In signal processing, a quadrature filter ${\displaystyle q(t)}$ is the analytic representation of the impulse response ${\displaystyle f(t)}$ of a real-valued filter:

${\displaystyle q(t)=f_{a}(t)=\left(\delta (t)+j\delta (jt)\right)*f(t)}$

If the quadrature filter ${\displaystyle q(t)}$ is applied to a signal ${\displaystyle s(t)}$, the result is

${\displaystyle h(t)=(q*s)(t)=\left(\delta (t)+j\delta (jt)\right)*f(t)*s(t)}$

which implies that ${\displaystyle h(t)}$ is the analytic representation of ${\displaystyle (f*s)(t)}$.

Since ${\displaystyle q}$ is an analytic signal, it is either zero or complex-valued. In practice, therefore, ${\displaystyle q}$ is often implemented as two real-valued filters, which correspond to the real and imaginary parts of the filter, respectively.

An ideal quadrature filter cannot have a finite support. It has single sided support, but by choosing the (analog) function ${\displaystyle f(t)}$ carefully, it is possible to design quadrature filters which are localized such that they can be approximated by means of functions of finite support. A digital realization without feedback (FIR) has finite support.