[SOLVED] algorithm matlab graph EEEN30160: Matlab Exercises 9

EEEN30160: Matlab Exercises 9
General Guidelines:
Remember to put your Student Number on the report
Remember to put the name of your partner in the report
Remember to label (both x and y axes) your graphs. In the labels put also the measurement unit in parenthesis (e.g. seconds or samples for time axes). For arbitrary signals use (A.U.), meaning Arbitrary Units, as measurement unit. Points will be subtracted from the score of each exercise for any missing label.
COMMENT YOUR CODE. A perfect code with no comments will count for half of the points assigned to the exercise.
Each exercise is worth the same number of points

De-noising and signal manipulation
In this exercise we will clean an EMG signal and design an automatic algorithm for the estimation of the activation timings of the EMG.
In the file noisy_EMG.mat you will find a signal relative to the recording of the EMG signal of the Vastus Medialis muscle during several repetition of a Leg Extension exercise.
The EMG is corrupted by various noises, specifically, a movement artifact noise and the 50 Hz interference. The sampling frequency is 1 KHz.
Keeping in mind that the EMG signal has useful frequency content between about 20 and 450 Hz:
Plot the noisy signal in the time domain and its spectrum in the frequency domain

Design a filtering routine for cleaning the data, based on the knowledge you gathered so far. Justify your design choices (e.g. why you picked certain cut-off frequencies, why you decided to use a specific filter, why you chose that order for your filter). Keep in mind that you can decide to sacrifice a little bit of information to obtain a better filtering. In this specific case the movement artifact overlaps a little bit with the frequencies of the EMG, then you can decide to keep a little bit of noise or filter a little bit of signal. Plot the resulting clean signal in time and its spectrum in the frequency domain.

Extract the envelope of the EMG. Check Lecture 9 for the processing steps. Use a low pass filter for the envelope with a cut-off frequency set at 5 Hz. Plot the envelope.

Design an algorithm to determine the activation timings of the EMG. Check lecture 9 for guidance. The output of the algorithm will be a vector that will have value 0 when the muscle is not active and 1 when the muscle is active. The decision will be based on a threshold.You can use the first 5 seconds of the signal, where the muscle is not active, to determine the threshold for your algorithm. The threshold will consist of the average + n*standard deviations of the signal in a point where the muscle is not active.

Try different values of n until your algorithm returns an activation signal that is equal to 1only during the 11 contractions that are clearly visible from the raw data. Divide the envelope by its maximum value and plot the envelope and the activation signal on the same plot.

Find the activation instants (e.g. the instants where the output of your algorithm goes from 0 to 1). An easy way to do it is to check when the derivative of the 0/1 activation signal is equal to 1. To calculate the derivative of a signal, use the command diff