Editing Linear phase (section)

{{Short description|Filter whose phase response is proportional to frequency}}

In [[signal processing]], '''linear phase''' is a property of a [[filter (signal processing)|filter]] where the [[phase response]] of the filter is a [[linear function (calculus)|linear function]] of [[frequency]]. The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the [[group delay]]. Consequently, there is no [[phase distortion]] due to the time delay of frequencies relative to one another.

For [[discrete-time]] signals, perfect linear phase is easily achieved with a [[finite impulse response]] (FIR) filter by having coefficients which are symmetric or anti-symmetric.<ref>{{cite web|last=Selesnick|first=Ivan|title=Four Types of Linear-Phase FIR Filters|url=http://cnx.org/content/m10706/latest/|work=Openstax CNX|publisher=Rice University|accessdate=27 April 2014}}</ref> Approximations can be achieved with [[infinite impulse response]] (IIR) designs, which are more computationally efficient. Several techniques are:
* a [[Bessel filter|Bessel]] transfer function which has a maximally flat group delay approximation function
* a [[Filter design#Phase and group delay|phase equalizer]]