Use Of Matched Filters In Digital Communication And In Radar Systems

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 s₁(t), in terms of the frequency response of the input S₁(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 S₁(f) of waveform s₁(t) representing the binary symbol ‘1”.

Assuming that the waveform s₁(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 y₁(t) of the matched filter

Express y₁(t) in terms of s₁(t) and h_opt(t). Express the spectrum Y₁(f) of the output y₁(t) of the matched filter in terms of the input spectrum S₁(f). What has the matched filter done to the magnitude spectrum of the input signal s₁(t) in producing the output y₁(t)?