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Delay operator in feedfoward filters

  1. May 12, 2010 #1
    1. The problem statement, all variables and given/known data

    The symbol z = e^(iw) is called the delay operator. Explain why (in terms of the phasor) z^(-k) corresponds to a delay of k sampling intervals.

    3. The attempt at a solution
    We really have only discussed how to manipulate the filter equations, not really waht teh delay operator does.

    I know a filter can be written as Y = b0*X + b1*X*Z^-1 + b2*X*Z^-2... etc

    Where X is the original signal... This can also be written as
    y[n] = b0*x[n] + b1*x[n-1] + b2*x[n-2]...etc

    Where y[n] is the output signal and x[n] is the input signal

    In the second form it is clear that x[n-1],x[n-2] is a delayed form of x[n], but i do not know how to explain why, in terms of the phasor, Z^-k corresponds ot the delay
     
  2. jcsd
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