that for any sample, the probability of each of its individual components of the noise voltage to be outside that threshold is proportional to the square root of the sum of the squares of all of its other components. So, for example, if there are 10 million voltages and the median is 11.5 (as it very often is), the probability of an individual voltage exceeding 11.5 microvolts is then the sum of the square root of 10 million times the (10 million times median) average value. As you can see, this sort of quantization is generally beneficial for practical applications, and is a key ingredient of some of the best scientific codes in the world. This topic is a bit far-fetched for now, but the idea has been discussed here: I will add more on this in the days and weeks to come.