Recursive Filter Impulse Response

A recursive filter has the difference equation y[n]=-0.8y[n-1]+0.1y[n-2]+x[n] a. Find the impulse response fpr the filter? b. How many nonzero terms does the impulse response contain?

Compute the 2D DCT

Compute the 2D DCT for the matrix (attached). Verify that the result is correct by computing the inverse 2D DCT.

Using z transforms to find the impulse response

Use z transforms to find the impulse response for the digital filter with the difference equation 1.2y[n] + 0.18y[n-1] - 0.084y[n-2] = 6x[n] - 0.3x[n-1]

Calculate the exponential Fourier series coefficients of a pulse train

the function is x(t) =Σ Aπ((t-t0-mT0)/(τ)), this is an example of the text book Signal and Systems, 3 rd. edition, Ziemer, Tranter, Fannin, page 115. It is an example 3-5. I think the author skip some calculation steps. I would like to see this example step by step.

Matlab work: linear time-invariant continuous system and Laplace transform

Please refer to attached. Please submit Matlab code along with plots and anwsers. Thanks. A linear time-invariant continuous-time system has the impulse response below: h(t) =[cos 2t + 4 sin 2t]u(t) (a) Determine the transfer function H(s) of the system. (b) Plot the system impulse response using MATLAB. (c) The input, x(t) is defined as x(t) = 5/7e^-t – 12/7e^-8t. Find X(s). (d) Compute the output response Y(s). (e) Compute and plot (using Matlab) y(t).