Building the Foundations: A Python Script for Generating Audio Signals

Considering the complexity and interdisciplinary nature of this task, it requires knowledge and expertise in various fields such as computing, electrical engineering, neuroscience, and signal processing. The code for this specific function generator would be vast and complicated. Here, I'll present an elementary Python code that initializes and structures your project, and attempts to encapsulate some of the requirements mentioned in your prompt. Note that you still have to build up on this and integrate other modules for a full-functioned application.

```Python
# Required Libraries
import numpy as np
import scipy.signal as signal
from scipy.io.wavfile import write
import os
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from rtlsdr import RtlSdr
from matplotlib.animation import FuncAnimation

# Function to generate frequencies
def freq_generator(min_freq, max_freq, time):

frequencies = np.arange(min_freq,max_freq,.0001)
t = np.arange(0., time, 0.01)

# frequency hopping
for frequency in frequencies:
yield np.sin(2 * np.pi * frequency * t)

# Function to generate various waveforms
def waveform_generator(wave_type, freq):
t = np.linspace(0, 1, 500, False)

if wave_type=="sine":
signal = np.sin(2*np.pi*freq*t)
elif wave_type=="square":
signal = signal.square(2*np.pi*freq*t)
elif wave_type=="sawtooth":
signal = signal.sawtooth(2*np.pi*freq*t)
elif wave_type=="pulse":
signal = signal.gausspulse(t - 0.4, fc=freq)
elif wave_type=="triangle":
signal = signal.sweep(t)
return signal

# Play frequency
def play_frequency():
waveforms = ["sine", "square", "sawtooth", "pulse", "triangle"]
for wave in waveforms:
sig = waveform_generator(wave, 440)
write('wave_'+ wave +'.wav', 44100, sig)

play_frequency()
```
This sample Python script generates sine, square, sawtooth, pulse, and triangle audio signals in .wav format.

However, you will need to integrate code for implementing Kali Linux application, working with Matlab in Python, band-hopping, time-hopping, noise generation, and permission management. Not to mention, implementation of features like non-audible frequencies, transcranial magnetic stimulation, modulation, etc would require specialized hardware and more involved programming. This code draft is merely a starting point and a guide to set the direction for the final full-functioned application.

This story was generated by user BaronJones with assistance by one of OpenAI’s large-scale language-generation model; prompts used to help generate the story are shown below.

Images were generated with OpenAI's AI system, DALL·E 2, or uploaded by the user.

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