Simulating Gyroscope with ARW, BI, and Spectral Density Using Physical BMI270 IMU Data

I'm currently working on a state estimation project that relies on IMU data. While I have access to a physical IMU, I'd like to simulate gyroscope data with specific parameters, including Angle Random Walk (ARW) and Bias Instability (BI). I already have a pseudocode that incorporates ARW and BI parameters, but I'm struggling to integrate Spectral Density into the simulation.

Could someone help me modify my existing code to include the Spectral Density parameter and complete the gyroscope simulation? Here's the code snippet I've been working with:

https://gist.github.com/michaelwro/126de51e3d2bcaeda3fb5609aa19f0e5[sudo code link]1

# Pseudocode for modeling a noisy gyro sensor
# Created By: MicWro Engr
# 'w' variables are supposed to be the Greek letter omega, used to denote the angular rate
# Remember: variance = (std_dev)^2
# Gyro model:
#   w_meas = w_true + bias + noise
# I obtained these values from my own gyro sensor! Details can be found at: https://mwrona.com/posts/gyro-noise-analysis/
# This Mathworks post is really useful: https://www.mathworks.com/help/fusion/ug/inertial-sensor-noise-analysis-using-allan-variance.html

import numpy as np

dt = 0.01 # [sec] sample rate

# Gyro bias parameters
w_bias = -0.01  # This is the constant offset in rate measurements. Also acts as the integrator's initial condition
bias_coef = 1.31e-4  # Bias instability coefficient
bias_var = ((2 * bias_coef**2) / np.pi) * np.log(2)  # bias instability variance

# Angle random walk (AWR) parameters
arw_coef = 4.54e-4  # ARW coefficient
arw_var = arw_coef**2 / dt  # [rad/sqrt(sec)] ARW variance

# simulation loop
while True:
    
    
    # obtain an actual rate from ground truth simulation
    w_actual = GroundTruth(...)
    
    # simulate bias instability noise
    w_bias += dt * np.random.normal(0, np.sqrt(bias_var))  # (mean, std_dev)
    
    # simulate angle random walk noise
    w_arw = np.random.normal(0, np.sqrt(arw_var))
    
    # simulated gyro measurement
    w_meas = w_actual + w_bias + w_arw

Any guidance, code examples, or explanations would be greatly appreciated. Thank you for your assistance!