Talk:Ambiguity function

Some discussion of the mathematical definition of the function and a sample calculation would be helpful.


 * I have added some discussion of the definition; however, the explicit calculation is just integration, which outside the scope of the article and also somewhat boring. Calculations of autocorrelations or convolutions (which are closely related to the ambiguity function integral) can be found in their respective articles. CjPuffin  05:22, 26 February 2007 (UTC)

Diagram
I think your ambiguity diagram is incorrect. The zero-doppler cut should be triangular in shape, not the zero-delay cut. The horizontal axes appear to be transposed.


 * You are correct. The discussion page for the image says as much. I have to make a new one. :( CjPuffin 04:15, 2 July 2007 (UTC)


 * Alright, uploaded a corrected diagram and fixed the article. Thanks for the heads up. CjPuffin 04:26, 2 July 2007 (U TC)

More diagrams
With regard to diagrams, I realize it is difficult to see what's going on when you can't manipulate the 3d graphs. I will entertain suggestions for how to make them more easy to see. I also have original Matlab code for generating the plots (that also works in Octave) which I will make available if there is interest. CjPuffin 18:57, 3 July 2007 (UTC)

Ambiguity function and energy spectrum
I changed the property (5) listed in the section Properties of Ambiguity function as I think the previous statement was inaccurate and somewhat confusing. The equation previously listed doesn't quite makes sense to me (unless someone can provide me with details of the derivation). The energy spectrum can be derived from the ambiguity function by setting the doppler shift to zero and applying Parseval's theorem, i.e.

$$\int_{-\infty}^{\infty} s(t)s^{*}(t-\tau) dt = \int_{-\infty}^{\infty} S(f)S^{*}(f)e^{j2\pi \tau f} df = \chi(\tau,0)$$

So, $$\chi(\tau,0)$$ is the inverse Fourier transform of $$S(f)S^{*}(f)$$ and so $$S(f)S^{*}(f)$$ can be recovered by taking the Fourier transform of $$\chi(\tau,0)$$ as I've written down in the article. twotonkatrucks 22:29, 4 November 2007 (UTC) ן —Preceding unsigned comment added by 117.195.233.59 (talk) 20:46, 8 December 2008 (UTC)

Wideband ambiguity function
I added a short explanation of the difference between the wideband and narrowband definitions - this explanation is based on my own understanding, which i have come to by scribbling on paper since I don't have a textbook with detailed information about the ambiguity function. If I made any mistakes, please correct them. 146.6.204.45 (talk) 19:30, 16 March 2010 (UTC)

\exp, not {\exp}
Writing \exp in TeX with a backslash, rather than just exp, does not only prevent italicization; it also causes proper spacing to be used. Thus:
 * a \exp b
 * $$ a \exp b \, $$

But when you write
 * a {\exp} b

Then it looks like this, without proper spacing:
 * $$ a {\exp} b \, $$
 * $$ a {\exp} b \, $$

Michael Hardy (talk) 03:13, 3 May 2011 (UTC)

Calculating the Ambiguity function
There are important applications in which rapidly "batch" computing the ambiguity function for two sampled and recorded signals is important. There is a fairly large literature on the subject. The classic reference is. Yaman32 (talk) 01:40, 31 July 2021 (UTC)