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.)

Johnny (Johnny Mathis album)

Johnny (1963) is the 19th album released by singer Johnny Mathis. It is his 15th original studio album, with four compilations of hit singles having been released by him at this point.

Overview

Collaborating once again with arranger/conductor Don Costa who had scored Rapture the previous year, Mathis is heard in a program of ballads and swingers. As with most of Mathis' albums around this time, the program is made up of well-known standards through to rarer material making for an interesting listening experience.

Track listing

Johnny (John Farnham album)

Johnny is the fifth studio album by Australian pop singer John Farnham, (who was billed then as "Johnny" Farnham) which was released on HMV for EMI Records in August 1971. It peaked at #24 on the Australian Kent Music Report Albums Charts. Farnham had earlier #1 singles with "Sadie (The Cleaning Lady)" in 1968 and his cover of "Raindrops Keep Fallin' On My Head" in 1970; a non-album single, "Acapulco Sun" was released in May 1971 but there were no charting singles from Johnny. The album features compositions from artists as diverse as George Harrison, Elton John, Stevie Wonder, Joe South and George Gershwin and Ira Gershwin

Background

Johnny Farnham's first #1 single on the Go-Set National Singles Charts was the novelty song "Sadie (The Cleaning Lady)". Selling 180 000 copies in Australia, "Sadie (The Cleaning Lady)" was the highest selling single by an Australian artist of the decade. His second #1 was a cover of B. J. Thomas' "Raindrops Keep Fallin' On My Head", which peaked at #1 for seven weeks in January–March 1970. A non-album single, "Comic Conversation" was released in October 1970 and peaked at #10 on the Go-Set National Top 60 Singles Chart and was still charting in March 1971. His fifth album, Johnny was released in August 1971, which peaked at #24 on the Kent Music Report Albums Charts. Another non-album single, "Acapulco Sun" had been released in May and peaked at #21 on the Go-Set Top 60, but there were no charting singles from Johnny. Aside from Johnny, Farnham also released a compilation, The Best Of Johnny Farnham, and a duet album with Allison Durbin, Together, all in 1971.

BioShock (series)

BioShock is a first-person shooter video game series developed by Irrational Games—the first under the name 2K Boston/2K Australia—and designed by Ken Levine. The first game in the series was released for the Windows operating system and Xbox 360 video game console on August 21, 2007 in North America, and three days later (August 24) in Europe and Australia. A PlayStation 3 version of the game, which was developed by 2K Marin, was released internationally on October 17, 2008 and in North America on October 21, 2008 with some additional features. The game was also released for the Mac OS X operating system on October 7, 2009. A version of the game for mobile platforms has also been developed by IG Fun. A sequel, BioShock 2, was released on February 9, 2010. On August 12, 2010, Irrational Games unveiled a trailer for a new game titled BioShock Infinite, released on March 26, 2013. With the release of BioShock Infinite selling over 11 million copies as of May 2015, the three games combined have more than 25 million copies sold.