# problems1 - sider further the Flter matched to ψ 1 t...

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Digital Modulation 1 - Problem Set 1 Problem 1 (Gram-Schmidt orthonormalization procedure) 1. Apply the Gram-Schmidt procedure to the four waveforms: 0 0 0 0 1 1 1 1 1 1 1 1 - 1 - 1 - 1 - 1 2 2 2 2 3 3 3 3 t t t t s 1 ( t ) s 3 ( t ) s 2 ( t ) s 4 ( t ) 2. Give the resulting vector representations of these waveforms. Verify your results with Matlab. 3. Compute the scalar product of these waveforms as well as the scalar product of their corresponding vectors. Verify the results with Matlab. 4. Compute the energies of these waveforms and compare them with the squared lengths of the vectors representing them. Problem 2 (Matched flter) Consider the orthonormal functions given in Appendix A.1 of the lecture notes. Con-
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Unformatted text preview: sider further the Flter matched to ψ 1 ( t ), referred to as matched Flter in the following. 1. Compute the output of the matched Flter for the input signal ψ 1 ( t ). Plot it with Matlab. 2. Compute the output of the matched Flter for the input signal ψ 2 ( t ). Plot it with Matlab 3. Discuss the meanings (properties) of the sample values at t = T of the two output signals calculated in the previous two questions. B±l, TPe. Digital Modulation 1 NavCom...
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