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Every time you generate discrete noise samples (Using MATLAB's randn / rand for instance) you actually generate a band limited noise.

All you need to do is the adjustment of the variance of the discrete samples to the variance of the "Continuous" noise those samples are allegedly taken from.

Given a continuous White Noise (Wide Sense) with variance $ \sigma^{2}_{cn} \delta (t) $ and you want sample it at rate of $ f_{s} $ you should generate discrete noise samples with variance of $ f_{s} \sigma^{2}_{cn} $.

This result is valid assuming before sampling the continuous noise you applied an ideal LPF filter with bandwidth of $ f_{s} / 2 $.

Full description is given here:
How to Simulate AWGN (Additive White Gaussian Noise) in Communication Systems for Specific Bandwidth

Every time you generate discrete noise samples (Using MATLAB's randn / rand for instance) you actually generate a band limited noise.

All you need to do is the adjustment of the variance of the discrete samples to the variance of the "Continuous" noise those samples are allegedly taken from.

Given a continuous White Noise (Wide Sense) with variance $ \sigma^{2}_{cn} \delta (t) $ and you want sample it at rate of $ f_{s} $ you should generate discrete noise samples with variance of $ f_{s} \sigma^{2}_{cn} $.

This result is valid assuming before sampling the continuous noise you applied an ideal LPF filter with bandwidth of $ f_{s} / 2 $.

Full description is given here - How to Simulate AWGN (Additive White Gaussian Noise) in Communication Systems for Specific Bandwidth.

Every time you generate discrete noise samples (Using MATLAB's randn / rand for instance) you actually generate a band limited noise.

All you need to do is the adjustment of the variance of the discrete samples to the variance of the "Continuous" noise those samples are allegedly taken from.

Given a continuous White Noise (Wide Sense) with variance $ \sigma^{2}_{cn} \delta (t) $ and you want sample it at rate of $ f_{s} $ you should generate discrete noise samples with variance of $ f_{s} \sigma^{2}_{cn} $.

This result is valid assuming before sampling the continuous noise you applied an ideal LPF filter with bandwidth of $ f_{s} / 2 $.

Full description is given here:
How to Simulate AWGN (Additive White Gaussian Noise) in Communication Systems for Specific Bandwidth

Every time you generate discrete noise samples (Using MATLAB's randn / rand for instance) you actually generate a band limited noise.

All you need to do is the adjustment of the variance of the discrete samples to the variance of the "Continuous" noise those samples are allegedly taken from.

Given a continuous White Noise (Wide Sense) with variance $ \sigma^{2}_{cn} \delta (t) $ and you want sample it at rate of $ f_{s} $ you should generate discrete noise samples with variance of $ f_{s} \sigma^{2}_{cn} $.

This result is valid assuming before sampling the continuous noise you applied an ideal LPF filter with bandwidth of $ f_{s} / 2 $.

Full description is given here:
How to Simulate AWGN (Additive White Gaussian Noise) in Communication Systems for Specific Bandwidth

Every time you generate discrete noise samples (Using MATLAB's randn / rand for instance) you actually generate a band limited noise.

All you need to do is the adjustment of the variance of the discrete samples to the variance of the "Continuous" noise those samples are allegedly taken from.

Given a continuous White Noise (Wide Sense) with variance $ \sigma^{2}_{cn} \delta (t) $ and you want sample it at rate of $ f_{s} $ you should generate discrete noise samples with variance of $ f_{s} \sigma^{2}_{cn} $.

This result is valid assuming before sampling the continuous noise you applied an ideal LPF filter with bandwidth of $ f_{s} / 2 $.

Every time you generate discrete noise samples (Using MATLAB's randn / rand for instance) you actually generate a band limited noise.

All you need to do is the adjustment of the variance of the discrete samples to the variance of the "Continuous" noise those samples are allegedly taken from.

Given a continuous White Noise (Wide Sense) with variance $ \sigma^{2}_{cn} \delta (t) $ and you want sample it at rate of $ f_{s} $ you should generate discrete noise samples with variance of $ f_{s} \sigma^{2}_{cn} $.

This result is valid assuming before sampling the continuous noise you applied an ideal LPF filter with bandwidth of $ f_{s} / 2 $.

Full description is given here:
How to Simulate AWGN (Additive White Gaussian Noise) in Communication Systems for Specific Bandwidth