Carl Sagan well described this case in Con­tact. In the sto­ry, the researchers, led by Dr. Ellie Arroway, detect the large unam­bigu­ous sig­nal from the star Vega:

Briskly she entered the con­trol area and approached the main console.

“Evening, Willie, Steve. Let’s see the data. Good. Now where did you tuck away the ampli­tude plot? Good. Do you have the inter­fer­o­met­ric posi­tion? Okay. Now let’s see if there’s any near­by star in that field of view. Oh my, we’re look­ing at Vega. That’s a pret­ty near neighbor.”

Her fin­gers were punch­ing away at a key­board as she talked.

“Look, it’s only twen­ty-six light-years away. It’s been observed before, always with neg­a­tive results. I looked at it myself in my first Areci­bo sur­vey. What’s the absolute inten­si­ty? Holy smoke. That’s hun­dreds of jan­skys. You could prac­ti­cal­ly pick that up on your FM radio.

“Okay. So we have a bogey very near to Vega in the plane of the sky. It’s at a fre­quen­cy around 9.2 giga­hertz, not very mono­chro­mat­ic: The band­width is a few hun­dred hertz. It’s lin­ear­ly polar­ized and it’s trans­mit­ting a set of mov­ing puls­es restrict­ed to two dif­fer­ent ampli­tudes.” ‑Con­tact, Carl Sagan, Chap­ter 4.

The bright­ness is huge. A hun­dred Jansky’s is bright for an astro­nom­i­cal radio source, though not the bright­est. Fig­ure 1 below shows the Con­tact source on a graph of the spec­trum of radio sources. Because of its bright­ness, only some of the bright­est radio objects in the sky are brighter. At the scale of this graph, the band­width of a few hun­dred Hertz is neg­li­gi­ble. Nat­ur­al objects have much larg­er band­widths and pro­duce a spec­trum of sig­nal across many frequencies.

The con­tent of the mes­sage is unam­bigu­ous at first. It is the count­ing of the prime num­bers. Since there is no nat­ur­al phe­nom­e­non to gen­er­ate prime num­bers, the sig­nal by def­i­n­i­tion is from some kind of intelligence.

Next, the loca­tion of the source is the star Vega. Point­ing the radio anten­nas off axis (away from the sig­nal source) caused the sig­nal to fade; this val­i­dat­ed the loca­tion. The cen­ter strongest point of the sig­nal is the star Vega. The big­ger the anten­na that is used, makes this a tighter cir­cle of focus (like a zoom for an opti­cal lens). In the sto­ry, one char­ac­ter sug­gests some­one faked the sig­nal. This would have been impos­si­ble. Satel­lites do not move like stars. For each observ­er on the Earth, the place in the sky where the satel­lite would be locat­ed is dif­fer­ent for each observ­er. Geo­sta­tion­ary orbit only fix­es the posi­tion of the satel­lite as seen from the ground. The satel­lite would still move across the night sky. Fix­ing the satel­lite against the night sky would require con­sid­er­able dis­tance-near­ly the edge of the solar sys­tem. And the motion would be con­trary to any orbit that gets it out far enough not to be noticed would not move cor­rect­ly. I’m sure Dr. Sagan was well aware of these facts. I think it was a con­ve­nient point to use a lit­er­ary license for the story.

Up to this point in the nov­el, this is a Case I first con­tact. Human­i­ty has detect­ed a trans­mis­sion from an alien civ­i­liza­tion. The dis­cov­ery of the mes­sage’s addi­tion­al con­tent showed that the aliens were respond­ing to a human mes­sage they had received. Con­se­quent­ly, Con­tact changes to a Case II first contact.

Anoth­er Case I first con­tact is pre­sent­ed in 2001 A Space Odyssey by Arthur Clarke. Here, human­i­ty dis­cov­ers an alien arti­fact on the Moon. The arti­fac­t’s alien ori­gin is undis­put­ed, and it left an unmis­tak­able non-nat­ur­al sig­na­ture, reveal­ing its pres­ence. Although buried, its anom­alous mag­net­ic sig­na­ture, dubbed Tycho Mag­net­ic Anom­aly one (TMA‑1), led to its discovery.

Anoth­er pic­ture flashed on the screen; it looked like a con­tour map, though it showed mag­net­ic inten­si­ty, not heights above sea lev­el, the lines were rough­ly par­al­lel and spaced well apart; but in one cor­ner of the map they became sud­den­ly packed togeth­er, to form a series of con­cen­tric cir­cles-like a draw­ing of a knot­hole in a piece of wood.

                Even to an untrained eye, it was obvi­ous that some­thing pecu­liar had hap­pened to the Moon’s mag­net­ic field in that region; and in large let­ters across the bot­tom of the map were the words: TYCHO MAGNETIC ANOMALY-ONE (TMA‑1). Arthur C. Clarke 2001: A Space Odyssey chap­ter 11.

Dig­ging up the arti­fact revealed the Mono­lith which sig­naled Sat­urn. (Note the nov­el is a jour­ney to Sat­urn instead of a jour­ney to Jupiter. The arti­fact exca­va­tion revealed that the Mono­lith builders had left behind the mono­liths on the Moon and at Sat­urn for them. Though 2001 stip­u­lates that the aliens had vis­it­ed human­i­ty in the dis­tant past, there is no sign that the aliens received our radio trans­mis­sion or found any of our arti­facts. Oth­er than the sig­nal to Sat­urn, the aliens of 2001 had sent no detectable signals.

Upon reach­ing Sat­urn, we dis­cov­er the aliens pos­sess faster than light capa­bil­i­ties. We could clas­si­fy this as a case III con­tact. How­ev­er, the orig­i­nal short sto­ry of Clarke’s for which 2001: a Space Odyssey is based,

Torn MacAlester’s Fabulae Lunae

The Lunadyne Incident  and Other Stories (buy now)

Fabulae Lunae 1

Thunder Moon Tussle (buy now)

Fabulae Lunae 2

Mask of the Joyful Moon