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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What can be the pole zero diagram [closed]
Does the pole zero plot for $$H(z)=(1-z^{-1})^3(1+z^{-1})^3$$ have 6 poles at origin and 3 zeroes at 1? Just answer yes or no, not your homework question knowledge
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Prove the following [closed]
If $$x_1[n]=A$$ where $A$ is a constant, $$x_2[n]=u[n]$$ and $$x_3[n]= \left \{ \begin{array}{l} 1, \mbox{for n=0}\\-1, \mbox{for n=1}\\ 0, \mbox{otherwise} \end{array}\right.$$
Prove that $$x_3[n]\...
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Alternative way to find fourier transform
Let $$x(t) = A \text{rect}_T({t-\tau})$$I calculated its fourier transform through the direct way: $$X(\omega) = Ae^{-i\omega \tau} \int_{-T/2}^{T/2} e^{-i \omega t} dt = Ae^{-i\omega \tau} \frac{\sin(...
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How can I identify possible tonal maskers from frequency and DFT coefficients?
I have a question given in my homework and I have no idea how to even approach it:
Given I have 5 frequencies that are inside the zone of a bark from 200-300 HZ ...
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Extract approximation and detail coefficients
I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
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Calculating connected component's central moments
I am learning about image's moments. As an exercise I got this:
For x̄ value I get 5 from this formula:
$$= \frac{\sum_{x=1}^{X} \sum_{y=1}^{Y} xf(x,y)}{\sum_{x=1}^{X} \sum_{y=1}^{Y} f(x,y)}$$
As ...
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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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Find constants such that the Nyquist criterion is satisfied [closed]
I have been given the following spectrum, and I want to find a and b such the pulse satisfies the Nyquist criterion, given that the bandwidth of the pulse is 2 kHz and the sampling frequency is 3 kHz. ...
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How can I find the following Fourier Transform without directly using FT pairs?
The question is to find the CTFT of $$x(t) = e^{-t}u(t)\cdot \sum_{n=-\infty}^{\infty} \delta\left(t-\frac{n}{2}\right)$$
Now I know that multiplication in time means convolution in the Fourier Domain ...
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Magnitude spectrum of LTI system output signal
First year student so please excuse my lack of knowledge.
As i understand i need to use convolution which is:
$$ y^{out}(t) = u^{in}(t) * h(t) $$
Or maybe my thoughts are wrong so please correct me.
...
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How many samples are needed to compute an DFT?
Given a signal $x(t) = \frac4{10}\cos(800πt) + \frac12\cos(820πt) + \frac1{10}\cos(880πt)$ and knowing that the sampling frequency is $4000$ Hz.
How many samples are needed at least to represent the ...
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Expressing 2N point DFT in terms of N point DFT
I have a problem with expressing odd samples of X2 in terms of X1. I understand that the resulting DFT will be more precise in terms of expressing the exact spectrum of signal x[n], due to more ...
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Verifying Linearity and Shift Invariance Under Summation
I am having some trouble working through verifying linearity and shift invariance when the transformation is under a summation.
The given transformation is as follows:
$$
y(m,n)=\sum_{i=-1}^{i=1}\sum_{...
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How to find the variance of a noise signal distorting an ADC measurement
Say we have a 12-bit ADC measuring a signal with a voltage range of 0-10V, but the signal is corrupted by uniformly distributed 3-bit white noise. What's the correct way to get the variance of the ...
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Trouble with subtracting a signal by a unit impulse
For my homework I was given the signal by the illustration:
I was asked to draw the illustration for $$x_1(t) = 3x(-1+0.5t) - \delta(-t+3)$$
I have figured out how to draw the $3x(-1+0.5t)$ part, but ...
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A discrete time signal $x[n]$ is defined in terms of unit impulse function.Express the signal $x[n]$ in terms of step signal
A discrete time signal $x[n]$ is defined in terms of unit impulse function as follows:
$$x[n]= 1-\sum_{r=3}^\infty \delta[n-1-r]$$
If $x[n]$ is expressed in terms of the unit step function as $x[n]=u[...
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What does it mean to find the steady state output in this case?
I have a given $h[n] = 0.96^n$ for $n \in \{0,1,...,119\}$ and a test signal $x[n] = \cos(0.05\pi n)$ for $n \in \{0,1,...,N_x -1\}$ where $N_x = 120,000$.
Now, I can analytically find the output $y[n]...
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How to find the following DFT?
Let $x[n] = \cos(\frac{\pi}{8}n)$ and $X(k) = \text{DFT}_{16} \{ x[n]\}$
In order to find $X(k)$ I write out the DFT sum:
$$X(k) = \sum_{n=0}^{N-1} x[n] e^{-j2\pi kn/N} = \sum_{n=0}^{15} \cos(\frac{\...
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Inserting zeros: effect on DFT
Let N be an even integer, and $x[n]$ be a finite length signal over the interval $n\in [0,N-1]$; let $X[k]$ be the N-pt DFT of $x[n]$.
Find the 2N-Pt DFT of $x_1[n]$ in terms of $x[n]$, where:
$$x_1[n]...
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How to compute the 2N-Point DFT in terms of N-Point DFT with other properties involved
Let's say the N-Point DFT of $x[n]$ is $X(k)$.
Now from this question, I know how to compute the 2N-Point DFT of the same $x[n]$ in terms of $X(k)$
However, this idea doesn't translate well if I have ...
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Inverse Fourier Transform of $\omega ^2$ in $[-\omega _0,\omega _0]$
I've been learning about signals for a while now, and I'm just starting to learn about Continuous time Fourier transforms. In this particular case, we were asked to get the inverse Fourier Transform ...
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Can anyone help with the properties of the DFT?
Let N be an even integer, and $x[n]$ be a finite length signal over the interval $n\in [0,N-1]$; let $X[k]$ be the N-pt DFT of $x[n]$.
Analytically find the DFT of each sequence below in terms of $X[k]...
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Plotting the amplitude and angle spectre of this signal
I am looking clarification that I have the appropriate solution to this question, thoughts and tips to improve my understanding are also welcome!
f(n) is a discrete sample of the following signal. ...
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Determining the full DFT values of X(k) given a partial sample [closed]
I have a sample of a signal lets say 8 values of a 16 value sequence. I am trying to obtain the full DFT from the partial.
I am thinking that I am going to work back, I read the matlab documentation ...
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proof of alias matlab sin wave and syntax for time array
I have been asked to prove the following;
Show that a sinusoid of amplitude 10V and frequency 2kHz sampled at
%fs = 10kHz is an alias of a 500Hz sampled signal.
I have develped the code for the 500hz ...
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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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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$$
Answer: yes, the system is invertible. I need some hint here, not the full ...
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Impulse response from the transfer function
The discrete system has poles at points $z_{1,2} = 0.8e^{\pm{i\pi /6}}$ and $z_{3,4}=0.8e^{\pm{i\pi/2}}$, and two-fold zeros at $1$ and $-1$. The task is to determine the impulse response of the ...
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Difference between causality and memorylessness
I have found the particular definitions.
Causality means that the output of the system does not depend on future inputs, but only on past input.
Memory-less - does not depend on previous values of ...
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What is the probability of binary digits produced
An information source produces a long sequence of three independent symbols A,B,C with probabilities 16/20, 3/20, and 1/20 respectively; 100 such symbols are produced per second. The information is to ...
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Compute output given input, transfer function and initial conditions
The problem statement is
Consider a causal LTI system whose transfer function $H(s)$ is given as $$H(s)=\frac{s+2}{(s+3)(s+4)}$$ Compute the output $y(t)$ for an input $x(t)=e^{-2t}u(t)$ when $y(0)=1$...
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How do I check for linearity for the following piecewise-defined system?
The problem at hand:
Where I'm currently stuck:
I'm not entirely sure about how to move on from this point, I'm trying to find the superposition of the responses of the two individual signals so I ...
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Trouble with inverse Z-transform and calculating of samples
I have a little problem. I have to solve this task but I can't.
Z-transform of sequence $\{x(k)\}$ describe by the formula:
$$X(z) = \frac{2.5 -3.15z^{-1} + 1.2 z^{-2}}{1-2.3z^{-1} + 1.2z^{-2}}$$
...
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Inverse z-transform. Where is mistake?
I've already wrote about that trouble (link here), but I don't understand where I've made a mistake.
Full description of the task is as follows:
Z-transform of sequence {x(k)} describe by the ...
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Axes of Discrete Fourier Transform
Problem
Given $X[k] = \sum_{n=0}^{N-1} x[n]e^{-j2\pi kn/N}, k = 0, ..., N-1$
What are the units on the x-axis and y-axis? Note that for the x-axis there are two answers.
Attempted solution
My first ...
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Find response of discrete time LTI system given input and impulse response
For this question the guide says to use $Y(e^{j\omega}) = H(e^{j\omega}) X(e^{j\omega})$.
I have been able to find the discrete time Fourier transform of the impulse function as $$H(e^{j\omega}) = \...
CommunityBot
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Impulse response $h[n]$ of a non linear I/O equation
my question concerns an assignment that was given to us at school.
We have been given a list of I/O equations and it is required, for each of them, to find the impulse response $h[n]$ and the ratio ...
CommunityBot
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How do I know what is causing the noise in my signal
I have a noisy audio file, available here (It is safe to download if you wish to)
https://ufile.io/pstrt
Now, I inspect it in matlab:
And then i plot it on normalised frequency:
Now I need to ...
CommunityBot
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Calculating tranfer function, poles, zeros and impulse response given input and outpul signals in matlab
I have been given an input and output signal.
input: x(n)=(0.3^n)*u(n) + (5^n)*u(-n-1)
output: y(n)=(3^n)*u(-n-1) - ((2^(n+2))/(3^n))*u(n).
or
x=(0.3.^n).*(n>=0) + (5.^n). *(n<=-1) --> in ...
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Plotting the Frequency Response of Zero-Order Hold
I'm trying to find the frequency response and the DC gain, then plot the response and find the cutoff frequency from the graph.
I start off with the impulse response
$$h(t)= 1 ; 0\leqslant t\leqslant ...
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How to do appcoef and detcoef using pyWavelets?
I am new to signal processing and currently doing a school project in wavelet transform using Python. I want to extract all details and approximations (Example: cA2, cA1, cD2, cD1), pywt could return ...
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Labels in speaker verification
I'm a beginner.
If I am using a Convolutional Neural Networks with Triplet Loss as a loss function (also combined with GAN and a Classifier) for building a model that performs Speaker Verification, ...
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Output of LTI (in time and frequency $\omega$ domain) : when input goes through LPF
I would like to raise a mathematical question :
Let's say we are been given :
$$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\
0 & \textrm{otherwise} ...
CommunityBot
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How do I find the ROC of a system if it has no poles
The output of a system of discrete time $y[n]$ is corellated with the input $x[n]$ through the equation $y[n]$.
$$y[n] = \frac 13\big(x[n-1]+x[n]+x[n+1]\big)$$
It then asks me to find the system ...
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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 ...
CommunityBot
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Ratio of the power in the sidebands to the total power in conventional AM
Message signal and carrier signal are given as
$m=\cos(2 \pi \cdot f_{m} \cdot t) $
$c=A_{c}\cdot \cos(2 \pi \cdot f_{c} \cdot t) $
I was asked to find modulation index $a$ so that ratio of the ...
CommunityBot
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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 ...
CommunityBot
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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 ...
CommunityBot
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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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Meaning of a formula about transient frequency bins
I'm trying to understand the following formula in this paper:
Sadly, the paper does not define most of the symbols it is using, so my guesses so far are:
$T_{tr}$ refers to the sampling interval
i....
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