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.
399
questions
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How to periodize a rectangular pulse?
A new signal u3p(t) has to be generated from u3(t) through periodic extension with a period T = Ti.
u3p(t) has to be drawn from -Ti ≤ t ≤ 2Ti.
I have a graph of the resulting periodic function (see ...
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Signal , discrete , random, independent
Let $x(n)$ be a discrete, random independent process, with Gaussian distribution with mean value $\mu_x = 1$ and standard deviation $ \sigma_x = 3$.
Compute the probability that $x(n) < 0$ and the ...
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Need help with deriving a recursive formula for a control system optimization integral
I need some help with a problem that appears in one of the exercises of "Introduction to Stochastic Control Theory" by Karl J. Åström: Chapter 5, page 141, problem 8.
It is about deriving a ...
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2
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Fourier series - finding its period from frequency representations
I’ve been given the following signal:
$$X^F(\omega) = \sum_{n=-\infty}^{\infty} 2\pi a[n] \delta(\omega - \omega_0 n)$$
and I was asked to:
find it’s period
given $|X^F(\omega)| \ne 0$ only at $|\...
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1
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realistic sampling - where am I wrong?
I’m given a signal $x(t)$, it's convolved with $h(t)$ and sampled at rate T=1. The result is called $\tilde{x}[n]$.
For $$h(t) = \begin{cases} 1 & -0.5<t\le 0.5 \\ 0 & \text{else} \end{...
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How to prove this system is not causal?
I set $x_1(t)=0$ and use the final rest property to get $y_1(t)=0$, and $y_2(t)=0$ for $t>1$. However, I cannot find general $y_2(t)$ for $x_2(t)$.
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Does the impulse response of every stable system have finite energy?
I need to show that the impulse response of every stable system has finite energy.
I have trouble solving this problem.
Since impulse input signal is unbounded, I can't apply BIBO stability of system ...
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Finding the Power Spectral Density of $x(t)$
Consider a binary signal $x(t) = \sum_{n=-\infty}^{\infty}a_ns(t-nT_b)$ where,
$$
s(t) = \left\{\begin{matrix}
1& t\in[0, T_b) \\
0& o.w.
\end{matrix}\right.
$$
and
$$
a_n = \left\{\begin{...
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Finding inverse $Z$ Transformation of a LTI system and switching of input output signal regarding to difference equation
I have 2 stuffs that are bothering me:
I have the equation:
$y[n]=8x[n]-2x[n-2]-x[n-4]$
When $x[n]$ input and $y[n]$ output.
Now, the system is swapped, $x[n]$ output and $y[n]$ input
The difference ...
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How to check if a NON LTI System is invertible?
$T\left\{x\left(t\right)\right\}=x\left(t\right)cos\left(\omega t\right)+1$
Can I say that? or there is another way?
$x\left(t\right)=\frac{T\left\{x\left(t\right)\right\}-1}{cos\left(\omega t\right)}$...
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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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Alternative way to find fourier transform
Let $$x(t) = A \text{rect}_T({t-\tau})$$I calculated its fourier transform through the direct way: $$X(\omega) = Ae^{-i\omega \tau} \int_{-T/2}^{T/2} e^{-i \omega t} dt = Ae^{-i\omega \tau} \frac{\sin(...
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How can I identify possible tonal maskers from frequency and DFT coefficients?
I have a question given in my homework and I have no idea how to even approach it:
Given I have 5 frequencies that are inside the zone of a bark from 200-300 HZ ...
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Find constants such that the Nyquist criterion is satisfied [closed]
I have been given the following spectrum, and I want to find a and b such the pulse satisfies the Nyquist criterion, given that the bandwidth of the pulse is 2 kHz and the sampling frequency is 3 kHz. ...
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How can I find the following Fourier Transform without directly using FT pairs?
The question is to find the CTFT of $$x(t) = e^{-t}u(t)\cdot \sum_{n=-\infty}^{\infty} \delta\left(t-\frac{n}{2}\right)$$
Now I know that multiplication in time means convolution in the Fourier Domain ...
user67157
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Magnitude spectrum of LTI system output signal
First year student so please excuse my lack of knowledge.
As i understand i need to use convolution which is:
$$ y^{out}(t) = u^{in}(t) * h(t) $$
Or maybe my thoughts are wrong so please correct me.
...
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How many samples are needed to compute an DFT?
Given a signal $x(t) = \frac4{10}\cos(800πt) + \frac12\cos(820πt) + \frac1{10}\cos(880πt)$ and knowing that the sampling frequency is $4000$ Hz.
How many samples are needed at least to represent the ...
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Verifying Linearity and Shift Invariance Under Summation
I am having some trouble working through verifying linearity and shift invariance when the transformation is under a summation.
The given transformation is as follows:
$$
y(m,n)=\sum_{i=-1}^{i=1}\sum_{...
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1
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148
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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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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:
$$X(k) = \sum_{n=0}^{N-1} x[n] e^{-j2\pi kn/N} = \sum_{n=0}^{15} \cos(\frac{\...
user67157
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1
answer
238
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Inserting zeros: effect on DFT
Let N be an even integer, and $x[n]$ be a finite length signal over the interval $n\in [0,N-1]$; let $X[k]$ be the N-pt DFT of $x[n]$.
Find the 2N-Pt DFT of $x_1[n]$ in terms of $x[n]$, where:
$$x_1[n]...
user64710
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382
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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]...
user67157
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1
answer
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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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1
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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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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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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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1
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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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2
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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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1
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728
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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
$$h(t)= 1 ; 0\leqslant t\leqslant ...
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0
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Labels in speaker verification
I'm a beginner.
If I am using a Convolutional Neural Networks with Triplet Loss as a loss function (also combined with GAN and a Classifier) for building a model that performs Speaker Verification, ...
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How to calculate the DFT for this sum of cosine's in the form $\sum A_i \cos(\omega_i n + \phi_i)$ for fixed $N$
I am stuck trying to calculate the DFT for a given $N$
Given the signal $x[n] = \cos(\frac{\pi}{2}n - \frac{\pi}{2})+2 \cos(\pi n + \frac{\pi}{2})$ and $N = 4$ I tried to calculate the DFT
$X[k] = \...
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397
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Fourier Series of a piecewise function
I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
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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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2
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How would one solve this question if no initial conditions are given? Which assumption can I make?
This was a question on our test, I know it can be easily solved by Z-transforms but there are no initial conditions specified. In this case, what would be the right approach?
Assume all initial ...
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1
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351
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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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1
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761
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How to design a Controller that would adjust the steady-state error of a system?
I have a simple model (input-plant-output) with a transfer function :
$$
T(s)=\frac{4}{s^{2}+2s+4}
$$
The goal of this problem is to design a system such that it has the following specification for a ...
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3
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What sampling frequency should I use if Nyquist is not available?
I have the following homework question that confuses me:
We have an audio emitter that can emit two signals:
It either emits a sine wave at 23 kHz or it emits a sine wave at 25 kHz.
The receiver has ...
- 313
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vote
1
answer
1k
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Fourier Transform of the conjugate of a complex function [closed]
Given that $x(t)$ Fourier Transforms to $X(f)$. What happens when you Fourier Transform $x^*(t)$, and your $x(t)$ and $x^*(t)$ are both complex functions??
-1
votes
1
answer
111
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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 ...
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votes
1
answer
36
views
Running a signal through a circuit with some odd components
I am studying a course in signal analysis and systems. Currently we are looking at aliiasing, samplig,DTFT and reconstruction.
I got stuck on an excercise.
For the in signal $x_{a}(t)=2\cos(2\pi F_{0}...
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1
vote
1
answer
82
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FInd the amplitude function to a system
I'm studying a course in signal analysis and have come across an exercise where I find the analytical part a bit tricky.
I am to find the amplitude function $|H( f )|$ for a system with the impulse ...
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votes
1
answer
34
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Zeroes and poles for a system
I have run into some issues on an exercise for the course in signal analysis and systems I am currently studying.
We are to create an echo effect and are using the system below:
I am to find the ...
- 53
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votes
3
answers
153
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Noise variance estimation under known channel
I have $N$ observations $\{y_i\}_{i=1..N}$
$$y_i = h_i x_i + w_i$$
where $\{x_i\}_i$ are the realizations of uniform distributed QPSK symbol $x$, i.e. $x_i \in \{\pm\frac{1}{\sqrt{2}} \pm j\frac{1}{\...
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1
vote
1
answer
91
views
Find $A$ and $G$ value to satisfy the requirement
Given a disturbance reduction system
Create a system that will reduce $U(s)$ noise to $100$ times its value. Find the A and G gain value to satisfy the requirement
My attempt:
I've analyzed the ...
- 113
0
votes
1
answer
487
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Finding transfer function from bode plot
Given a bode diagram
From the figure, I see that when $\omega = 100 \text{ rad/s}$ the magnitude response starting to go down and when $\omega = 1000 \text{ rad/s}$ the slope become higher. Then
$$H(...
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