The use of matched filters in digital communication and in RADAR systems. We will be using matched filters to detect binary symbols in the presence of noise and then identifying the 7bit ASCII character that was transmitted over a noisy channel.

Based on below Fig , we will determine the energy E of a symbol waveform representing a binary '1'. What is the energy of symbol waveform representing binary ‘0’?

Derive a general expression for the frequency response H_{opt}(f) of the matched filter receiver, matched to a signal s_{1}(t), in terms of the frequency response of the input S_{1}(f). Hence, determine the frequency response of the matched filter H_{opt}(f) for the matched filter designed in part (b) for Fig . Compare this with the frequency spectrum S_{1}(f) of waveform s_{1}(t) representing the binary symbol ‘1”.

Assuming that the waveform s_{1}(t) for symbol '1' appears at the input of the matched filter you have designed above , without any noise or distortion (ie: the channel is ideal). Sketch the output y_{1}(t) of the matched filter

Express y_{1}(t) in terms of s_{1}(t) and h_{opt}(t). Express the spectrum Y_{1}(f) of the output y_{1}(t) of the matched filter in terms of the input spectrum S_{1}(f). What has the matched filter done to the magnitude spectrum of the input signal s_{1}(t) in producing the output y_{1}(t)?

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