Triangular function

A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often this is an <a href="/facts/Isosceles_triangle/rvLe3yqK">isosceles triangle</a> of height 1 and base 2 in which case it is referred to as the triangular function. Triangular functions are useful in <a href="/facts/Signal_processing/Npaja6zb">signal processing</a> and communication systems engineering as representations of idealized signals, and the triangular function specifically as an <a href="/facts/Integral_transform/AB2yjHJJ">integral transform</a> kernel function from which more realistic signals can be derived, for example in <a href="/facts/Kernel_density_estimation/NmznyEW8">kernel density estimation</a>. It also has applications in <a href="/facts/Pulse-code_modulation/5gdfjtH3">pulse-code modulation</a> as a pulse shape for transmitting <a href="/facts/Digital_signal_(electronics)/pKYKbxfK">digital signals</a> and as a <a href="/facts/Matched_filter/Tl8Bm687">matched filter</a> for receiving the signals. It is also used to define the triangular window sometimes called the <a href="/facts/Bartlett_window/5Xj7h2ah">Bartlett window</a>.

Triangular function open-in-new

Triangular function