Question

f. The amplitude of a cosine can be observed at the origin (t=0) when there is no phase shift. Find a simplified solution for the convolution integral below for t=0. +∞ output(t) = h(t)∗ s(t) = −∞ 3 rect(3x) cos(2π f0 (t − x)) dx Hint: Set t=0, sketch the situation to help set up the integral and remember the properties of odd and even functions to simply the calculation. g. The above result gives a general expression for the output cosine amplitude as a function of f0

. Expand your table to include several more input frequencies between 0 and 10 Hz until you can determine with confidence the behavior of this linear system as a function of input frequency. Use the result from above to check your answers with the computed amplitude at frequency f0. Use MATLAB to plot the relationship you have observed between output amplitude and signal frequency f0 for this system. Input cosine f0 Hz Output frequency (Hz) Output amplitude for f0 Computed amplitude for f0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

Answer 1