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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35 views

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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1answer
19 views

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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1answer
29 views

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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61 views

Is this an energy or power signal?

Is the given input signal x[n] an energy or power signal? The image shows what I did so far. Is it correct? Thank you! EDIT: I solved it again, please tell me if I did it correctly this time. $$E= \...
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1answer
58 views

Find the length of the impulse response for the given output and input

Homework Question: Consider a signal $x[n]=\alpha e^{j \omega_{0} n}+\beta e^{j \omega_{1} n}+\gamma e^{j \omega_{2} n} .$ What is the length of impulse response $h[n]$ of a system (non-trivial) such ...
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1answer
53 views

Inverse discrete time Fourier transform with differentiation

Consider a signal x[n] and its DTFT $X(e^{jω})$ . Assume $X(e^{jω})$ is differentiable. Compute the inverse DTFT of $j\frac{dX(e^{jω})}{d\omega}$ You should write your answer in terms of $x[n]$ and ...
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1answer
38 views

Finding causal impulse response given the imaginary part of the frequency response

I understand that I would need to calculate inverse Discrete Time Fourier Transform (iDTFT) to find $h(n)$. Since $h(n)$ is real, iDTFT of the imaginary part of $H(e^{j\omega})$ gives the odd part of ...
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1answer
39 views

What is the Z-transform of $0.8^{n+2}u(n-1)$?

I have 2 signals. One is $x(n)=(-0.5)^nu(n)$ and the other one is $y(n)=0.8^{n+2}u(n-1)$. I know that for the first one it is $X(z)= 1/(1+0.5z^{-1})$, but what about the other one? I know $y(n)$ is ...
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2answers
222 views

DFT exercise in the book Understanding digital signal processing 3 Ed

I am trying to solve exercises from the book Understanding digital signal processing 3 Ed - Richard Lyons. I will repeat the question as it is in the book: 3.3 We want to calculate an N-point DFT ...
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1answer
89 views

How can I find the transfer function of the following block diagram?

I've the following image and I want to find the transfer function from input $x(t)$ to output $y(t)$. I know that I have to apply Laplace Transform, so the integrator becomes $\dfrac{1}{s}$, but I don'...
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1answer
58 views

Can time-invariance be determined from a given a transfer function?

I've the following function. $$ G(z) = 2 + \frac{-1+5z^{-1}}{(1-0.5z^{-1})(1-z^{-1})}$$ Calculating it's inverse using $\mathcal Z$-Transform, I get the following function: $$g[n] = 2\delta[n] + 8u[n] ...
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1answer
36 views

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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1answer
62 views

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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2answers
63 views

Showing error energy goes to zero

Let $$\hat{x}[k] = \frac{1}{2\pi}\int_{-W}^{W}X(e^{j\omega})e^{j\omega k}d\omega,\label{ift}\tag1$$ where $$X(e^{j\omega}) = \sum_{n=-\infty}^{+\infty} x[n]e^{-j\omega n}\label{dft}\tag2$$ Also, $$d[k]...
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1answer
45 views

Fourier transform of an integrator filter

I have to find the Fourier transform , and $y(t)$ of an $ x(t) = e^{- \frac {t}{T} } u(t) $ that passes into a integrator filter. I know that $ Y(f) = X(f) H(f) $ so I first calculate the Fourier ...
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1answer
81 views

Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$

Find the Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$ I thought of making it to be a sinc, but at the bottom there is $n+3$ and if I replace $n+3$ then I don’t know how ...
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1answer
32 views

Simplfiying a system output equation

I have a problem getting the final (simplified) version of the system's (in the figure below) output equation y[n]: For this system, I know that $$w[n] = x[n] + aw[n − 1]$$ and $$y[n] = w[n] + bw[n − ...
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2answers
97 views

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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2answers
78 views

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: $$y(t)=\int_{-t}^{\infty}x(-3\tau)d\tau$$ ...
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1answer
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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1answer
29 views

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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1answer
46 views

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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3answers
70 views

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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0answers
43 views

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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1answer
45 views

Given a signal and its Fourier transform, find FS coefficient of the shifted sum of the signal

Given $x_1(t),X_1(j\omega), x_2(t)=\sum_{k=-\infty}^{\infty}x_1(t-6k)$, find Fourier series coefficient of $x_2(t)$. Looking up the FT table, I got $X_2(j\omega)=\sum_{k=-\infty}^{\infty}e^{-j\omega ...
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1answer
376 views

Calculating the Fourier transform of shifted scaled unit step function

I have $x_1(t)$ here. To get $x_2(t)$, I need to differentiate $x_1(t)$. Express $x_2(t)$ as $2u(t+2)-4u(t)+2u(t-2)$. From Fourier transform definition integral, I got $X_2(j\omega)=\frac{2e^{j\omega ...
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1answer
184 views

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 ...
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1answer
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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1answer
47 views

Adaptive equalization vs inverse of transfer function

I have the following equalization problem as shown in the figure below: Now I can compute the coefficients for my adaptive FIR filter c (dim(c) = N) the following: $\mathbf{c_{opt}} = (\mathbf{H}^T\...
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34 views

Adaptive interference calcellation

I've got a question regarding an adaptive filter for interference calcellation: Here, the interference is a periodic signal: $x[n] = \cos(\pi/4\cdot n + \varphi_1) + \cos(3\pi/4\cdot n + \varphi_2)$ ...
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1answer
75 views

Discrete Fourier Transform in Signal Processing - Interpreting graphs of transformed signals

Given above are the real parts of the signals I to IV. Which of the following statements are correct? (i): Signal III is the result of the discrete Fourier transform of signal I. The associated ...
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1answer
26 views

Change phase of the output of a buffer

I have a question about changing the phase of a buffer. Question - How to change the output phase of a buffer by 90 degrees, 180 degrees, and 270 degrees? I know to change the phase by 180 degrees, ...
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0answers
29 views

Explain if the following processes are stable or not

I have got a question about my homework and was wondering if anybody could help. In the picture below you can see the processes. I need to determine whether they are stable or not. Now I have only ...
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2answers
71 views

DFT frequency resolution exercise [closed]

I have a discrete signal that goes as follows: $$x[n]=[-1,4,-1,0]$$ I have already done the DFT for the signal, with the following result: $$X[0] = 2, X[1]=-4i,X[2]=-6,X[3]=4i$$ But for some reason, I ...
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1answer
36 views

To find the impulse repsonse using the difference equation

A causal linear time-invariant filter has transfer function a) Denote the input signal by x[n] and the output signal by y[n]. Find the difference equations for the filter. f) Find the impulse ...
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36 views

Signal to Quantization noise problem

a full scale signal of bandwidth 5 khz is sampled by an 10-bit ADC at a sampling rate of 2 Msa/sec calculate the Signal to Quantization noise of the resulting DT signal repeat for a 14-bit ADC at ...
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1answer
48 views

How can I obtain the response signal for this question?

In particular I am having trouble with 6b). From what I understand, we can split a difference LTI equation into two sums, the sum of the previous responses, and the sum of the previous inputs. ...
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1answer
49 views

Fourier Series representation of a signal

Use the defining equation for the Fourier Series coefficients to evaluate the Fourier Series representation of the following signal: $$x(t)=\sum_{m=-\infty}^{+\infty}=(\delta(t-m/3)+\delta(t-2m/3))$$...
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1answer
63 views

ROC and impulse response

For the LTI system given below, there are three regions of convergence. $$H(z)=\frac{5-3z^{-1}}{1-\frac53z^{-1}-\frac23z^{-2}}$$ a) Find all possible regions of convergence for this filter. b) For ...
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1answer
34 views

To find the filter Co-efficients of the following equation

Given $y[n]=h_1[n]x[n]+h_2[n]x[n-1]+h_3[n]x[n-2]$ is an LTI system with unity gain at $\omega =0$ and zero gain at $\omega =\pi$. $h[n]\neq0$ .Also given that the system has a linear phase. Compute $...
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2answers
427 views

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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1answer
100 views

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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1answer
79 views

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 ...
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1answer
157 views

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 ...
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1answer
82 views

Recovering a signal after filtering

A signal $x[n]$ is to be transmitted over a communication channel. The communication channel is described by an FIR filter of length $M$ such that the received signal is given by $$r[n]=\sum_{k=0}^...
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2answers
223 views

Determine the Given system is linear or nonlinear [closed]

Does the following define a linear or nonlinear system? $$ y(n) -4 y(n)y(2n)=x(n) $$
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0answers
35 views

Calculating the number of MACs in a system

I want to calculate the number of MACs. I am looking for the method. How would I do it if I know the domain equations from a biquadratic digital filter. I have already calculated the Z domain ...
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1answer
71 views

Computing response of LTI system in terms of its step response

I have solved a problem, Kindly help me in determing if I solved it correctly. I will post the question and my own working below. Problem My working
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1answer
854 views

How to prove a filter has linear phase response?

I have designed an FIR filter to have linear phase response using odd-symmetry design. The coefficients of this filter are {2,1,3,1,0,-1,-3,-1,-2}. I am now being asked to prove it has linear phase ...
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2answers
435 views

Question About Sampling White Noise

Assuming that we have a continuous signal $v(t)$ $$v(t) = \int_0^t g(u)\, \mathrm du\tag1$$ where $g(t)$ is white noise.Then take the derivative of it. $$\frac{\mathrm d}{\,\mathrm dt} v(t) = g(t)\...

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