idk

ME_2046/HW3/simplifying.py

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+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())
+
+

NUCE_2113/lab5/.~lock.labviz.ods#

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+,danesabo,danesabo-laptop,24.02.2025 15:04,file:///home/danesabo/snap/libreoffice/336/.config/libreoffice/4;

NUCE_2113/lab5/viz.py

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+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()