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:

    “One definition of man is “an intelligence served by organs.””
    —Ralph Waldo Emerson (1803–1882)

    “It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
    —Jane Adams (20th century)

    “Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
    —Nadine Gordimer (b. 1923)