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1. ### Ideal Filter - Windowed - DTFT/Highpass

Homework Statement Given: H_{dd}\left(e^{j\omega}\right)=j\omega e^{\frac{-j\omega}{2}}, \left|\omega\right|\le\pi Find: H_{3}\left(e^{j\omega}\right) where H_{3}\left(e^{j\omega}\right) is the spectrum of h_{dd}\left(n\right)\left(W_N\left(n\right)\right) and W_N\left(n\right)=1 for...
2. ### Inverse Discrete Time Fourier Transform (DTFT) Question

1. Given: The DTFT over the interval |ω|≤\pi, X\left ( e^{jω}\right )= cos\left ( \frac{ω}{2}\right ) Find: x(n) 2. Necessary Equations: IDTFT synthesis equation: x(n)=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}X\left ( e^{jω} \right ) e^{j\omega n}d\omega Euler's Identity...
3. ### Finding Zeros of System Function using Eigenvalues

Hi all - working on this problem wanted to see if anyone had any advice - thanks! As shown in section 4.4, the poles of the system H(z) with state matrices \mathbf{A, b, c^t, } d are given by the eigenvalues of \mathbf{A}. Find: Show that, if d\neq0, the zeros of the system are given by the...