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I don't think it's a good idea to add random noise to frequency response. In general, you should add noise to the input or output signal. You should be clear that at which stage the noise in introduced. According to the different stages of noise introduction, there are two main transfer function estimators, $H_1$ estimator and $H_2$ estimator.

1. $H_1$ assumes that there is no noise on the input and consequently that all the input measurements are accurate. All noise is assumed to be on the output.

$$ \hat{Y}(\omega) = H(\omega) X(\omega) + N(\omega) $$ where $\hat{Y}(\omega)$ is the observed output signal, which is polluted by additive noise $N(\omega)$. And you will see that there is a deviation between the estimated frequency response and the real one.

$$ \hat{H}(\omega) = \frac{\hat{Y}(\omega)}{X(\omega)} = H(\omega) + \frac{N(\omega)}{X(\omega)} $$

This estimator tends to give an underestimate of the frequency response if there is noise on the input.

2. $H_2$ estimator assumes that there is no noise on the output. Noise is assumed to be only on input.

$$ Y(\omega) = H(\omega) \Big[X(\omega) + N(\omega)\Big] $$

This estimator tends to give an overestimate of the frequency response if there is noise on the output.

Check here Transfer function estimate

I don't think it's a good idea to add random noise to frequency response. In general, noise is added to the input or output signal. You should be clear that at which stage the noise is introduced. According to the different stages of noise introduction, there are two main transfer function estimators, $H_1$ estimator and $H_2$ estimator.

1. $H_1$ assumes that there is no noise on the input and consequently that all the input measurements are accurate. All noise is assumed to be on the output.

$$ \hat{Y}(\omega) = H(\omega) X(\omega) + N(\omega) $$ where $\hat{Y}(\omega)$ is the observed output signal, which is polluted by additive noise $N(\omega)$. And you will see that there is a deviation between the estimated frequency response and the real one.

$$ \hat{H}(\omega) = \frac{\hat{Y}(\omega)}{X(\omega)} = H(\omega) + \frac{N(\omega)}{X(\omega)} $$

This estimator tends to give an underestimate of the frequency response if there is noise on the input.

2. $H_2$ estimator assumes that there is no noise on the output. Noise is assumed to be only on input.

$$ Y(\omega) = H(\omega) \Big[X(\omega) + N(\omega)\Big] $$

This estimator tends to give an overestimate of the frequency response if there is noise on the output.

Check here Transfer function estimate

I don't think it's a good idea to add random noise to frequency response. In general, you should add noise to the input or output signal. You should be clear that at which stage the noise in introduced. According to the different stages of noise introduction, there are two main transfer function estimators, $H_1$ estimator and $H_2$ estimator.

1. $H_1$ assumes that there is no noise on the input and consequently that all the input measurements are accurate. All noise is assumed to be on the output.

$$ \hat{Y}(\omega) = H(\omega) X(\omega) + N(\omega) $$ where $\hat{Y}(\omega)$ is the observed output signal, which is polluted by additive noise $N(\omega)$. And you will see that there is a deviation between the estimated frequency response and the real one.

$$ \hat{H}(\omega) = \frac{\hat{Y}(\omega)}{X(\omega)} = H(\omega) + \frac{N(\omega)}{X(\omega)} $$

This estimator tends to give an underestimate of the frequency response if there is noise on the input.

2. $H_2$ estimator assumes that there is no noise on the output. Noise is assumed to be only on input.

$$ Y(\omega) = H(\omega) \Big[X(\omega) + N(\omega)\Big] $$

This estimator tends to give an overestimate of the frequency response if there is noise on the output.

I don't think it's a good idea to add random noise to frequency response. In general, you should add noise to the input or output signal. You should be clear that at which stage the noise in introduced. According to the different stages of noise introduction, there are two main transfer function estimators, $H_1$ estimator and $H_2$ estimator.

1. $H_1$ assumes that there is no noise on the input and consequently that all the input measurements are accurate. All noise is assumed to be on the output.

$$ \hat{Y}(\omega) = H(\omega) X(\omega) + N(\omega) $$ where $\hat{Y}(\omega)$ is the observed output signal, which is polluted by additive noise $N(\omega)$. And you will see that there is a deviation between the estimated frequency response and the real one.

$$ \hat{H}(\omega) = \frac{\hat{Y}(\omega)}{X(\omega)} = H(\omega) + \frac{N(\omega)}{X(\omega)} $$

This estimator tends to give an underestimate of the frequency response if there is noise on the input.

2. $H_2$ estimator assumes that there is no noise on the output. Noise is assumed to be only on input.

$$ Y(\omega) = H(\omega) \Big[X(\omega) + N(\omega)\Big] $$

This estimator tends to give an overestimate of the frequency response if there is noise on the output.

Check here Transfer function estimate

I don't think it's a good idea to add random noise to frequency response. In general, you should add noise to the output signal.

$$ \hat{Y}(\omega) = H(\omega) X(\omega) + N(\omega) $$ where $\hat{Y}(\omega)$ is the observed output signal, which is polluted by additive noise $N(\omega)$. And you will see that there is a deviation between the estimated frequency response and the real one.

$$ \hat{H}(\omega) = \frac{\hat{Y}(\omega)}{X(\omega)} = H(\omega) + \frac{N(\omega)}{X(\omega)} $$

I don't think it's a good idea to add random noise to frequency response. In general, you should add noise to the input or output signal. You should be clear that at which stage the noise in introduced. According to the different stages of noise introduction, there are two main transfer function estimators, $H_1$ estimator and $H_2$ estimator.

1. $H_1$ assumes that there is no noise on the input and consequently that all the input measurements are accurate. All noise is assumed to be on the output.

$$ \hat{Y}(\omega) = H(\omega) X(\omega) + N(\omega) $$ where $\hat{Y}(\omega)$ is the observed output signal, which is polluted by additive noise $N(\omega)$. And you will see that there is a deviation between the estimated frequency response and the real one.

$$ \hat{H}(\omega) = \frac{\hat{Y}(\omega)}{X(\omega)} = H(\omega) + \frac{N(\omega)}{X(\omega)} $$

This estimator tends to give an underestimate of the frequency response if there is noise on the input.

2. $H_2$ estimator assumes that there is no noise on the output. Noise is assumed to be only on input.

$$ Y(\omega) = H(\omega) \Big[X(\omega) + N(\omega)\Big] $$

This estimator tends to give an overestimate of the frequency response if there is noise on the output.