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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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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 $|\...
Piratemetaldrinkingcrew's user avatar
0 votes
1 answer
80 views

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{...
Piratemetaldrinkingcrew's user avatar
0 votes
0 answers
25 views

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 $x_2(t)$.
LSK's user avatar
  • 1
2 votes
1 answer
145 views

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 ...
karma123's user avatar
0 votes
0 answers
57 views

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{...
albusSimba's user avatar
0 votes
0 answers
51 views

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 ...
Ben Shaines's user avatar
0 votes
1 answer
39 views

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? $x\left(t\right)=\frac{T\left\{x\left(t\right)\right\}-1}{cos\left(\omega t\right)}$...
Ben Shaines's user avatar
1 vote
0 answers
58 views

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
Bitsaa's user avatar
  • 21
0 votes
2 answers
89 views

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(...
MOHAMED SALHI's user avatar
0 votes
0 answers
29 views

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 ...
Sotiris Siatiras's user avatar
2 votes
0 answers
42 views

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. ...
Gustav's user avatar
  • 21
2 votes
3 answers
749 views

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 ...
user avatar
0 votes
1 answer
61 views

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. ...
Illia Zakharov's user avatar
0 votes
0 answers
92 views

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 ...
Toxicone 7's user avatar
0 votes
0 answers
35 views

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_{...
pflykyle's user avatar
2 votes
1 answer
131 views

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 ...
Mikayla Eckel Cifrese's user avatar
1 vote
1 answer
167 views

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 ...
Halfy's user avatar
  • 13
0 votes
1 answer
128 views

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]...
Ahsan Yousaf's user avatar
  • 1,533
0 votes
0 answers
129 views

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{\...
user avatar
0 votes
1 answer
201 views

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]...
user avatar
1 vote
1 answer
350 views

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 ...
Ahsan Yousaf's user avatar
  • 1,533
1 vote
1 answer
393 views

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 ...
Fern Mendiz's user avatar
1 vote
1 answer
222 views

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]...
user avatar
1 vote
1 answer
54 views

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. ...
Tam's user avatar
  • 17
0 votes
1 answer
62 views

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 ...
Tam's user avatar
  • 17
0 votes
1 answer
63 views

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 ...
Tam's user avatar
  • 17
0 votes
0 answers
136 views

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 ...
In the blind's user avatar
0 votes
0 answers
71 views

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 ...
Nothing's user avatar
1 vote
1 answer
366 views

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 ...
sjaustirni's user avatar
0 votes
2 answers
176 views

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 ...
Irmantas Želionis's user avatar
0 votes
1 answer
676 views

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 ...
April Crude's user avatar
1 vote
0 answers
84 views

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, ...
yba's user avatar
  • 11
0 votes
1 answer
216 views

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] = \...
OuttaSpaceTime's user avatar
0 votes
1 answer
251 views

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 & \...
ian's user avatar
  • 1
0 votes
1 answer
155 views

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 ...
Christine's user avatar
0 votes
2 answers
150 views

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 ...
needbrainscratched's user avatar
1 vote
1 answer
325 views

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 ...
Megan's user avatar
  • 11
2 votes
1 answer
715 views

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 ...
CynthiaZ1998's user avatar
20 votes
3 answers
4k views

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 ...
NN amateur's user avatar
1 vote
1 answer
1k views

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??
Minato Namikaze's user avatar
-1 votes
1 answer
108 views

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 ...
canuel's user avatar
  • 17
0 votes
1 answer
33 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}...
Aedrha's user avatar
  • 53
1 vote
1 answer
75 views

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 ...
Aedrha's user avatar
  • 53
0 votes
1 answer
33 views

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 ...
Aedrha's user avatar
  • 53
0 votes
3 answers
144 views

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}{\...
Cath Maillon's user avatar
1 vote
1 answer
90 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 ...
love you's user avatar
  • 113
0 votes
1 answer
454 views

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(...
love you's user avatar
  • 113
0 votes
1 answer
1k views

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[...
prabhat Singh's user avatar
-1 votes
1 answer
354 views

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}) = \...
Eiv's user avatar
  • 1
1 vote
1 answer
356 views

Unit step function symbol

I've been studying communications and i see that the book used the symbol $u_{-1}(t)$ for unit step function , why ?
Elias's user avatar
  • 147

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