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.
390
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The error probability of 16QAM
The signal constellation for a communication system with 16 equiprobable symbols is shown as below. The channel is AWGN with noise power spectral density of $N_ 0/2.$Using the union bound, find a bound ...
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1
answer
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Transmitting over Unknown Fading Channel
I have a system with no diversity and the channel's coefficients change every $T = 10\text{ bits}$ transmitted. The channel estimation system has a flaw and detects the channel's coefficients equal to ...
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2
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Problem identifying the analytic expression of such determined signal
I came across this problem
I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal.
The teacher suggests that I should consider ...
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1
answer
443
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Reconstruction of a signal using an ideal DAC
I think I was able to do part (a) correctly, but now am stuck on part (b). I don't know how to approach this part or what is the theory behind it.
My MATLAB code is shown below. Please let me know if ...
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1
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Relating transfer functions with step responses
Relate the transfer function to its' corresponding step response.
First, I tried setting up the poles and zeros of the transfer functions. This helped a bit since I know that $G_A (s)$, $G_B(s)$ and $...
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Smallest sampling frequency to fully reconstruct a signal
Given the spectrum of analog signal $x_a(t)$ which is imaginary and band-limited, find the lowest sampling frequency to be able to reconstruct $x_a(t)$ from samples $x[n]$.
My attempt: Bandwidth of ...
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4
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2
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115
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Filtering without using any transforms
A composite signal is defined as
$$x(t) = \sin(2\pi 10t) + \sin(2\pi 40t) + \sin(2\pi 60t) + \sin(2\pi 50t)$$
Separate the four frequencies without using any of the transform techniques.
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1
answer
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Plotting the discrete time signal
Consider the following analog signal
$$x(t) = 2 \sin(100\pi t)$$
The signal $x(t)$ is sampled with a sampling rate $F_s=50\textrm{Hz}$. Determine the discrete time signal. Plot the discrete time ...
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2
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Fourier series coefficient of signal when Time period is twice the fundamental period
My try:
First of all I tried observing the symmetry but I did'nt find any.So I tried to calculate the fourier series coefficient of the signal like this
First I differentiated the signal $x(t)$ so ...
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1
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Finite moving average filter
I am trying to solve this problem but I need a lot of help. Below are my answers for the separate parts, please check and tell me where I am wrong because I am weak on the fundamental concepts of this....
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3
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LTI system phase response given $z$-transform
I have been given this question
\begin{equation}
H\left(z\right)\:=\:\frac{1}{6}\left(1+z^{-2}\right)^6
\end{equation}
(a) Compute and plot the phase response of the system.
(b) Determine ...
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4
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Signal periodicity in discrete-time
Let $x[n]$ be a discrete-time signal, and let
$$y_1[n]=x[2n]$$
You have to show that if:
$x[n]$ is periodic, then $y_1[n]$ is periodic. $y_1[n]$ is periodic,
then x[n] is periodic.
So for the ...
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1
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Determine proper coefficients for the transfer function
The problem says that we have the information (actually a .mat file that contains the data) of 1 pixel from an IR camera from an object with 26° of temperature. Because of the noise, the output is ...
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Find the minimum sampling rate
As the signal $m(t)$ is Baseband signal after modulation it wil be bandpaas signal will look like this
So I need to use the Baseband sampling
Here $f_L=15kHz,f_H=25kHz,B=5kHz,$Now Undersampling ...
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which filters are these?
Location of poles are given in unity circle and 4 zeros are given at origin for every plot,How to check which plot shows which filters?
For the Option (C) i am doing like this
I can write the ...
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DT unit impulse function properties proof
How to prove the following properties of DT unit impulse function. If anyone got link to a proof please mention it. I have search on the web. But only found the properties, not a proper method of ...
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calculating estimate of a state for a system with two observations of the state from different times
I'm struggling with a problem that I just can't seem to get a grasp of. I'm supposed to calculate an estimate for state $x(k)$ at times $k=1,2,3$ from the state-space
$
\begin{align}
x(k+1) &= A ...
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Find the impulse response of an LTI system?
why there is a 3/2 in the (b) problem? Does the impulse response even exist?
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Is this system invertible or not?
Prove that the following system is invertible.
$$y(t) = \mathcal{T}\{x(t)\} = \int_{-\infty}^{3t} x(\tau) \,\mathrm d \tau$$
Answer: yes, the system is invertible. I need some hint here, not the full ...
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Linearity, Causality and Stability of a System
Consider a system:
$$
y[n] = y[n-1] + u[n],
$$
where $y[n]$ is the output and $u[n]$ is the unit step function.
Is this system causal, linear, time-invariant and stable ?
My attempt at the ...
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What will be the filtered output?
I tried to solve this question from basic
Here is my work
Image 1
Image 2
But the correct answer is Option $(B)$.What is the mistake i am doing?
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obtaning discrete-time system impulse response $h[n]$ from step response $s[n]$ [duplicate]
The discrete-time system of figure below a step response: $$s[n] = \left[ 5 - 4 \left( \frac{4}{5} \right)^n \right] u[n]$$
Find the impulse response of the system and verify it from the system
...
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2
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Minimum number of Poles and zero of transfer function H(z)?
Suppose $G(z)=H(z)(1-\frac{1}{2}z^{-1})$ now in question its saying ROC of G(Z) is entire Z plane except Z=0,so here we need not to add anything because G(Z) already a right sided signal with ROC ...
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1
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Find the nyquist sampling rate?
I have a signal $x(t)$ for which I want to find the Nyquist frequency :
$$ x(t) = \frac{\sin{\pi t/2}}{\pi t/2} \ast \sum^\infty_{n=-\infty}\delta(t-10n)$$
I am trying to solve this in the time ...
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which of the analog sinusoidal frequency can not pass through the filter?
First time I am encountering this type of question so i just tried but not getting whether my logic correct or not.
First let the sinusoidal signal be $X(t)=\cos(2\pi ft)$.
After sampling this ...
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1
answer
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Deriving statistics of band limited Random Noise
The question is:
Consider a continuous random number with a Gaussian distribution of mean $\mu$ and variance $\sigma$ . The RV is measured from time $t=-\infty$ to $t=\infty$. This time domain signal ...
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answer
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LTI system $y(t)=x(t-T)$ with or without memory
How can I verify if the LTI system ($T$ is a real number, $y(t)$ output, $x(t)$ input):
$$y(t)=x(t-T)$$
is with or without memory? I know that, if $y(t)$ depends only on $x(t)$, the LTI system will ...
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Under what circumstances is a non-uniform quantizer preferable over a uniform quantizer? [closed]
I am studying btech ECE 3rd year. I want answer that question. Please tell me.
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How to add two signals?
If x(t) is the curve shown in the image
how can I find (x(2t)+x(2t+2))?
I know how to find the individual terms but don't know how to add them!
And how can I express my answer in terms of the unit ...
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1
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Convolution by differentiation property of convolution
This is the question
when i am trying to do it by the deravative property of convolution
https://en.wikipedia.org/wiki/Convolution#Differentiation like this
Actual answer should come like this
$...
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homework impulse response of system [closed]
Problem
A student is given an unknown DT system. Upon entering a test signal x_tst[n] = [-1, 1] into the system, an output y_tst[n] = [0,-1,-1,2] is observed. Determine the impulse response of the ...
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What do I with the sampling period when I inverse $\mathcal Z$-transform?
Given the input
$$e(kT_s) = {0.4, 0.8,1.2, - 0.9}, \quad k = 0,1,2,3$$
and transfer function
$$T\left(z^{-1}\right)=\frac {z^{-1}-0.8z^{-2}}{1-1.1z^{-1}+0.3}$$
Find the output $Y(kT_s),\...
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Would anyone be able to help out with the following discrete convolution question?
I have been trying to attempt this question for quite a while and I am not sure how to approach it. Would anyone be able to help out with the working?
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Filter design with zero - pole placement method
I have some question for you about Filter design.
Α. Calculate the transfer function in order to stop the frequency of $300\textrm{ Hz}$ for sampling frequency at $12\textrm{ kHz}$. Use the
zero – ...
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2
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What are two different continuous-time signals when sampled at $10\textrm{ Hz}$ would produce the sequence $x(n)=\cos(n\pi/8)$?
The answer is:
$\cos(1250\pi t)$ and $\cos(21250\pi t)$
I’m not able to verify.
My understanding is that when you periodically increase $t$ by $1/10$ ($10$ here is the frequency, so $1/10$ is ...
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1
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Signal to Quantization Noise Ratio (SQNR)
I have this problem in my homework (following picture).
How do find the signal to quantization noise ratio at the output?
I don't want the solution. I just want to know a better approach to tackle ...
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1
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Tracking an object in a video with
I need to track an object in a video with MATLAB. There is an example frame from the video above. I need to track that car that carries the pendulum. But my problem is there is a bar behind the car ...
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1
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Periodicity of signals
$$x(t) = \cos(2 \pi t) \cdot u(t)$$
$$y(t) = x(t) + x(-t)$$Is $y(t)$ periodic. If so, what is the $T$?
$$x(t) = \sin(2 \pi t) \cdot u(t)$$
$$y(t)= x(t) + x(-t)$$
Is $y(t)$ periodic?
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Compute filter output with given values of $n$
\begin{align}
x[n] &=\begin{cases}
1& \text{for}\quad n \ge 0\\
0& \text{otherwise}
\end{cases}\\
h[n] &= \delta[n] - \delta[n-1]\\
y[n] &= x[n]*h[n]
\end{align}
Find the ...
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1
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Gravity center of a discrete signal
One of the problems of my home assignment was this.
If i use the definition to solve this(I'm not seeing other way) i have an expression like $\sum\sum nx[n]e^{-j\omega n}$ on the numerator and $\sum\...
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2
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Stability of a system
Is the system $y[n] = x[n] - x[n-1]$ stable or unstable ?
If unstable, can you please give some examples of input signals for which the system becomes unstable?
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Fourier transform of $\sum_{n=-\infty }^\infty e^{-|t-2n|}$
I need to find Fourier transform of
$$\sum_{n=-\infty }^\infty e^{-\lvert t-2n\rvert }$$
I found the solution online. But I think the choice of limits in equation (1) of the solution is wrong. It ...
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Does anyone can help me with signal processing problem?
(c)A linear time-invariant system with impulse response $h(t)=e^{-\alpha t} u(t)$ is driven by the input $x(t)=e^{-\beta t} u(t)$ . It is assumed that $\alpha, \beta > 0$.
(i) Using ...
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2
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Fourier Transform of shifted Impulse
I'm new here and I hope you can help me.
I started studying the Fourier Transform now at University and I have a lot of doubts about this subject.
My teacher sent to us one list of exercises and I don'...
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2
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Poles and Zeroes - Z Domain
2nd order Butterworth transfer function:
$$H(z) = \frac{ 0.0201z^2 + 0.0402z + 0.0201 } { z^2 - 1.5609z + 0.6413 }$$
I'm a bit uncertain about the factorization at the denominator. Here's what I ...
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1
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$\mathcal Z$-transform of an equation [Exam question]: Verifying the solution
I'm studying for exams at the moment and I'm trying to reproduce a solution from my professor (I have the solutions). The following signal is given:
The excercise says:
Calculate the Fourier ...
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2
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127
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Simplification after sampling an analog signal [closed]
$80\textrm{ Hz}$ Sampling rate produces the $x[n] = 3\cos(5\pi n/4)$ signal, the original analog signal is $x(t) = 3\ cos(100\ π t)$.
This is a solved problem used as an example. In the solution it's ...
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2
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336
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Showing linear-phase frequency response when only real part is known
I'm studying for an exam, and this particular practice problem is missing the solution:
Given a causal LTI system where only the real part of the frequency response is known,
$$\Re\left\{H(j\...
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1
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1
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576
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A property of all-pass filters
Let $G(z)$ be a real coefficient stable all-pass transfer-function with
degree greater than zero. Then it can be shown that $|G(z)| < 1$ for
$|z| > 1$: Given that the poles occur in complex ...
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85
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Analogue filter analysis (band-pass)
The transfer-function:
$$G(s) = \frac{\beta s}{s^2 + \beta s + \omega_0^2}$$
is to be used in an application that requires the magnitude of the frequency response to be of the band-pass form.
...
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