# Tag Info

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### What sampling frequency should I use if Nyquist is not available?

HINT When you sample at below the Nyquist rate, aliasing happens. That means frequencies higher than half the sampling rate get folded back down to below half the sampling rate. Have a read about ...
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### What sampling frequency should I use if Nyquist is not available?

As correctly stated in Peter K.'s answer, this question is about aliasing. Since you can't sample at a rate that is sufficiently high to avoid aliasing - i.e., $f_s>50\textrm{ kHz}$ - you have to ...
• 90.8k
Accepted

### Why is $A\cos(2\pi f_ct)$ a non-stationary process?

A random process is a collection of random variables, one random variable for each time instant. It is best to write the random process as $$\{X(t)\colon -\infty < t < \infty\} \tag{1}$$ where ...
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• 6,650
Accepted

### What will be the filtered output?

First note that: $$\cos(2\pi 50 t) \longleftrightarrow 0.5 \delta(f+50) + 0.5\delta(f-50)$$ $$\sin(2\pi 150 t) \longleftrightarrow 0.5 j \delta(f+150) -j 0.5\delta(f-150)$$ Hence the baseband ...
• 28.3k
Accepted

### Transmitting over Unknown Fading Channel

The strategy depends heavily your "realistic scenario", e.g. which estimator, which equalizer, which estimation error, etc. In general scenario, you cannot trust the estimate of $h$, it means that ...
• 6,650
Accepted

The standard meaning of white noise includes an insistence (whether implicit or explicit) that the mean is $0$. Thus, what you want to prove is trivially true: since $$Y[n] = \sum_{k=-\infty}^\infty ... • 20.6k 4 votes ### Fourier components of \cos(2\pi f_1t) HINT: Going from your last equation,$$\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)$$This can be simplified further down ... • 3,416 4 votes Accepted ### Expressing 2N point DFT in terms of N point DFT Consider N-point sequence x[n] whose N-point DFT is X[k]. To compute 2N-point DFT, X_2[k], of x[n], one should append N-zeroes to x[n], and make it a 2N-point sequence, denoted x_2[n]. ... • 28.3k 4 votes ### Difference between causality and memorylessness A memoryless system's output is determined by the current input value only, hence, every memoryless system must also be causal (a system is causal if its output does not depend on the future input ... • 28.3k 4 votes ### Finite impulse response FIR filters In order for H(z) to be a linear phase filter, it must zeros both on the inside of the unit circle and at the complementary locations (1/z) which are outside the unit circle. Therefore a linear phase ... • 53.3k 4 votes Accepted ### Discrete-time Fourier transform of \frac{\cos(\frac{n\pi} 6)}{(n+3)\pi} HINT:$$\frac{\cos(n\pi /6)}{(n+3)\pi}=\frac{\cos[(n+3)\pi/6 -\pi/2]}{(n+3)\pi}=\frac{\sin[(n+3)\pi/6]}{(n+3)\pi}
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Purely by inspection of the block diagram the system is causal, because the output is the sum of the current input sample and stuff that's delayed -- there's no $z$ blocks in there to predict the ...