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Fixed errors reported by @K41-B
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spors committed Apr 17, 2023
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6 changes: 3 additions & 3 deletions quantization/linear_uniform_quantization_error.ipynb
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"\\end{split}\n",
"\\end{equation}\n",
"\n",
"It now can be concluded that the SNR decays approximately by 6 dB per additional bit spend. This is often referred to as the 6 dB per bit rule of thumb for linear uniform quantization. Note, this holds only under the assumptions stated above."
"It now can be concluded that the SNR increases approximately by 6 dB per additional bit spend. This is often referred to as the 6 dB per bit rule of thumb for linear uniform quantization. Note, this holds only under the assumptions stated above."
]
},
{
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"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.9"
"version": "3.9.16"
}
},
"nbformat": 4,
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6 changes: 3 additions & 3 deletions quantization/noise_shaping.ipynb
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"\n",
"* The overall average SNR is lower than for the quantizer without noise shaping. Why?\n",
"\n",
"Solution: The average power per frequency is lower that without noise shaping for frequencies below $\\Omega \\approx \\pi$. However, this comes at the cost of a larger average power per frequency for frequencies above $\\Omega \\approx \\pi$. The average power of the quantization noise is given as the integral over the PSD of the quantization noise. It is larger for noise shaping and the resulting SNR is consequently lower. Noise shaping is nevertheless beneficial in applications where a lower quantization error in a limited frequency region is desired."
"Solution: The average power per frequency is lower than without noise shaping for frequencies below $\\Omega \\approx \\pi$. However, this comes at the cost of a larger average power per frequency for frequencies above $\\Omega \\approx \\pi$. The average power of the quantization noise is given as the integral over the PSD of the quantization noise. It is larger for noise shaping and the resulting SNR is consequently lower. Noise shaping is nevertheless beneficial in applications where a lower quantization error in a limited frequency region is desired."
]
},
{
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],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.9"
"version": "3.9.16"
}
},
"nbformat": 4,
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4 changes: 2 additions & 2 deletions random_signals/superposition.ipynb
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"\\end{cases}\n",
"\\end{equation}\n",
"\n",
"The [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem) states that a superposition of independent random variables tends towards a normal distribution for an increasing number of superpositions. Numerical simulation for a high bus finite number of independent uniformly distributed random signals yields"
"The [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem) states that a superposition of independent random variables tends towards a normal distribution for an increasing number of superpositions. Numerical simulation for a high but finite number of independent uniformly distributed random signals yields"
]
},
{
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
"version": "3.9.16"
}
},
"nbformat": 4,
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