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The question is not very specific so this will also be just a general answer. The stability of a composite linear-time-invariant (LTI) system composed of smaller LTI systems cannot be deduced from the stability of the component systems if the composition introduces feedback. Instead, you should test the stability of the full composite system. The system is ...


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How to calculate the variance of the noise samples $n[j]$ in terms of $N_0$ and $B$, where $n[j]$=$n_f(jT_s)$ and $T_s$ is the sampling period? Do you know how to calculate the variance of the process $\{n_f(t) \colon -\infty < t < \infty\}$? No? Hint: it is the area under the power spectral density curve of $\{n_f(t)\colon -\infty < t < \...


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I think you are confused by negative frequencies and what they mean so let me add this explanation. When you see a spectrum that contains "positive" and "negative" frequencies, each of the frequencies are of the form: $$e^{j\omega t}$$ Where $\omega$ is the frequency (in this case angular frequency as $2\pi f$ with f being the frequency in Hz. The ...


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If your time domain data is in units of vertical acceleration, then you can simply multiply the normalized (divide by N) raw fft values times the complex conjugate of itself and then take the square root. Each result will be the rms acceleration at that frequency. Note, if your data is sampled at 100 Hz, you are going to see the content from 0 to 50 Hz of ...


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Yes you are right. Aliasing only happens when you sample (either analog to digital conversion or during digital downsampling) a signal and refers to the overlap of signal spectrum due to an inadequate sampling rate; sampling rate below the Nyquist rate. Aliasing cannot happen at the output of a DAC (digital to analog converter). What happens is, if you do ...


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I believe you are running into stability issues in an output power control loop design. See below a diagram of similar power control loops that I have implemented, where for stability reasons any filtering in the loop is minimized and only done with the loop filter itself which is designed for stability. The noise you are trying to filter gets filtered by ...


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I cannot recall a meaningful difference between the ideal impulse train sampling and the uniform sampling relation indicated by the expression $t_n = n T_s$. Given a continuous-time bandlimited signal $x_c(t)$, when you sample this with an ideal impulse train $\delta_{T_s}(t) = \sum_k \delta(t - k T_s)$, then the relation between the obtained discrete-time ...


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This is to explain what actually sampling is and why and how it's done. Here I've generated a simple continuous-like sinusoidal signal with frequency fm = 10kHz. In order to make it appear as a continuous signal when plotting, a sampling rate of fs=500kHz is used Pretending the above-generated signal as a “continuous” signal, we would like to convert the ...


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For example, if you double the sampling rate, energy will be boosted by 3db. But power will remain same. Simply, because you have now double samples.


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