Rectangular function

The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as:

Alternative definitions of the function define to be 0, 1, or undefined.

Relation to the boxcar function

The rectangular function is a special case of the more general boxcar function:

Where u is the Heaviside function; the function is centered at X and has duration Y, from X-Y/2 to X+Y/2.

Another example is this: rect((t - (T/2)) / T ) goes from 0 to T, so in terms of Heaviside function u(t) - u((t-T) / T )

Fourier transform of the rectangular function

The unitary Fourier transforms of the rectangular function are

using ordinary frequency f, and

using angular frequency ω, where is the unnormalized form of the sinc function.

Note that as long as the definition of the pulse function is only motivated by the time-domain experience of it, there is no reason to believe that the oscillatory interpretation (i.e. the Fourier transform function) should be intuitive, or directly understood by humans. However, some aspects of the theoretical result may be understood intuitively, finiteness in time domain corresponds to an infinite frequency response. (Vice versa, a finite fourier transform will correspond to infinite time domain response.)

Roller coaster

A roller coaster is an amusement ride developed for amusement parks and modern theme parks. LaMarcus Adna Thompson obtained a patent regarding roller coasters on January 20, 1885, which were made out of wood, but this patent is considerably later than the "Russian mountains" described below. In essence a specialized railroad system, a roller coaster consists of a track that rises in designed patterns, sometimes with one or more inversions (such as vertical loops) that briefly turn the rider upside down. The track does not necessarily have to be a complete circuit, as shuttle roller coasters demonstrate. Most roller coasters have multiple cars in which passengers sit and are restrained. Two or more cars hooked together are called a train. Some roller coasters, notably wild mouse roller coasters, run with single cars.

History

Russian mountain

The oldest roller coasters are believed to have originated from the so-called "Russian Mountains", which were specially-constructed hills of ice, located in an area that would later become St. Petersburg. Built in the 17th century, the slides were built to a height of between 21 and 24 m (70 and 80 feet), consisted of a 50 degree drop, and were reinforced by wooden supports.

Fasten Your Seatbelt (film)

Fasten Your Seatbelt (Hangul: 롤러코스터; RR: Rolleo Koseuteo; lit. "Rollercoaster") is a 2013 South Korean comedy film written and directed by actor Ha Jung-woo, in his directorial debut. The film made its world premiere at the 18th Busan International Film Festival, and was released in theaters on October 17, 2013.

Plot

A plane headed from Tokyo's Haneda Airport to Seoul's Gimpo Airport with a Hallyu star on board runs into an unexpected storm and is in danger of crashing. A plane full of absurd characters―both crew members and passengers such as a businessman, a monk and a paparazzo—go through a series of comical shenanigans.

Cast

Rollercoaster (B*Witched song)

"Rollercoaster" is a song recorded by Irish pop girl group B*Witched for their debut album, B*Witched (1998). It was written by group members Lindsay Armaou, Edele Lynch, Keavy Lynch and Sinead O'Carroll along with Ray "Madman" Hedges, Martin Brannigan and Tracey Ackerman, who also served as producer for the song.

On 29 September 1998, the group released "Rollercoaster" as their second single from the album, following "C'est la Vie" four months earlier. The track peaked at number one in the UK Singles Chart in October 1998 for two weeks.

Track listings

Charts and certifications

References

External links