Finite Impulse Response - Definition

Definition

The output y of a linear time invariant system is determined by convolving its input signal x with its impulse response b.

For a discrete-time FIR filter, the output is a weighted sum of the current and a finite number of previous values of the input. The operation is described by the following equation, which defines the output sequence y in terms of its input sequence x:

\begin{align} y &= b_0 x + b_1 x + \cdots + b_N x \\ &= \sum_{i=0}^{N} b_i x \end{align}

where:

  • is the input signal,
  • is the output signal,
  • are the filter coefficients, also known as tap weights, that make up the impulse response,
  • is the filter order; an th-order filter has terms on the right-hand side. The in these terms are commonly referred to as taps, based on the structure of a tapped delay line that in many implementations or block diagrams provides the delayed inputs to the multiplication operations. One may speak of a 5th order/6-tap filter, for instance.

Read more about this topic:  Finite Impulse Response

Famous quotes containing the word definition:

    “The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
    —Ralph Waldo Emerson (1803–1882)

    “The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
    —Jean Baudrillard (b. 1929)

    “Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?”
    —Richard Eberhart (b. 1904)