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import math
# Speed of light in vacuum (m/s)
C0 = 299792458
# Dictionary of common media and their approximate phase velocities for EM waves
MEDIA_VELOCITIES = {
# Gases (at 0°C and 1 atm, for visible light ~589 nm)
"Vacuum": C0,
"Air (at sea level)": C0 / 1.000293,
"Helium": C0 / 1.000036,
"Carbon Dioxide": C0 / 1.00045,
# Liquids (for visible light ~589 nm)
"Water (distilled, 20°C)": C0 / 1.333,
"Ethanol": C0 / 1.36,
"Glycerine": C0 / 1.473,
"Benzene": C0 / 1.501,
"Carbon Disulfide": C0 / 1.628, # notable for high dispersion
# Solids (for visible light ~589 nm)
"Ice": C0 / 1.31,
"Teflon (PTFE)": C0 / 1.35,
"Fused Silica (Glass)": C0 / 1.458,
"Crown Glass (typical)": C0 / 1.52,
"Polyethylene": C0 / 1.54,
"Polystyrene": C0 / 1.59,
"Flint Glass (dense)": C0 / 1.65,
"Sapphire": C0 / 1.77,
"Glass (amorphous semiconductor)": C0 / 1.8,
"Diamond": C0 / 2.42,
"Gallium Phosphide (GaP)": C0 / 3.5,
# Special Cases (Important for RF/Microwave Engineering)
"Human Body Tissue (muscle, ~3 GHz)": C0 / 7.14, # Relative permittivity ε_r ~51, n=√ε_r
}
# Permittivity of free space in Farads per meter (F/m)
EPSILON_0 = 8.854e-12
# Value ranges for random parameter generation to ensure diverse problems.
# Frequencies are kept as integers for clarity in the problem statement.
FREQUENCY_RANGE_HZ = (50, 2000)
AMPLITUDE_RANGE = (1.0, 50.0)
PHASE_RANGE_DEG = (-180, 180)
PHASE_RANGE_RAD = (-math.pi, math.pi)
# The continuous frequency Omega will be a multiple of pi. This range defines the multiplier.
OMEGA_MULTIPLIER_RANGE = (100, 1000)
SAMPLING_FREQ_RANGE_HZ = (1000, 8000)
F0_RANGE_HZ = (500, 3000)
# The gain of the discrete-time system
GAIN_K_RANGE = (0.5, 5.0)
# The delay (in samples) of the discrete-time system
DELAY_N0_RANGE = (1, 10)
# The integer factor by which the signal is downsampled.
DECIMATION_FACTOR_M_RANGE = (2, 5)
# Define the pool for denominators of the omega_0 fraction.
# Using larger numbers allows for more granularity in creating frequencies.
OMEGA_DENOMINATOR_RANGE = (8, 20)
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