Write a MATLAB script that does the following: When the signal g ( t ) goes through a filter h ( t ) where the frequency domain definition of the filter is: 5 @ . @ S 20 H(@) = 0. elsewhere the results in a time domain output signal: m( t). (a) Using convolution theorem, calculate the frequency domain output signal M (w). Plot the magnitude and phase of M(w) in a 2x1 subplot for the interval W=-31. 4:0.01:31.4. (b) Evaluate m( t ) using the definition of Inverse Fourier Transformation. Plot Re(m(t) ) and Im(m( t) ) in a 2x1 subplot for the interval t=-100:0. 1: 100. Where g(t) is defined as: 8 (1) = ]G(w) du and G(@) is defined as: 2, 5 5 @ $10 G(w) = 0, elsewhere1. In the lab we analyzed filtering 60 Hz power-line noise from ECG signal using a digital (signal processing) filter. Now let's try to an analog (circuit) filter approach to remove the 60 Hz line-noise. Following is an active twin-T notch filter with transfer function: Z(@) (1+m)((2joRC) +1) R H(@) = X(@) (2joRC) +4(1-m)joRC+1 X Z 2R 2R Here m is the ratio of the two feedback resistance which determines the gain and quality 2C MR R for the filter. The drop frequency of this twin-T notch filter is fdrop=1/4ARC. For designing a 60 Hz drop filter, let's use R=10 kQ and C=133 nF. (a) Form={0.8, 0.9} plot the magnitude and phase response of H( W ) with a range of f=w/2n=[0, 200 Hz]. (b) Consider the ECG signal used during the class (ecg_signal . mat) as the input (x(t)=ecg) of a 60 Hz twin-T notch filter with m=0 . 9. Using the functions fft( ) and ifft ( ), determine the X (w), Z (@), and z ( t ) [z (t ) is the output signal from the twin-T notch filter]. Plot x ( t ), X( f ), Z( f ), and z ( t ) in a 4x1 subplot for the range of -250 f 250 and O Sts 2.5. [Please pay attention to the proper use of fitshift( ) and ifftshift ( ) while solving this problem.] 2. Calculate the energy of time domain signal x ( t ) and z ( t ) for the range of 0 St$2.5. Also calculate the energy of these signals in frequency domain using Parseval's theorem. Plot Energy (X) and Energy ( Z ) as a function of frequency f in a 2x1 subplot (Energy vs frequency plot is know as energy spectrum of a signal).Write a general matlab program to calculate the THD value for a clipped sinewave signal Use for example (0.9 up clip /0.7 down clip) A Sim (wot) write a general matlab program to calculate the THD value for a clipped sinewave signal Use for example (o.9 up clip /0.7 down clip) signal and system\fSuppose you would write a MATLAB script to construct a mathematic sequence: a1, a2, a3, CA . .. The wh element of the sequence d, (7 = 1, 2, 3, ...) is constructed according to the following rule: 3-n+1, if n s 20 an = 15 - n - 39, otherwise Your script should construct a longest series as above so that the sum of its elements will not exceed a target value (e.g., 2000), which is provided by the user input. Also, your program should display the length of the constructed series and the sum of its elements as follows: "The series contains elements and has a sum ." In the message, should be the number of elements in the constructed series, and should be the sum of these elements. Note: Your script does NOT need to plot the trajectories of the projectiles