Broken (Seether song)

"Broken" is a song by post-grunge/alternative metal South-African band Seether featuring American singer Amy Lee, the lead singer of Evanescence and former girlfriend of Seether vocalist Shaun Morgan. It was recorded in 2004 and was later included in Disclaimer II. This version includes electric guitar and violins. It peaked at No. 20 on the Billboard Hot 100 and at No. 3 on the ARIA singles chart. It was later certified Gold by the Recording Industry Association of America (RIAA) and Platinum by the Australian Recording Industry Association (ARIA). It is the band's biggest pop hit and the band's only Top 40 hit, reaching #20 on the Billboard Hot 100 chart. Although, until the 2014 release of "Words as Weapons", it was often considered Seether's most popular track and the only song to enter and crossover to the pop and adult contemporary charts, it is not their highest-charting single on the Mainstream Rock Tracks chart and Modern Rock Tracks chart where a few singles, such as "Fine Again" and "Fake It", charted higher. Despite this, it was the most played song on most rock radio formats due to the pop success of the song. In addition, it still charted high peaking #9 on the Mainstream Rock Tracks chart and #4 on the Modern Rock Tracks chart.

Broken (House)

"Broken" is the joint title for the first and second episodes of the sixth season of the television series House. It is a two-part season premiere, being first broadcast on the Fox network on September 21, 2009. The narrative follows series protagonist Dr, Gregory House (Hugh Laurie) as he overcomes his vicodin addiction and psychological problems at Mayfield Psychiatric Hospital.

Receiving season-high ratings, the episodes garnered positive reviews from critics. The performance of Hugh Laurie was also applauded.

Plot

House awakens in the Mayfield Psychiatric Hospital after suffering through the painful effects of Vicodin withdrawal. He asks to leave knowing that they legally cannot keep him because he voluntarily committed himself. However, Dr. Nolan (Andre Braugher) refuses to sign a recommendation to the board of medicine saying he is able to return to work. House resigns himself to stay at the hospital and get his clearance. He meets his manic-depressive roommate, Alvie (Lin-Manuel Miranda), and begrudgingly participates in group therapy with Dr. Beasley. He also meets and is intrigued by Lydia (Franka Potente), a woman who plays piano for her sister-in-law Annie (Ana Lenchantin), an unresponsive patient in the ward who was a cellist.

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.)