Search results

  1. E

    Partial Fraction Expansion (Inverse Z-Transform)

    Homework Statement H(z) = \frac{6-z^{-1}}{1+0.5z^{-1}} + \frac{2}{1-0.4z^{-1}} = k + \frac{A}{1+0.5z^{-1}} + \frac{2}{1-0.4z^{-1}} where A = (6-z^{-1}) is evaluated at z^{-1}=-2. Homework Equations Partial fraction expansion. The Attempt at a Solution Why is z^{-1} set equal to -2? I...
  2. E

    Group delay of LTI system

    Homework Statement Show that the group delay of an LTI discrete-time system characterized by a frequency response H(e^{j\omega}) can be expressed as \tau(\omega)= Re\left\{\frac{j\frac{dH(e^{j\omega}}{d\omega}}{H(e^{j\omega}}\right\} . Homework Equations The...
  3. E

    Sum of a finite exponential series

    Homework Statement Given is \sum_{n=-N}^{N}e^{-j \omega n} = e^{-j\omega N} \frac{1-e^{-j \omega (2N+1)}}{1 - e^{-j\omega}}. I do not see how you can rewrite it like that. Homework Equations Sum of a finite geometric series: \sum_{n=0}^{N}r^n=\frac{1-r^{N+1}}{1-r} The Attempt at a...