# Questions tagged [homework]

Homework means the asker is requesting help with school homework. This lets potential answerers know that they should guide the student in solving the problem, rather than simply showing the complete answer.

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### How does range of input distribution affect SQNR of a uniform quantizer?

I learnt a formula in class for $$SNR = 1.76 + 6.02B$$ in $\rm dB$ where $B$ are the number of bits. Why is it independent of the range of distribution and only dependent on B? Given $n$ levels and a ...
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### How can I find expansion coefficients of the a vector in a given basis?

How can I find the coefficient of the vector $\mathbf y$? And how can the inner product be done on these vectors? Let $\mathbf y = \begin{bmatrix}1\\2\\0\\1\end{bmatrix}$ What are the expansion ...
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### How to find average and power of a signal

I need to find the average and the power of this signal: $$x(n)=\sum_{k=1}^{\infty}2^{-k}e^{j2{\pi}kn}$$ The problem is that the summation starts at 1 and not at 0, and a part of that how can I find ...
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### Compute output given input, transfer function and initial conditions

The problem statement is Consider a causal LTI system whose transfer function $H(s)$ is given as $$H(s)=\frac{s+2}{(s+3)(s+4)}$$ Compute the output $y(t)$ for an input $x(t)=e^{-2t}u(t)$ when $y(0)=1$...
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### Deriving of magnitude, phase response and impulse response of transfer function

I have a transfer function as $$H(z) = \frac{-0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z - 0.0625}{z^4}$$ I want to derive magnitude and phase response of this equation. can someone help me from here I ...
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### impulse response cascaded with time reversed of itself

Consider a filter with real-valued impulse response $h[n]$. The filter is cascaded with another filter whose impulse response is $h'[n] = h[-n]$, i.e. whose impulse response is the time-reversed ...
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### Determining time-invariance of a system

I have a question about determining time-invariance of a linear system. We are given this system and we need to determine if it is time-invariant or not: $$y(t)=\int_{-t}^{\infty}x(-3\tau)d\tau$$ ...
56 views

### Determine the Z-Transform for the following sequence: $|n|(\frac{1}{2})^{|n|}$

Determine the Z-Transform for the following sequence: $$|n|(\frac{1}{2})^{|n|}$$ I have tried to solve the above problem. However, the answer that I got is the negative of what is given in the ...
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### Finding inverse Z Transform

Find the inverse Z transform: I have done the solution but my answer does not match with the one given in the textbook. What I may have done wrong?
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### How to determine whether a filter is high/low or band pass from the Z transform?

How to solve questions of these kind? I have tried by replacing $z=re^{jw}$ and taking the limits from $0$ to $\infty$. But I am not sure what $e^{j\infty}$ is.
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### Invertibility of an ideal differentiator

Is the system $y(t)= dx(t)/dt$ invertible or not? If yes, please determine the inverse system for it.
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### Finding the frequency response $H(\omega)$ of a shifted sinc function

Given $$h[n]=\frac{\sin\left(\frac{\pi}{3}n-\frac{\pi}{3}\right)}{\pi n-\pi}\text,$$ use the table to find the frequency response $H(\omega)$. I don't have any clue that how to deal with the ...
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### Calculating the magnitude spectrum and phase spectrum

From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$. Then, I want to calculate its magnitude spectrum and phase spectrum. The ...
107 views

### How to match zero-pole diagrams to their frequency responses (Discrete Time)

I get confused when there are a lot of zeros/poles in the zero-pole diagram and I find difficulty understanding their frequency response. I know the following: 1. Complex conjugates cause double ...
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### Finite impulse response FIR filters

If H(Z) is linear phase FIR filter, then what can 1/H(Z) represent? Can it be causal and stable? Can it be stable if it is not required to be causal? I think it represents non linear phase FIR ...
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### Sampling period

The signal $x(t)=e^{-t^2}\text{sinc}(t)$ was sampled at interval $T$. It was then found that the discrete time Fourier transform of the sampled signal is: $X(e^{j\omega})=1$. What is the minimum $T$ ...
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### Derive DFT of $x((n+1)/2)$

If $X(k)$ is the $N$-point DFT of $x(n)$, and $y(n)= x\left(\frac {n+1}{2}\right)$ for odd $n$, and $0$ for even $n$. What is the $2N$ point DFT of $y(n)$ in terms of $X(k)$? So far, I've ...
### Which of these signals have same Nyquist rate as $x(t)$?
The options are: $x^2(t)$ $x(2t)$ Time derivative of $x(t)$ Convolution of $x(t)$ with itself I guess, the Nyquist rate remains the same as long as bandwidth of $X(w)$ remains the same, as Nyquist ...