In signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, the adjoint filter mask
of a filter mask

Linear filter

Linear filters in the time domain process time-varying input signals to produce output signals, subject to the constraint of linearity.This results from systems composed solely of components classified as having a linear response....

 
is reversed in time and the elements are complex conjugate

Complex conjugate

In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs...

d.

Its name is derived from the fact, that the convolution with the adjoint filter
is the adjoint operator of the original filter
with respect to the Hilbert space

Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...

  of the sequence

Sequence

In mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...

s
with respect to the Euclidean norm.

The autocorrelation

Autocorrelation

Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...

of a signal
can be written as .

Properties

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