Talk:Chirp

message: I added the examples to the article, which I have now been told were wrong, and made the graphs with the same equations.  I haven't put in the time to understand the differences regarding instantaneous frequency, but, in the meantime, can someone post some references that show these equations?  (I don't see any references at all right now.)  I want to know for certain that this is what people actually use to make Doppler-immune chirp radars and such.  It's a little confusing. — Omegatron 14:37, 4 June 2006 (UTC)
thread_title:  Graphs 

message: How can we say that a chirp signal is bandlimited as well as time limited? does the term time-limited make sense? please explain. —The preceding unsigned comment was added by Krishna2531985 (talk • contribs) 05:13, 23 January 2007 (UTC)
thread_title:  Nature of chirp signal 

message: Surely the geometric and exponential chirps are the same. If the frequency is k^t, say, then k^(t+const) = (k^const)*(k^t), ie the frequency at t2 = (t1 + c) is a fixed multiple of the frequency at t1.  —Preceding unsigned comment added by 86.150.1.188 (talk) 18:01, 17 January 2008 (UTC)
thread_title:  Geometric same as exponential 

message: Based on computer experimentation, I believe that the hyperbolic frequency modulated (aka linear period modulation, aka logarithmic phase modulation) chirp \phi_i(t) = \frac{ln(T_0 + \beta t)}{\beta} has the property of ideal Doppler tolerance - is it possible for more than one type of waveform to have this property? That seems strange to me. If not, are these two different chirps somehow describing the same waveform? 146.6.204.185 (talk) 22:39, 22 March 2010 (UTC)
replies: text: I think there is a mistake in the article - isn't it the case that the Doppler effect modifies the instantaneous frequency as f_{Doppler}(t) = c f_{Original}(ct)? In that case, f_{Doppler}(t) = c f_{Original}(t) would be wrong, and that equation seems to be the basis of the claim that the exponential chirp is Doppler tolerant.
You are absolutely correct. The article is completely wrong about the doppler discussion. (Constant) Doppler simply scales the time axis, i.e., received signal is s_{Doppler}(t) = x(ct) for some c. For doppler tolerance, we need the originally transmitted (non-time scaled) chirp to line up with the received stretched/compressed chirp. I.e., s_{Doppler}(t) = x(ct) = c_1 x(t-shift). This holds for the hyperbolic chirp, but not for the exponential chirp.
The entire claim of doppler tolerance hinges on the claim that f(t)_{\mathrm{Doppler}} = c f(t)_{\mathrm{original}}, which is simply not true. In fact, it is true that f(t)_{\mathrm{Doppler}} = c_1 f(c_2 t)_{\mathrm{original}}, as per the explanation above. Note that the instantaneous frequency is defined as f(t) = f_0 k^t. Doppler results in c_1 f(c_2 t) = c_1 f_0 k^{c_2 t} = c_1 f_0 (k^{c_2})^t, which cannot be written as f(ct) = c_3 f(t).  — Preceding unsigned comment added by 24.15.198.199 (talk) 17:24, 2 December 2012 (UTC)
thread_title:  Exponential chirp vs hyperbolic chirp 

message: Noted that short-pulse (or high datarate) laser chirp interacts with optical fiber material disperion, increasing or decreasing pulse dispersion as the signal propagates. It does not change material dispersion, a fixed property of the fiber.  
Fabrice002 (talk) 12:49, 23 September 2011 (UTC)
thread_title:  Laser chirp 

message: Seems not existing anymore.  — Preceding unsigned comment added by 93.71.78.42 (talk) 17:17, 25 May 2012 (UTC)
thread_title:  Ref. 2 

message: I have written an overview on the derivation and properties of chirp spectra, which is currently at User:D1ofBerks/sandbox (and called "The Spectrum of a Chirp").  Originally it was submitted, incorrectly, as a new article but it is actually an addition, so doesn't need an intro of its own.  If the article is considered to be O.K., how do I get it transferred into the main article?   I think it would fit best after the subsection 'Uses and occurrences' and before 'See also'.  Please advise D1ofBerks (talk) 10:18, 16 May 2014 (UTC)
thread_title:  Transferring New Content 

message: In general, if a chirp has frequency f_0 at time t_0 and the frequency changes exponentially to f_1 at time t_1, the correct expression for instantaneous frequency is
f(t)=f_0\left[\frac{f_1}{f_0}\right]^\frac{t-t_0}{t_1-t_0}=f_0k^\frac{t-t_0}{t_1-t_0}
Note that this gives the correct instantaneous frequencies at t=t_0 and t=t_1.
Assuming t_0=0, this simplifies to
f(t)=f_0 k^\frac{t}{t_1}
But the currently published expression is
f(t)=f_0 k^t
I feel some change is needed to make the exponent dimensionless (and the expression correct). And the expression for Instantaneous Phase should have similar changes.
If on the other hand, if  t  describes some normalized/dimensionless time vector, this wasn't clear.  — Preceding unsigned comment added by 65.112.5.1 (talk) 19:29, 26 July 2014 (UTC)
thread_title:  Potential confusion in Expressions for Instantaneous Frequency and Phase of Exponential Chirp 

message: This most certainly needs a separate article, linked from and summarized (one paragraph max) in chirp. Also, although it's not WP:OR, it's bordering on WP:SYNTHESIS, so please be careful about the drawing conclusions not given in the sources cited. 
The tone should be more encyclopedic and less tutorial; e.g., it shouldn't explain what is a Fourier transform or why the FFT is preferable in practice. Also, figures in the DFT section seem to have wrong x-label: it should be in frequency units, not time units (i.e., hertz nor seconds). Finally, very little is said about the phase spectrum, which is crucial to discriminate between a chirp and an impulse function, both having similar power spectra. Fgnievinski (talk) 12:15, 14 November 2014 (UTC)
replies: text: @D1ofBerks,I also suggest that you develop a new article, as both @Binksternet and @Fgnievinski have suggested, with context, explanatory motivation, etc. DoctorTerrella (talk) 12:33, 14 November 2014 (UTC)

text: @D1ofBerks, in the spirit of constructive progress, yes, I'm cool with restoring the material I originally deleted, but please, then, move to a separate work in progress Sandbox. I'm glad to see that we all appreciate the utility of explanatory paragraphs for this material. Indeed, when I look at technical books, I usually prefer those with more words and less equations. Intuition is essential, maths can then follow from there. Thank you, DoctorTerrella (talk) 15:42, 15 November 2014 (UTC)
replies: text:  No need to sandbox it, it can go into an article of its own; improvements can be made live. Fgnievinski (talk) 16:35, 15 November 2014 (UTC)
replies: text: O.K., whatever works. DoctorTerrella (talk) 16:39, 15 November 2014 (UTC)

text: The problematic figures have x axis labeled "number of samples" but y axis labeled power spectral density; the x-label should be in frequency units. Also, it's funny you say the stationary phase method doesn't require phase information; you're working on the real (or imaginary) components, so its amplitude times cosine of phase -- phase is present. Finally, if the phase spectra plots look unpleasant, try unwrapping phase. Fgnievinski (talk) 16:35, 15 November 2014 (UTC)

text: As you well described, "sample number" is ambiguous; I'd strongly recommend multiplying the sample number by the sample time spacing and frequency spacing, then labeling x axes as time or frequency and their respective units. Fgnievinski (talk) 00:00, 16 November 2014 (UTC)
thread_title: Notability

message: When talking about the rate of change in frequency, the article calls it "chirpiness" and has two different spelling in the article (chirpyness and chirpiness). Should the spelling be homogenized to chirpiness? How widespread is this term? I can't find dictionaries mentioning this definition of chirpiness. Joancharmant (talk) 11:33, 10 September 2023 (UTC)
replies: text: If it is not in the dictionary, it would be best to rewrite to eliminate the word. Can we just replace these instances with rate of change in frequency? ~Kvng (talk) 13:09, 15 September 2023 (UTC)
thread_title:  Spelling of chirpiness 

message: Maybe there is typo in the definition of parameter k.
Shouldn't it just be f1 / f0, without any exponent? 2A0E:CB01:4B:D400:A57A:83E6:64:4F3A (talk) 12:39, 14 March 2024 (UTC)
thread_title:  Exponential chirp formula