$H(z)=\frac{1-z^{-1}}{(1-0.2z^{-1} -0.15z^{-2)}}$ 1.Find the difference equation 2.Draw Direct Form-I and Direct Form-II realization structure. 3.Draw cascade form, parallel form realization.

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In a certain concert hall, echoes of the original audio signal x(n) are generated due to the reflections at the walls and ceiling. The audio signal experienced by the listener y(n) is a combination of x(n) and its echoes. Let ...

Problem 1: Given the signal xt)={2, 0, 2, 4}. Prove the Discrete Fourier Transform is a unique invertible transformation using: DFT/IDFT- definition FFT/IFFT- Decimation in Time FFT/ IFFT- Decimation in Frequency.

4. Consider the interconnection of LTI systems as shown in the figure. (1) Determine h(n) when h1(n)=,,,,,,,,, (2) Please determine the response of the system y(n) for the input x(n)=g(n+2)+3g(n-1)-4g(n-3)

3. Compute the convolution y(n)=x(n) * h(n) of the following signals. (1) x(n)={1,2,4} and h(n) = {1,1,1,1,1,} (2) x(n) = {1,2,-1} and h(n) = x(n)

2. Please calculate the convolution: y(n)=x(n)*h(n) Sketch your result of y(n).

1. Resolve the following sequence x(n) into a sum of weighted impulse sequences. (1) x(n) = {1,1,0,1,2,4} (2) x(n) = {0,0,5,1,3,0,0,1,3} (3) x(n) = ,,,,,,,, (4) x(n) = 5n[u(n-1)-u(n-5)]

5. Please determine whether the following systems are time-invariant or time-variant system (Detailed calculation steps are needed)

4. Please determine whether the following systems are linear or not (Detailed calculation steps are needed).

3. Please find the even and the odd parts of the following signals.