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    What is circular convolution?

    I would offer that we don't particularly want circular convolution, but it is a necessary by-product of the finite-length DFT operations. Circular convolution also drives the need for windowing and filtering to remove all of the translated spectral images. Learning to mitigate the negative...
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    Ideal Filter - Windowed - DTFT/Highpass

    Found my mistake - it turns out that the above is actually correct and corresponds to Sum( (-1)^(n-1/2)/(denom) * e^-jwn). There was an error in my MATLAB code (ridiculous error) where my for loop looked like: for i=length(n) instead of for i=1:length(n) hence the reason I was only...
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    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...
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    Inverse Discrete Time Fourier Transform (DTFT) Question

    Collinsmark, Thank you for the response - the bit about being periodic but not sinusoidal was very helpful. I did not recognize that before (my fault in not sketching the magnitude plot - I need to remember to do that). As for the example at the bottom - I understand the relationship between...
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    Z-transform and even/odd signals.

    Sorry none of the spacing worked.... I think you get the idea.
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    Z-transform and even/odd signals.

    That is all correct. To use poles/zeros you just need to realize that real values create complex-conjugate pairs, so one real input will give you |a|e^jb and |-a|e^-jb making a z-plane plot look something like this: . |Im . | x ...
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    Z-transform and even/odd signals.

    If x(n) is real valued then: x(n)=x*(n) DTFT x(n) <-------> X(e^jw) DTFT x*(n) <-------> X*(e^-jw) X(e^jw)=Re{X(e^jw)} + jIm{X(e^jw)} X*(e^-jw)=Re{X(e^-jw)} - jIm{X(e^-jw)} since x(n)=x*(n), X(e^jw)=X*(e^-jw) thus Re{X(e^jw)} + jIm{X(e^jw)}= Re{X(e^-jw)} - jIm{X(e^-jw)} so |Re{X(e^jw)} +...
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    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...
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    Finding Zeros of System Function using Eigenvalues

    doh! Yes absolutely it makes sense. I got the answer now too - the key was to back it into state space equations and re-solve. Thank you for the response! -DR
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    Finding Zeros of System Function using Eigenvalues

    Thank you for your response donpacino. Unfortunately I'm not seeing it. (both the way to implement the equation and the error in 3) I considered MATLAB but I was hesitant to take a deterministic approach and go with "if it works this once it will always work" kind of deal. Maybe i'l do that.
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    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...
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