diff --git a/ME_2046/HW3/simplifying.py b/ME_2046/HW3/simplifying.py new file mode 100644 index 0000000..5d92933 --- /dev/null +++ b/ME_2046/HW3/simplifying.py @@ -0,0 +1,103 @@ +import sympy as sm +import numpy as np +sm.init_printing() + +s = sm.symbols('s') +z = sm.symbols('z') +T = sm.symbols('T') + +######################################################### +print('PROBLEM 2:') +print('Part a:') + +ZOH = (1-sm.exp(-s*T))/(s*T) + +G_1_s = 1/s*ZOH + +bilinear_s = 2/T *(z-1)/(z+1) + +G_1_k = G_1_s.subs({s:bilinear_s}).simplify() + +print("G_1_k = ") +sm.pprint(G_1_k) + +print('Part b:') + +theta_s_r_s = ZOH*1/s**2 +theta_k_r_k = theta_s_r_s.subs({s:bilinear_s}).simplify() +print("theta_k_r_k = ") +sm.pprint(theta_k_r_k) + + +######################################################### +print('PROBLEM 3:') +A = sm.Matrix([[0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1], + [1, 0, 0, 0]]) +B = sm.Matrix([0, 0, 0, 1]) +C = sm.Matrix([1, 0, 0, 0]).transpose() +D = sm.Matrix([1]) + +print('System Matricies A, B, C, D') +sm.pprint(A) +sm.pprint(B) +sm.pprint(C) +sm.pprint(D) + +#Recursive Solution +k = sm.symbols('k', integer = True, real = True, positive = True) + +def y(k,u): + term_1 = C * A**k * x_0 + + term_2 = sm.Matrix([0,0,0,0]) + for j in range(np.size(u)): + term_2 = term_2 + A**(k-j-1) * B * u[j] + term_2 = C*term_2 + + term_3 = D*u[-1] + + return term_1+term_2+term_3 + +print('Part c:') +x_0 = sm.Matrix([2, 1, 3, 0]) +u = sm.Matrix([0]) + +output = y(k, u) +output = output[0].expand().simplify() +print('y(k) = ') +sm.pprint(output) + + + +print('Part d:') +x_0 = sm.Matrix([0, 0, 0, 0]) +u = sm.Matrix([2, 1, 3, 0]) +output = y(k, u) +output = output[0].expand().simplify() +print('y(k) = ') +sm.pprint(output) + +print('Part e:') +print('These are the same exact response between parts C and D. This makes sense, becasue we defined our states as just being delays in a chain. The result is that the input at timestep k trickles down through each state in k+1, k+2, and k+3. This means that our states save our input in a way, s.t. loading this initial state mathematically produces an identical result as loading those inputs in one time step at a time. \n \n This is reflected by the two algebraeic expressions being the same.') + +######################################################### +print('PROBLEM 4:') +print('Part a:') + +""" +x(k+2) - x(k+1) + 0.25 x(k) = u(k+2) + +Applying Z transform: +z^2 X - z X + 0.25 X = z^2 U +X (z^2 - z + 0.25) = z^2 U +X/U = z^2 / (z^2 - z + 0.25) +""" +# Use SymPy to do partial frac +z = sm.symbols('z') + +X_U = z**2/(z**2 - z + 0.25) +sm.pprint(X_U.apart()) + + diff --git a/NUCE_2113/lab5/.~lock.labviz.ods# b/NUCE_2113/lab5/.~lock.labviz.ods# new file mode 100644 index 0000000..7f601a6 --- /dev/null +++ b/NUCE_2113/lab5/.~lock.labviz.ods# @@ -0,0 +1 @@ +,danesabo,danesabo-laptop,24.02.2025 15:04,file:///home/danesabo/snap/libreoffice/336/.config/libreoffice/4; \ No newline at end of file diff --git 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index 0000000..b261d26 Binary files /dev/null and b/NUCE_2113/lab5/2025-02-18LAB5-UNKNOWN_EX5.3.png differ diff --git a/NUCE_2113/lab5/combined_spectrum.png b/NUCE_2113/lab5/combined_spectrum.png new file mode 100644 index 0000000..f43d442 Binary files /dev/null and b/NUCE_2113/lab5/combined_spectrum.png differ diff --git a/NUCE_2113/lab5/labviz.ods b/NUCE_2113/lab5/labviz.ods new file mode 100644 index 0000000..171b348 Binary files /dev/null and b/NUCE_2113/lab5/labviz.ods differ diff --git a/NUCE_2113/lab5/spectrum.png b/NUCE_2113/lab5/spectrum.png new file mode 100644 index 0000000..86c4039 Binary files /dev/null and b/NUCE_2113/lab5/spectrum.png differ diff --git a/NUCE_2113/lab5/viz.py b/NUCE_2113/lab5/viz.py new file mode 100644 index 0000000..c54e943 --- /dev/null +++ b/NUCE_2113/lab5/viz.py @@ -0,0 +1,101 @@ +import glob +import os +import numpy as np +import matplotlib.pyplot as plt + +def load_spectrum_data(filename): + """ + Load spectrum data from a text file in the provided format. + + This function: + - Reads the file line by line. + - Finds the "$DATA:" section. + - Skips the first line after "$DATA:" (assumed to be the channel range header). + - Collects all subsequent lines (until the next section indicated by a line starting with '$'). + - Parses these lines into a NumPy array. + + Parameters: + filename (str): Path to the spectrum file. + + Returns: + numpy.ndarray: Array of count values. + """ + with open(filename, 'r') as f: + lines = f.readlines() + + data_lines = [] + in_data_section = False + skip_first_data_line = True # flag to skip the channel-range header + + for line in lines: + # Look for the beginning of the data section + if line.strip().startswith("$DATA:"): + in_data_section = True + continue + if in_data_section: + # If we hit a new section header, exit the data section + if line.strip().startswith("$"): + break + # Skip the first line after "$DATA:" if it contains exactly two numbers (channel range header) + if skip_first_data_line: + parts = line.strip().split() + if len(parts) == 2: + skip_first_data_line = False + continue + skip_first_data_line = False # even if not two numbers, do not skip subsequent lines + # Append non-empty lines + if line.strip(): + data_lines.append(line.strip()) + + # Combine the collected lines into one string and parse numbers + data_str = " ".join(data_lines) + # Convert the string of numbers into a NumPy array + data = np.fromstring(data_str, sep=' ') + return data + +# Get a list of all .Spe files in the current directory +spe_files = glob.glob("*.Spe") + +# To store data for the combined plot +combined_data = [] + +for file in spe_files: + # Load the spectrum data + spectrum_data = load_spectrum_data(file) + # Create an array for channel numbers (one per data point) + channels = np.arange(len(spectrum_data)) + + # Store the data for the combined plot (use file name without extension for legend) + base_name = os.path.splitext(os.path.basename(file))[0] + combined_data.append((base_name, channels, spectrum_data)) + + # Plot individual spectrum + plt.figure(figsize=(10, 6)) + plt.step(channels, spectrum_data, where='mid', color='blue') + plt.xlabel('Channel') + plt.ylabel('Counts') + plt.title(f"Spectrum: {base_name}") + plt.grid(True) + plt.tight_layout() + + # Save individual figure as PNG + output_filename = base_name + '.png' + plt.savefig(output_filename) + plt.close() # Close the figure to free memory + +# Now create a combined plot with all spectra +plt.figure(figsize=(12, 8)) +for name, channels, spectrum_data in combined_data: + # Do not specify a color so that the default cycle gives different colors for each curve + plt.step(channels, spectrum_data, where='mid', label=name) + +plt.xlabel('Channel') +plt.ylabel('Counts') +plt.title("Combined Spectrum Data") +plt.grid(True) +plt.legend() +plt.tight_layout() + +# Save and display the combined plot +plt.savefig('combined_spectrum.png') +plt.show() diff --git a/NUCE_2113/lab5/viz2.py b/NUCE_2113/lab5/viz2.py new file mode 100644 index 0000000..e69de29