Discrete-time signal through a PAM

[svippe]

A discrete-time signal x[n] is filtered through a PAM p(t). The shapes of these signals are described in the attached image.

i) Calculate and plot the output y(t) from this pulse amplitude modulation.
ii) Let y[n])=y(nTs) be the sampled signal of y(t). Calculate and plot y[n]
iii) Determine a general connection between x[n] and y[n], which is valid for any arbitrary x[n]

I have only tried my luck on i) but gets stuck at the plotting. Anyone with a better knowledge of how to solve this problem?

Kind regards, Christian

 

[Valkarie]

i) To calculate the output y(t) from the pulse amplitude modulation, we can use the convolution integral. The convolution integral is defined as: y(t) = ∫ x(τ)p(t-τ) dτWhere x(τ) is the input signal and p(t) is the PAM pulse. We can use a computer program (e.g. MATLAB) to calculate the convolution integral for us. We can then plot the result to get the output y(t).ii) To calculate y[n], we need to sample y(t) at regular intervals. We can do this by setting y[n] = y(nTs), where n is an integer and Ts is the sampling interval. We can then plot y[n] to get the sampled signal.iii) The general connection between x[n] and y[n] is given by the convolution integral: y[n] = ∑ x[k]*p[n-k]Where p[n] is the sampled version of the PAM pulse. This equation is valid for any arbitrary x[n].