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1. 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...
2. 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...
3. 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...
4. 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...
5. Z-transform and even/odd signals.

Sorry none of the spacing worked.... I think you get the idea.
6. 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 ...
7. 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)} +...
8. 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...
9. 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
10. 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.
11. 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...