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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How to Implement the moving average filter in time domain in MATLAB? [closed]
I have a sinusoidal x(t) = sin(500πt) signal is corrupted by random noise. The corrupted signal is sampled with sampling frequency fs = 5 kHz and passed through a 5-point moving average filter to ...
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1
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Calculate the power of a discrete-time signal
We got this question in our test :-
$$S(t) = 5\cos(10πt - π/2) + 6\sin(15πt)\cos(15πt)$$
My Solution :-
$$S(t) = 5\cos(10πt - π/2) + 3\sin(30πt)\qquad \textrm{[Using $\sin(2A) = 2\sin(A)\cos(A)$]}$$...
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Finding the impulse response given response to another signal
I was trying to solve this question :
I respresented $x(t) = u(t+1)-u(t-1)$
writing the convolution as $[u(t+1)-u(t-1)]*h(t) = y(t)$
I then used the property of differentiation to convert from the ...
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Impulse Response of real coefficient, LTI System
I'm trying to obtain the impulse response $h[n]$ of a system whose frequency response is $H(e^{j\omega})=R(\omega)e^{-25j\omega}$. I believed that $h[n]=h[n-25]$, would be the correct answer, however ...
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Stft of sinusoids
I have a sinusoidal signal of 10 minutes. For the first 5 minutes, the signal has a frequency of 100 Hz and for the next 5 minutes, the signal has a frequency of 200 Hz.
1 - If I look at the ...
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Minimum sampling frequency, quantization, and bitrate calculation
An analogue sensor has a bandwidth which extends from very low frequencies up to a maximum of 14.5 kHz. Using the Sampling Theorem what is the minimum sampling rate (number of samples per second) ...
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DTFT Pairs confusion
When I am in the DT Fourier Domain, and I want to come back to the time domain, which pair do I use? Asking because both pairs have the exact same "form" in the Fourier domain, and that is ...
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Find the autocorrelation function of signal $x(t) = u(t) - u(t-1)$
I have used the energy-type signal autocorrelation function:
$$\mathcal{R}_{xx}(\tau)=\int_{-\infty}^{\infty}x(t)x^*(t+\tau)dt$$
I have rewritten the equation as:
$$\begin{align}
\int_{-\infty}^{\...
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Is this system causal or not?
My efforts of solving this question are below.
I came to a conclusion that this system is causal, since:
$$
\begin{cases}
w[k]+5w[k-1]+6w[k-2]=x[k] \\
y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3]
\end{cases}
$$...
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MIT 6.003 HW#8 Problem 4 - Fourier Coefficients of Triangle Wave
In the mentioned homework, part of the solution involves finding the Fourier coefficients of the triangle wave.
The solution mentions that we can express this function as follows:
What does that ...
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Find power of a sum of sinusoids
We got this question to solve:
Calculate the power of the signal:
$$s(t) = 8\cos\left(20\pi t-\frac \pi4\right) + 4\sin(15\pi t)$$
Now, I thought of two approaches :
Use Parseval theorem, so first ...
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Determine if system is linear time variant
The system equation is given as:
$$y(n)=(n-1)x(n-1)+(n+1)x(n+1)$$
I solved that the system is time variant:
\begin{align}
y(n-k)&=(n-k-1)x(n-k-1)+(n-k+1)x(n-k+1)\\
H[x(n-k)]&=(n-1)x(n-k-1)+(n+...
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Convert complex valued sinusoid to real valued sinusoid
This is the homework problem: convert $x[n]=je^{j\pi n/8}-je^{-j\pi n/8}$ to a real valued sinusoid.
I understand that $\sin\theta=\dfrac{e^{j\theta}-e^{-j\theta}}{2j}$
In the solution, the answers ...
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Linear systems: Square root of input product
Hi guys i'm studying signals and systems, and my professor ask us if this signal is linear or not
$$y(t) = \big[x(t − 1)x(t + 1)\big]^{\frac 12}$$
the fact that is in the form of $x\cdot x$ told me ...
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Confusion for two-sided signal
Given a continuous LTI system with transfer function
$$H(s)= -\frac{2s}{(s+6)(s+2)}$$
Plot the location of the pole(s) and zero(s)
Find all possible regions of convergence
From the problem above find ...
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2
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Determining Causality and Time-Invariance of a system
Consider the following system:
$$y(t-1)=\int_{-\infty}^\infty x(𝜏)u(𝜏-t) d𝜏 $$
where $u(t)$ is the unit step function, which is zero for $t<0$ and equals $1$ for $t>0$.
$(1)$ Is the system ...
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Output of LTI (in time and frequency $\omega$ domain) : when input goes through LPF
I would like to raise a mathematical question :
Let's say we are been given :
$$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\
0 & \textrm{otherwise} ...
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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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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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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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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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1
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207
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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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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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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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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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1
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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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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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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,
$$d[k]...
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Fourier transform of an integrator filter
I have to find the Fourier transform , and $y(t)$ of an $ x(t) = e^{- \frac {t}{T} } u(t) $ that passes into a integrator filter. I know that $ Y(f) = X(f) H(f) $ so I first calculate the Fourier ...
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Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$
Find the Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$
I thought of making it to be a sinc, but at the bottom there is $n+3$ and if I replace $n+3$ then I don’t know how ...
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Simplfiying a system output equation
I have a problem getting the final (simplified) version of the system's (in the figure below) output equation y[n]:
For this system, I know that $$w[n] = x[n] + aw[n − 1]$$ and $$y[n] = w[n] + bw[n − ...
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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:
$$y(t)=\int_{-t}^{\infty}x(-3\tau)d\tau$$
...
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1
answer
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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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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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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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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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vote
1
answer
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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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1
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376
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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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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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1
answer
142
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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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vote
0
answers
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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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2
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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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1
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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 ...