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:

    “Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
    —Elaine Heffner (20th century)

    “... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
    —George Eliot [Mary Ann (or Marian)

    “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)