Determine the peak value of the output of the matched filter from your sketch in (d) and the time instant during which this peak occurs. What is the peak instantaneous signal power S_{o} at the output of the matched filter.

Suppose now the same symbol shown in Fig 1 (**help with programming in matlab**) is applied to the above matched filter at the receiver but assume that there is noise which is corrupting the symbol waveform during transmission. You are now going to determine the peak instantaneous signal-to-noise power ratio at the output of the matched filter (So/No) for this symbol and compare this with the theoretical expression given in the lecture notes. You have already found the peak instantaneous signal power at the output of the filter in (e). The task now is to find the average noise power at the output of the matched filter, given the input noise characteristics. Step (g) asks you to do this.

Assume that no signal is applied to the matched filter designed for detecting symbol 1 and that the channel is noisy. ie: the input to the receiver is simply the channel noise. If the input noise to the matched filter is assumed to white and Gaussian with single sided power spectral density N = 0.8, determine the noise power N_{o} at the output of your matched filter

Using the above result in (f) for the instantaneous peak output signal power and the result in (g) for the average output noise power, determine the ratio of peak signal power-to-average noise power at the output of the matched filter (S_{o}/N_{o}) for the given detection process

*Now you will compare this value calculated for* (S_{o}/N_{o}) in (h) *with the theoretical value of (S _{o}/N_{o}). We *Provide

Write down the equation (from notes) for the maximum instantaneous signal power-to-average noise power of the receiver output (So/No), in terms of the energy E of the transmitted symbol and the noise single sided power spectral density N at the input to the matched filter. Substitute the value of E found in (a) and using N = 0.8 and calculate value of (S_{o}/N_{o}) given by this equation.

Compare the value of (S_{o}/N_{o}) given by the equation in the notes obtained in (i) and the calculated value in (h). They should give the same result for peak signal-to-noise power ratio (S_{o}/N_{o}) at the output of the matched filter

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