Negative frequency: Revision history

2 June 2024

• curprev 22:5722:57, 2 June 2024‎ Bob K talk contribs‎ m 7,383 bytes +28‎ add whitespace between math formula and {{EquationRef}} template undo

11 February 2024

• curprev 21:1821:18, 11 February 2024‎ Bob K talk contribs‎ 7,355 bytes −109‎ →‎Further reading: delete misleading link, as per talk page undo

29 January 2024

• curprev 01:5501:55, 29 January 2024‎ Em3rgent0rdr talk contribs‎ 7,464 bytes +45‎ →‎Sinusoids: format fractions as {{Fraction}} undo Tag: Visual edit

28 January 2024

• curprev 21:5821:58, 28 January 2024‎ Bob K talk contribs‎ 7,419 bytes −1,834‎ →‎Sinusoids: simplified undo Tag: Visual edit: Switched

27 January 2024

• curprev 22:1522:15, 27 January 2024‎ Bob K talk contribs‎ 9,253 bytes −786‎ Re-simplify the lead, and remove incorrect example. undo Tag: Visual edit

23 November 2023

• curprev 18:0318:03, 23 November 2023‎ Cewbot talk contribs‎ m 10,039 bytes +4‎ Fixing broken anchor: 2023-04-26 #Rectangular vectors→Vector notation#Rectangular coordinates undo

27 September 2023

• curprev 06:4006:40, 27 September 2023‎ Citation bot talk contribs‎ 10,035 bytes −17‎ Removed parameters. | Use this bot. Report bugs. | #UCB_CommandLine undo

21 September 2023

• curprev 21:4521:45, 21 September 2023‎ Sdkb talk contribs‎ m 10,052 bytes +14‎ Correcting section link formatting, general fixes undo Tag: AWB

14 June 2023

• curprev 22:0822:08, 14 June 2023‎ 51.219.141.160 talk‎ 10,038 bytes −5‎ →‎Simplifying the Fourier transform: Corrected "most well-known" (grammatically incorrect) in first sentence of this section to "best-known". undo

13 February 2023

• curprev 15:4615:46, 13 February 2023‎ MatthiasSchneller talk contribs‎ m 10,043 bytes +1‎ →‎Applications: Correct a typo. undo

31 December 2022

• curprev 17:3517:35, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 10,042 bytes +5‎ →‎Sinusoids: emphasize "...only." undo Tag: Visual edit
• curprev 17:3417:34, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 10,037 bytes +55‎ →‎Sinusoids: Have "The sign of the underlying phase slope is ambiguous." be the introductory sentence for the next paragraph. And then instead of saying "The ambiguity is resolved when the cosine and sine operators can be observed simultaneously, ..." I try to explain how that ambiguity is resolved a bit better: "...the ambiguity about the phase slope is resolved simply by observing a cosine and sine operator simultaneously and seeing which one leads the other." undo Tag: Visual edit
• curprev 17:2417:24, 31 December 2022‎ Em3rgent0rdr talk contribs‎ m 9,982 bytes +3‎ "which" slightly better than "but" here I think. undo Tag: Visual edit
• curprev 17:2117:21, 31 December 2022‎ Em3rgent0rdr talk contribs‎ m 9,979 bytes −2‎ I guess should stick to "rotation" instead of "revolution" which can be said to have a distinct meaning. undo Tag: Visual edit
• curprev 17:1917:19, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,981 bytes +50‎ →‎Sinusoids: finally found a smaller negative sign for sin by using "text{-}" instead of just "-" in latex. Now I can write the pi-phase-shifted version of this sine wave with simply a negative sign, so readers can better see how this is from sine's odd function property. undo Tag: Visual edit
• curprev 17:0617:06, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,931 bytes −48‎ →‎Sinusoids: The phrase "e^(i*omega*t) clearly contains more information" was too big of claim to for "clearly". I'd think reader would need to see some bit of analysis to see why. I suppose the reason is because it contains both a frequency and a phase information. However that would have to be written out instead of just "clearly", and this sentence was already long enough that it would have to be a new sentence or paragraph, so I've deleted. Maybe analytic signal can explain instead. undo Tag: Visual edit
• curprev 16:5416:54, 31 December 2022‎ Em3rgent0rdr talk contribs‎ m 9,979 bytes 0‎ correction "clockwise" undo Tag: Visual edit
• curprev 16:5316:53, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,979 bytes +301‎ The rotating vector example was inside of "Sinusoids" section. However, I moved that example with its picture up to the introduction instead, which is explained as a sub-bullet under the first bullet point about a rotating object, and avoided using omega for frequency but rather explained them as +/-1 radian per unit of time. And explained in the caption a bit more. undo Tag: Visual edit
• curprev 16:2016:20, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,678 bytes +2‎ →‎Sinusoids: "the" instead of "a" vector, so is more clear we are talking about a specific vector, rather than just any vector. (Though "a" still works, I think "the" is better.) undo Tag: Visual edit
• curprev 16:1916:19, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,676 bytes +40‎ →‎Sinusoids: hyperlinked "vector" to Vector notation#Rectangular vectors so in case a reader isn't too clear what type of vector this is, they can figure out that it is an (x,y) vector from the link. undo Tag: Visual edit
• curprev 16:1416:14, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,636 bytes −25‎ →‎Sinusoids: deleted "in polar coordinates" because really this expression (\cos(\omega t), \sin(\omega t)) for a vector is for a cartesian coordinate system (first entry is x coordinate, second entry is y coordinate). In polar, these vectors would be represented as (radius=1,angle=+/-omega). undo Tag: Visual edit
• curprev 05:1905:19, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,661 bytes −238‎ agh...never mind, but that would be good to include *if* it was accompanied by an animation. undo Tags: Manual revert Visual edit
• curprev 05:1805:18, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,899 bytes +238‎ →‎Sinusoids: a vector of cos(wt),sin(wt) polar coordinates is mentioned in sinusoids. I think it is a good example to add to my bullet list at the top (would be really cool to show an animation of this!) undo Tags: Reverted Visual edit
• curprev 04:5904:59, 31 December 2022‎ Em3rgent0rdr talk contribs‎ m 9,661 bytes +5‎ →‎Simplifying the Fourier transform: reformat using {{slink}} so appears like "Euler's formula § Relationship to trigonometry" undo Tag: Visual edit
• curprev 04:5504:55, 31 December 2022‎ Em3rgent0rdr talk contribs‎ m 9,656 bytes +2‎ →‎Sinusoids: Too many identical words "cosine wave cos()" and "sine wave sin()". I find it reads better using "sinusoid" so at least the same words repeat themselves right next to eachother. undo Tag: Visual edit
• curprev 04:4004:40, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,654 bytes −42‎ →‎Sinusoids: I want to include <math>-\sin(\omega t - \varphi)</math>, but unfortunately the math formatting for '-' makes it look bad inside paragraph text, so I guess I will delete this negative but equivalent sine wave. undo Tag: Visual edit
• curprev 04:3804:38, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,696 bytes −93‎ →‎Sinusoids: forgot some '\' before sine\cos in <math>. Also since I already mentioned odd & even, I can delete my later invocation of trig identity. undo Tag: Visual edit
• curprev 04:2304:23, 31 December 2022‎ Em3rgent0rdr talk contribs‎ m 9,789 bytes 0‎ →‎Sinusoids: shift sinusoid hyperlink to first instance of the word. undo Tag: Visual edit
• curprev 04:2104:21, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,789 bytes +531‎ →‎Sinusoids: did a change of variables naming from theta to phi. Why? Because sine wave article that is the hyperlink for sinusoids uses phi for phase, and I believe should try to stick to same variable naming when possible. Also I use math formatting because it makes math equations look consistent. Also break off the cos & sin example into their own little paragraph that starts with invoking concept of odd and even functions and simplify wording a bit. undo Tag: Visual edit
• curprev 02:3502:35, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,258 bytes +88‎ clarify this bullet applies to functions represented in a Cartesian coordinate system undo Tag: Visual edit
• curprev 02:2102:21, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,170 bytes −9‎ trimmed down the absolute value meaning to just read as "how often some repeating event occurs". (I had forgot to include "...per unit of time" earlier). This new wording is better cause is more brief. Now this intro gets to the sign quicker. undo Tag: Visual edit
• curprev 02:1702:17, 31 December 2022‎ Em3rgent0rdr talk contribs‎ 9,179 bytes +746‎ revamped intro. First be as general as possible. Then provide three examples. "Sense" wasn't very useful to describe at all imho, and "rotation" was merely one very specific example. I spent a while thinking and came up with a more general wording in that sign expands upon the concept of frequency "...to also have a positive or negative sign representing one of two opposing orientations for occurrences of those events." undo Tag: Visual edit

30 December 2022

• curprev 23:4423:44, 30 December 2022‎ Em3rgent0rdr talk contribs‎ 8,433 bytes +26‎ →‎Sinusoids: slight tweak clarification, and broke up the stuff about aliasing into separate paragraph. undo Tag: Visual edit
• curprev 22:4222:42, 30 December 2022‎ Em3rgent0rdr talk contribs‎ 8,407 bytes +217‎ →‎Sinusoids: expanding with some clarification. The sum *involves* a cancellation...it is not only a cancellation (the real parts to add constructively). And the ambiguity about negative freq relates to cosine identify. And specify that "one of the two frequencies is a false positive" to be slightly more clear than just "includes". undo Tag: Visual edit
• curprev 22:1922:19, 30 December 2022‎ Em3rgent0rdr talk contribs‎ 8,190 bytes −5‎ →‎Sinusoids: Instead of using undefined pronouns ("it" & "this"), I'd prefer to spell out. And minor adjust: I think slightly better to use singular form of "frequency" by saying "a positive and a negative frequency" instead of "frequencies" so it is clear that it is *just* *two* frequencies. undo Tag: Visual edit
• curprev 22:1222:12, 30 December 2022‎ Em3rgent0rdr talk contribs‎ 8,195 bytes +7‎ →‎Sinusoids: inserted "merely" before "results in an ambiguity" to emphasize that this ambiguity isn't really that big of a deal, and give a heads up to prepare reader for the subsequent sentences that explain why. undo Tag: Visual edit
• curprev 22:0122:01, 30 December 2022‎ Em3rgent0rdr talk contribs‎ 8,188 bytes +100‎ →‎Sinusoids: I think it dramatically helps readers to spell out that this is a cancellation of imaginary components and write out the math for the imaginary sinusoids that are being cancelled. undo Tag: Visual edit
• curprev 21:5121:51, 30 December 2022‎ Em3rgent0rdr talk contribs‎ 8,088 bytes +14‎ →‎Sinusoids: I'm inserting "somewhat misleading" before interpretation so the reader is prepared to accept the next sentence that this sum is actually a cancellation. Maybe there is a better adjective to insert before "interpretation". undo Tag: Visual edit
• curprev 20:3720:37, 30 December 2022‎ Em3rgent0rdr talk contribs‎ m 8,074 bytes 0‎ →‎Simplifying the Fourier transform: minor text formatting opinion: "idealized" is what is better to be italicized, cause we are emphasizing that this is the *idealized* Fourier transform. undo Tag: Visual edit
• curprev 20:2720:27, 30 December 2022‎ Em3rgent0rdr talk contribs‎ 8,074 bytes +78‎ →‎Simplifying the Fourier transform: Because I deleted "Although most functions do not comprise pure sinusoids (infinite duration), that idealization is the easiest and most common way of understanding this topic." from slink{{Fourier_transform|Complex_sinusoids_and_negative_frequency}}, I've readded extra wording from that here where I think it belongs better and tweaked the wording slightly and broke it into its own little "Note that" paragraph cause it is sortof an "aside". undo Tag: Visual edit: Switched

29 December 2022

• curprev 13:4013:40, 29 December 2022‎ Bob K talk contribs‎ 7,996 bytes +253‎ →‎Further reading: add a reference undo

28 December 2022

• curprev 14:5214:52, 28 December 2022‎ Bob K talk contribs‎ m 7,743 bytes +9‎ →‎Simplifying the Fourier transform: clarification undo

19 December 2022

• curprev 19:3119:31, 19 December 2022‎ Bob K talk contribs‎ 7,734 bytes 0‎ →‎Sinusoids: make a vague claim more specific undo Tag: Visual edit

17 November 2022

• curprev 16:5616:56, 17 November 2022‎ 154.121.31.107 talk‎ 7,734 bytes 0‎ Correct 'in' to 'it' undo

11 May 2022

• curprev 15:3215:32, 11 May 2022‎ Bob K talk contribs‎ m 7,734 bytes +5‎ →‎Simplifying the Fourier transform: reword a sentence undo

19 March 2022

• curprev 15:0915:09, 19 March 2022‎ Bob K talk contribs‎ 7,729 bytes +247‎ →‎Sinusoids: add one sentence undo
• curprev 13:1413:14, 19 March 2022‎ Bob K talk contribs‎ 7,482 bytes +43‎ →‎Simplifying the Fourier transform: replace "more complicated" with hyperlink to "spectral leakage" undo

15 March 2022

• curprev 18:5918:59, 15 March 2022‎ Bob K talk contribs‎ 7,439 bytes +382‎ →‎Simplifying the Fourier transform: use an example undo
• curprev 13:3213:32, 15 March 2022‎ Bob K talk contribs‎ 7,057 bytes −78‎ →‎Sinusoids: remove unnecessary detail undo
• curprev 04:4104:41, 15 March 2022‎ Em3rgent0rdr talk contribs‎ m 7,135 bytes +1‎ typo undo Tag: Visual edit: Switched