# Tag Info

### Covariance vs Autocorrelation

According to your definition of autocorrelation, the autocorrelation is simply the covariance of the two random variables $Z(n)$ and $Z(n+\tau)$. This function is also called autocovariance. As an ...
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### Understanding the mathematical proof for the alias frequencies in a sampled sine wave

The reason is that if it is true for any $m$, it is also true for $m=kn$. I will sketch the proof in another way. Call $f_s = 1/t_s$ sampling frequency where $t_s$ is sampling period, the two signal ...
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### Fourier components of $\cos(2\pi f_1t)$

HINT: Going from your last equation, $$\frac{\sqrt{T}}{2}\bigg(\frac{e^{j2\pi (f_1T-n)}-1}{j2\pi (Tf_1-n)} + \frac{e^{-j2\pi (f_1T+n)}-1}{-j2\pi (Tf_1+n)}\bigg)$$ This can be simplified further down ...
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### Derivation of $R_{N(t)}(\tau)$ from its $f_{N(t)}(\eta)$

As @MattL points out in a comment, a Gaussian pdf does not imply whiteness. Indeed, it can be argued that the assumption that the process is a continuous-time white noise process is contrary to the ...
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