student id: 55769100

4. Consider a radar system and it transmits a sinusoidal pulse of 50 samples: s[k] = 2 cos(0.2k +), k= 1, 2, ... ,50 where o is your student ID number: (a) Compute the energy of s[k] using MATLAB. The energy is defined as: E. = $? [ki] 50 (b) Consider after certain time interval, the radar system receives x[k]. This can mean presence (H1) or absence (740) of target: 10:2[k] = a[0]; Hi : x[k] = s[k] + n[k], k = 1,2,..., where nk) N(0,02) is independent Gaussian noise. ,50 Given z[k], k = 1, 2, ... , 50, we need to decide whether there is a target or not. A conventional method is to use the energy detector. That is, we compute the energy of the received signal r[k]: , = 2[] 50 and then compare E, with a threshold 7: if E, > ?, H is picked while Ho is assumed for E, <. use randn to generate n with g and produce sets of r correspond ho the remaining hi receiver operating characteristic curve command perfcurve or by other means. note that roc is sensitivity versus you can base on data construct roc. an illustration procedure be found at also in electrical engineering specificity probability detection false alarm respectively. denote event deciding target present as t we write p="P(TH)" pfa="P(T|Ho)." when transmit signal s known another popular method matched filter which computes matching function: mo="*[k]s[ki" energy detector x plot filter. compare results detector. has better performance what are your findings consider a radar system it transmits sinusoidal pulse samples: cos k="1," ... where o student id number: compute using matlab. defined as: e.="$?" after certain time interval receives this mean presence absence target: : nk independent gaussian noise. given z need decide whether there not. conventional received then e threshold if> ?, H is picked while Ho is assumed for E, <. use randn to generate n with g and produce sets of r correspond ho the remaining hi receiver operating characteristic curve command perfcurve or by other means. note that roc is sensitivity versus you can base on data construct roc. an illustration procedure be found at also in electrical engineering specificity probability detection false alarm respectively. denote event deciding target present as t we write p="P(TH)" pfa="P(T|Ho)." when transmit signal s known another popular method matched filter which computes matching function: mo="*[k]s[ki" energy detector x plot filter. compare results detector. has better performance what are your findings>