Suppose we want to process the continuous-time signal

\[x_{\mathrm{a}}(t)=3 \cos (2 \pi 1000 t)+7 \sin (2 \pi 1100 t)\]

using a discrete-time system. The sampling frequency used is 4000 samples per second. The discrete-time processing carried out on the signal samples \(x(n)\) is described by the following difference equation.

\[y(n)=x(n)+x(n-2) .\]

After the processing, the samples of the output \(y(n)\) are converted back to continuoustime form using Equation (1.188). Give a closed-form expression for the processed continuous-time signal \(y_{\mathrm{a}}(t)\). Interpret the effect this processing has on the input signal.