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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10
votes
1answer
6k views

Roberts Edge Detector how to use?

I am trying to use Roberts edge detection to process an image. Do I just apply both of the masks to the image and perform convolution as normal? Could someone give me the breakdown of how to use this ...
10
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2answers
3k views

How to Deduce a Linear System's Impulse Response from a Set of Input and Output Signals?

I want to know how to solve those types of problems.. is it by inspection ? Consider the linear system below. When the inputs to the system $x_1[n]$, $x_2[n]$ and $x_3[n]$, the responses of the ...
9
votes
3answers
3k views

Intuitive interpretation of Laplace transform

So I am getting to grasps with Fourier transforms. Intuitively now I definately understand what it does and will soon follow some classes on the mathematics (so the actual subject). But then I go on ...
9
votes
1answer
656 views

Solving a Convolution Problem of a 1D Signal

I'm finding in trouble trying to resolve this exercise. I have to calculate the convolution of this signal: $y(t)=e^{-kt}u(t)*\frac{\sin\left(\frac{{\pi}t}{10}\right)}{({\pi}t)} $ where $u(t)$ is ...
8
votes
3answers
382 views

Gesture recognition using only simple techniques

I'm following a computer vision course and I have this exercise: write a program that, given an hand image, it can recognize if the hand is open, closed, in a punch, or holding an "ok" posture, using ...
7
votes
3answers
552 views

Fourier series representation

Conceptually when we want to represent a peroidic series, for example a pulse train, we find the Fourier coefficients and get a representation in the time domain. However what is conceptually wrong ...
7
votes
1answer
213 views

Deriving 2-D discrete Fourier transforms

I have a problem in DFT. It was one of my past-year exam papers questions. Question: Let $F(u,v)$ be the 2-D Fourier transform of a 2-D continuous function $f(x,y)$. Derive in terms of $F(:,:)$ ...
6
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1answer
539 views

How to combine a rotation matrix and a stretch matrix into a single matrix for easy Fourier Transform

For full disclosure, this is related to homework. I have to find the Fourier Transform of a function that I've boiled down to the following. I have a function $f(x,y)$ that I can think of as another ...
6
votes
1answer
9k views

How to find frequency response, stability, and causality of a linear system?

I have the following transfer function: $$H(s)=\frac{s}{(s+1)(s+2)}$$ How can I find the gain and phase response of the above system? I know the first step has something to do with substituting $s = ...
5
votes
1answer
3k views

When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?

Heads up, this is for homework. I never took a signals and systems course, so I'm behind on this stuff. I want to compute the convolution of two rectangular regions. I know the standard equation ...
5
votes
2answers
255 views

Find the frequency response of a system

I'm trying to find the frequency response $$H(\omega) = Y(\omega)/X(\omega)$$ for this system- the signal equations are given: $$y[n] = v[n - M] - g * v[n]$$ $$v[n] = x[n] + g * v[n - M]$$ I've tried ...
4
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2answers
350 views

Why is $A\cos(2\pi f_ct)$ a non-stationary process?

I am studying analog communication and having Communication system - Simon Hykin as one of the reference. There is a question Consider the sinusoidal process$$X(t) = A\cos(2\pi f_ct)$$where the ...
4
votes
2answers
1k views

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 ...
4
votes
2answers
594 views

FFT vs DFT Run Time Comparison (Complexity Analysis) in MATLAB

So we were given an assignment to plot the time taken by the FFT algorithm by MATLAB and a DFT algorithm written by me in MATLAB.G The expected output should have been the DFT algorithm following the ...
4
votes
2answers
101 views

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.
4
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2answers
117 views

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?
4
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2answers
6k views

Polyphase Decomposition in Matlab

I created the lowpass filter h = firls(100, [0 .2 .25 1], [ 1 1 0 0],[.001 60]); My goal is to get four filters $H_{k}(z) = H(W_{4}^{k}z) k =0,1,2,3$ From my ...
4
votes
1answer
1k views

how to compute a discrete fourier transform on fragmented data

I have a list of collected data points that I need to take a DFT of, however with the problem that about one quarter of the data points in the middle are missing, and so even though the existing data ...
4
votes
1answer
164 views

Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
3
votes
3answers
2k views

LPF and HPF Confusion - Rectangular and Circular Cut-Offs

Interpreting some homework, I'm a little confused on what it's asking for. I'm asked to filter in the frequency domain (easy enough, just a fft2 and ifft2 when I'm done) a 256x256 8bit grayscale tiff ...
3
votes
2answers
289 views

Question about zero-phase filter bank

I found what I believe is a valid solution to the following assignment problem but the answer is bothering me. Let $$H_0(z) = 1+2z^{-1}+3z^{-2}+2z^{-3}+z^{-4}\quad\textrm{and}\quad H_1(z)=H_0(-z).$$...
3
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2answers
339 views

Given the Graph of a Fourier Series $\sum c_k e^{2\pi ikx}$ Find the Graphs of $\sum c_{3k} e^{2\pi ikx}$ and $\sum (c_k)^2 e^{2\pi ikx}$

Define a 1-periodic function on $\mathbb{R}$ by: $f(x) :=$ $\left\{\begin{matrix} 1 & if & 0<x<\frac{1}{10}\\ 0 & if & \frac{1}{10}<x<1 \end{matrix}\right.$ with ...
3
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2answers
105 views

Question About Sampling White Noise

Assuming that we have a continuous signal $v(t)$ $$v(t) = \int_0^t g(u)\, \mathrm du\tag1$$ where $g(t)$ is white noise.Then take the derivative of it. $$\frac{\mathrm d}{\,\mathrm dt} v(t) = g(t)\...
3
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2answers
346 views

Determine whether the system is linear?

$T(x[n]) = ax[n] + b$ $ T(\alpha_{1}x_{1}[n] + \alpha_{2}x_{2}[n]) = \alpha_{1}ax_{1}[n]+ \alpha_{2}ax_{2} [n] +b $ $ \alpha_{1}T(x_{1}[n] ) + \alpha_{2}T(x_{2}[n]) = \alpha_{1}(ax[n]+b) + \alpha_{...
3
votes
1answer
149 views

What transformations have been applied to this image to yield four derivatives?

In a few days I have an exam of image processing. I'm currently having a look at the example exam and I came across this question. "Which transformation of this image is being done here. Explain the ...
3
votes
3answers
4k views

Minimum period of a signal

What is the minimum period P (in samples) of the signal $e^{j(\frac{M}{N} )*2πn}$ for the following values of M and N? M=1,N=3 M=5,N=7 M=35,N=15 I have got the answer for the first ...
3
votes
1answer
469 views

How to 'interpret' the Fourier Transform (specifically, of a convolution kernel)

As part of a homework assignment, I had to take the Fourier transform of the kernel I was using to convolve a signal. The kernel was a constant rectangular function, that was 1 within the square $(-1,...
3
votes
2answers
279 views

Question on 2-D Convolution

This was a question on one of my past year paper questions. Question: Prove $$f(m,n)*g(m-r,n-s) = f(m-r,n-s) *g(m,n)$$ where $f(m,n)$ and $g(m,n)$ are 2-D discrete functions, $r$ and $s$ ...
3
votes
1answer
261 views

Use polyphase representation to construct a perfect reconstruction filter bank

I'm posting this question in response to Question about zero-phase filter bank This is a homework question for which I found an answer, but I didn't do it the way I was supposed to. I'm wondering ...
3
votes
1answer
102 views

Erosion in image

I don't if I am posting my question in the correct place. I have tried hard to solved it but I am unsuccessful. I have an structuring element shown below: ...
3
votes
1answer
292 views

Filtering $ n \times n $ Images by Separable $ m \times m $ Filters. Computation Time for Filtering Using FFT, 2D Convolution and Two 1D Convolutions

Consider filtering square $n\times n$ images by square, separable $m\times m$ filters. Give general equations for the computation time for the following approaches to this: Filtering using FFT 2-D ...
3
votes
0answers
54 views

Solving the PDE of a signal in an optical fiber

Disclaimer Please let me know if this is not the right place to ask this question. Disclaimer Part 2 I have no background in signals. My focus is in mathematics. In my programming class, we are ...
3
votes
0answers
362 views

Implementing blind deconvolution in MATLAB

I want to implement blind deconvolution for the signal $ r(n) = h(n) \star s(n) + a(n)$ in MATLAB where $r(n)$ is the recorded speech $h(n)$ is impulse response of room acoustics $s(n)$ is desired ...
3
votes
0answers
1k views

How do I check controllability and observability using Gramian matrixes?

I have a pending exam and this is one of the must-know questions. It will be about checking controllability/observability of a simple MIMO linear system, using Controlability Gramian/Observability ...
3
votes
0answers
106 views

Finding the output for an input sequence

So I think I have the answer I just want to make sure I'm doing things correctly. Let a be in the open unit disk, $F_s > 0$, and $0<f_0 < \frac{F_s}{2}$. Let $h[n]=0$ for $n < 0$ and $h[...
3
votes
0answers
133 views

Find $Y(\omega)$ as a function of $X(\omega)$ [closed]

I have a question regarding my homework. Let's assume that the transform of $x[n]$ is $X(\omega)$. Find $Y(\omega)$ as a function of $X(\omega)$: $$ y[n] =\cases{x[n/2],&\text{if } n \...
2
votes
2answers
2k views

how to evaluate derivative of convolution integral?

If the signal $x(t)$ has ordinary first derivative $\dot x(t)$, then $\dfrac{d}{dt}\big(x(t)\star y(t)\big)$ is: (a) $\dot x(t)y(t)$ (b) $x(t)\dot y(t)$ (c) $\dot x(t)\star y(t)$ (d) $\...
2
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2answers
2k views

Find h[n] using DTFT properties

Using the DTFT property, find h[n] of a system where: Is it an FIR or IIR system?
2
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1answer
6k views

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 – ...
2
votes
2answers
1k views

Finding the frequencies given in a wav file

I have a wav file containing a series of chords, each containing 3 or 4 notes, played concurrently. I need to find the frequencies of each note in each chord, and I can use matlab to do any ...
2
votes
4answers
2k views

Find $v_3$ such that $\{v_0, v_1, v_2, v_3\}$ is an orthogonal basis of $\mathbb{R}^4$?

In this question, we consider the Hilbert space of vectors in $\mathbb{R}^4$ with one of its basis $\{v_0, v_1, v_2, v_3\}$. Given the first three basis vectors $$v_0=\left[\begin{array}{c} 1/2\\ 1/2\\...
2
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1answer
54 views

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 ...
2
votes
1answer
3k views

IIR filter design in matlab

I have to design 2 IIR bandpass filter with the following specifications: Sampling frequency 1000 Hz Pass-band 50 Hz to 200 Hz Order 6 using bilinear transform and impulse invariance with Butterworth ...
2
votes
1answer
617 views

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 $...
2
votes
3answers
971 views

Obtaining the Impulse response from the frequency of a discrete system

I have the following discrete system's transfer function (Z domain): $$h[z] = {z \over z - \frac{1}{2} }$$ I need to obtain the following: The frequency response. The impulse response. The fourier ...
2
votes
1answer
515 views

Interpolation algorithms in computer graphics

I'm looking for an image-processing algorithm that uses interpolation (polynomial, spline, doesn't matter). I have to implement such algorithm to process a bitmap for my labs. It can't be image ...
2
votes
2answers
95 views

Finding the correct $x[n]$ from a given DFT $x[k]$ [closed]

I'm struggling to solve this question from an exam. The question gives you a set of IDFTs from a given DFT, only one of those is the correct. The first thing I did is notice that $2\sin(\pi k)$ will ...
2
votes
1answer
232 views

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 ...
2
votes
1answer
466 views

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 ...
2
votes
1answer
98 views

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),\...