*When we implement a matched filter using correlation techniques we correlate the received signal y(t) with a reference signal which is a replica of the transmitted signal s(t). So we are essentially correlating the received signal y(t) with the transmitted signal s(t). Assuming that there is no noise in the system and no distortion, the received signal is y(t) is given s(t-d) where d is return signal delay. So we are correlating s(t-d) with s(t) which is essentially the autocorrelation of s(t). It follows that if the auto correlation of s(t) (ie: correlation of s(t) with itself) has a small spread then the RADAR resolution will improve. So one of the methods to ensure that adequate range resolution is obtained without compromising for the signal to noise ratio at the output of the matched filter, is to use a transmit signal with very low values of the autocorrelation except when delay is zero. A type of signal that will allow this is the chirp signal.*

*A chirp signal is defined as*

*In a new Radar system, a chirp pulse of 30µs duration with amplitude A=1, f _{o} = 1.2MHz and k = 18e9. The Radar system had polled the environment and stored the received signal in Chirp1.mat.*

Plot *s(t)* using Matlab using exactly 1000 points.

Perform an auto correlation of the signal and comment on the result

. Load your received signal in Chirp1.mat and detect the presence of the objects with a optimum filter that has a impulse response matched to that of *s(t)*. Provide a plot at the output of the matched filter and hence determine the distance of the objects.

In this section we examine the use of Chirp signals to detect multiple objects. Load MultipleDetectionChirp.mat and extract your data. Detect the presence of the objects. State the number of objects present in the scan and calculate their distances from the receiver

In the second part (Part 2) of the assignment, you will explore the use of matched filters in RADAR applications and use it to calculate the distance of the objects from a RADAR receiver.

You must answer all questions from (a) to (t) in Part 1 and all question from 1 to 17 in Part 2. Marks for each question have been indicated. Format of the final Report and Submission Requirements are given below.

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