Basic Discrete-Time Signals

Unit impulse and unit step signals

Some basic signals play an important role in discrete-time signal processing. We discuss two of them below.

  1. A unit impulse is a signal that is 0 everywhere, except at n=0, where its value is 1. Mathematically, it is denoted as \delta[n] and defined as

        \begin{equation*} \delta[n] = \left\{ \begin{array}{l} 1, \quad n = 0 \\ 0, \quad n \neq 0 \\ \end{array} \right. \end{equation*}

    The unit impulse signal is shown in Figure below.

  2. A unit impulse signal

  3. A unit step signal is 0 for past (n<0) values, while 1 for present (n=0) and future (n>0) values. To be precise, it is denoted as u[n] and defined as

        \begin{equation*}     u[n] = \left\{ \begin{array}{l}     1, \quad n \geq 0 \\     0, \quad n < 0 \\     \end{array} \right.     \end{equation*}

    The unit step signal is shown in Figure below.

  4. A unit step signal

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