4.2.1 Write the Function M-file x(t) = N RXkej 2лfkl k=1 N x(t) = Σ Ak cos(2π fkt + k) k=1 (7) (8) Write an M-file called syn_sin.m that will synthesize a waveform in the form of (7). Although for loops are rather inefficient in MATLAB, you must write the function with one loop in this lab. The first few statements of the M-file are the comment lines-they should look like: function %SYN_SIN [xx, tt] = syn_sin (fk, Xk, fs, dur, tstart) Function to synthesize a sum of cosine waves ge usage: = syn_sin (fk, Xk, fs, dur, tstart) (these could be negative or positive) fk = vector of frequencies [xx, tt] 응 op g op Xk = vector of complex amplitudes: Amp*e (j*phase) fs dur the number of samples per second for the time axis total time duration of the signal tstart = starting time (default is zero, if you make this input optional) xx = vector of sinusoidal values g tt = vector of times, for the time axis. op op Note: fk and Xk must be the same length. op op Xk (1) corresponds to frequency fk (1), Xk (2) corresponds to frequency fk (2), etc. The MATLAB syntax length (fk) returns the number of elements in the vector fk, so we do not need a separate input argument for the number of frequencies. On the other hand, the programmer (that's you) should provide error checking to make sure that the lengths of fk and Xk are the same. See help error. Finally, notice that the input fs defines the number of samples per second for the cosine generation; in other words, we are no longer constrained to using 20 samples per period. Include a copy of the MATLAB code with your lab report.