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 man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
    —William James (1842–1910)

    “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)

    “No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
    —Florence Nightingale (1820–1910)