Talk:Chirp spectrum

A typo

In the definition of the linear chirp, there is a factor of "2" in the denominator. I think this should not be there. — Preceding unsigned comment added by Elee1l5 (talk • contribs) 22:34, 2 October 2016 (UTC)

Response to 'A typo'

The phase, as a function of time, is given by $\theta (t)={\frac {\Delta \Omega }{2.T}}.t^{2}$
Differentiate this to find the frequency function $\omega (t)={\frac {d\theta }{dt}}={\frac {\Delta \Omega }{T}}.t$
This is a linear change of frequency, with time, starting at $-{\frac {\Delta \Omega }{2}}$ when $t=-{\frac {T}{2}}$ and finishing at $+{\frac {\Delta \Omega }{2}}$ when $t=+{\frac {T}{2}}$, giving a total linear sweep of $\Delta \Omega$ as required.
D1ofBerks (talk) 17:17, 26 October 2016 (UTC)

Reads like original research

Requires motivation, especially in the lead, where the material presented below should already be summarized in standard references. Isambard Kingdom (talk) 01:03, 21 March 2015 (UTC)

Deriving a Waveform from a Target Frequency Spectrum

There are a number of errors in this article and I will get around to addressing them but this section has a glaring one, which needs to be fixed asap. Yes, it is a great idea to construct the desired chirp in the Fourier domain, specifying the desired amplitude shape (constant amplitude - a rectangle). and then guessing the phase required to give an acceptable crest factor. The resulting inverse transform is not of semi-infinite duration. If you construct the spectrum with N points in the positive frequencies, then there are of course 2N points and there will be 2N points in the time series. Actually, of course you would include both zero and the Nyquist frequency in your spectrum, so you design with N+1 points to obtain a time series with 2N points. Most numerical packages (NAG library, Matlab, Igor Pro etc) automatically take a spectrum with an odd number of points and fold it appropriately to get an even number, which can then be inverse transformed.

Also, I don't understand this dwelling on the delta-T product - surely it's just N/2? Frank van Kann 04:12, 8 September 2022 (UTC) — Preceding unsigned comment added by Frank van kann (talk • contribs)

The expression for n in the Linear Chirp section

In the expression for n in the Linear Chirp section, the ω₀ term should be replaced with ΔΩ. In this section ω₀ is zero. When ω varies from -ΔΩ/2 to ΔΩ/2, n varies from -3 to -1 regardless of the bandwidth supporting the author's claim that the result depends solely on the time bandwidth product. Quantumken (talk) 19:36, 20 April 2023 (UTC)

Linear chirp

Hi, I have several comments about the linear chirp section:

1. The second sentence says that the frequency range is $[-\Delta F/2,\Delta F/2]$, implying a central frequency of $\omega _{0}=0$. In that case, the expression for s(t) should have only the quadratic term; the linear term implies that the central frequency is $\Delta \Omega$ (compare to the first formula in Chirp spectrum#Chirp pulse).
2. Why limit to the case of $\omega _{0}=0$ (or of $\omega _{0}=\Delta \Omega$ for that matter)? The same derivation works perfectly with any $\omega _{0}$, so that the chirp sweep can become much more general, with a total sweep of $\Delta \Omega$ around a central frequency of $\omega _{0}$. The current definition of $n$ in the article actually complies with this generalized derivation (see @Quantumken's comment in the previous topic of this talk page).

E L Yekutiel (talk) 15:14, 17 March 2024 (UTC)