Question

Question 6: We will consider a piece-wise constant 1D signal in this part. Assume the signal (a function f(t)) contains S = 10 discrete sub-intervals of equal length. Each sub-interval contains 50 samples. This signal is given below in the variable signal acquired at sample locations sampling_locations (also provided below). Plot the 1D signal, create one plot with the regular plot commands and one plot with the stem command (use subplots to plot the two next to each other in a row). Label all axes and give the plots titles. The X-axis values should be the sample locations in [0, 10]. # Provided variables num_samples = 500 num_subintervals = 10 signal = np.array([ 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, | 6, 6, 6, 1, 1, 1, 6, FPE ១ ០ ០ ០ ០ ០ FEE PPPO0000OPP o o o o o - ២ ០ ០ ០ ០ - o o o ០ ០ ០ អនកឧឧ កកកោ ហិ ហិ ហិ = o o o o “អន ៣៣៣ ៣ ហិ ហិ ហិ = = ១ ពក ៣ ៣ ហិ ហិ ហិ ។ ៣៣៣៣៣ ហិ ហិ ហិ = ១ ចា ចា ចា ទី ៧៧០ ០ ០ ០ ០ ០ -៧។ននិន ព៣៣៣៣ រោ រោ រោ រ ចា ចា ចា , ក ច ន់ - o o > > > ចា ចា ចា យ យ យ យ យ យ ទ === ---០ ០ ០ ០ ០ ០ -ដ- ---០ ០ ០ ០ ០ ===ឱ ---០ ០ ០ ០ ០ ០ ===ឱ ២ ២ ២ === ០ o o o o ០ ===ឱន ---០ ០ ០ ០ ០ ០ ---០ o o o ០៥-មន ២ ២ - ---០ ០ ០ ០ ០ ០ ---ះនក ព ក ក ក ព រោ រោ ណ = ១ ០ ០ ៣ ៣ ១១ ១ ១១១ === ០ ០ ០ ០ ០ ០ ===ះឧក ក ក ក ៣ ហិ ហិ ហិ ១ ។ ចា ចា ចា ៖ ក ភាគ ៣ ហិ ហិ ហិ = = = ភោ ៣ ហិ ហិ ហិ ១៣ ៣៣៣៣ ហិ ហិ = = = ចា ចា ចា ---០ ០ ០ ០ ០---ះនន្ទ ក ក ក ព ៣ ហិ ហិ ហិ = ១ ចា ចា ចាត ៣ ៣ ៣ ៣ ហិ ហិ ហិ = = ក ព ក ព រោ ហិ ហិ = = = ចា ចា ចា ១ ចា ចា ចា ១ ១ ១ ចា ចា ចា ។ DOOR DUUvwwwwww 4, 4, 4,4 4 , 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9,99,9,99, 9. 9, 9, 9,99, 9,9 9 , 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,9 9, 9, 9, 9]) sampling_locations=np.arange(0,10,10/num_samples) #create an array with the sample loca # Put your pseudocode, in the form of comments, and code here Question 7: Generate an array of the same length as the 1D signal, whose elements are drawn from a random Gaussian distribution with mean zero and standard deviation o = 3. Look up the normal() submodule under numpy.random . Example syntax is mu = 9 #_mean sigma = 3 # standard deviation noise = np. random.normal(mu, sigma, n) Generate a new signal by adding the piece-wise constant signal from above and your new random Gaussian array (noise). Plot this new signal both as a line and stem plot (use subplot() again) over the sampled points. Label all axes and give the plots titles. What do you observe has happened to the signal? # Put your pseudocode, in the form of comments, code, and your observations here Question 8: Think about how you can remove the noise in the signal using the ideas from Question 4 and 5. Assume you know that the underlying signal is piece-wise constant and you know the location of the constant subintervals. Think in terms of averages and the law of large numbers. Describe your algorithm briefly below and explain why it would work. Put your answer here

Answer 1

#please ask 1 question at a time

#i have done 6th and 7th since they were similar

#question 6
import matplotlib.pyplot as plt#dont include this line if already imported

plt.subplot(1,2,1)
plt.plot(sampling_locations,signal)
plt.xlabel('Sampling Locations')
plt.ylabel('Signal')
plt.title('Simple line plot')

plt.subplot(1,2,2)
plt.stem(sampling_locations,signal,use_line_collection=True)
plt.xlabel('Sampling Locations')
plt.ylabel('Signal')
plt.title('Stem plot')
plt.tight_layout()
plt.show()

#question 7
import matplotlib.pyplot as plt#dont include this line if already imported

n=len(signal)
mu = 0 # mean
sigma = 3 # standard deviation
noise = np.random.normal(mu, sigma, n)
newSignal = signal+noise
plt.subplot(1,2,1)
plt.plot(sampling_locations,newSignal)
plt.xlabel('Sampling Locations')
plt.ylabel('Signal with noise')
plt.title('Using Plot')

plt.subplot(1,2,2)
plt.stem(sampling_locations,newSignal,use_line_collection=True)
plt.xlabel('Sampling Locations')
plt.ylabel('Signal with noise')
plt.title('Using Stem')
plt.tight_layout()
plt.show()