# 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 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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: $$y(t)=e^{-kt}u(t)\frac{\sin\left(\dfrac{{\pi}t}{10}\right)}{({\pi}t)}$$ where $u(t)$ is ...
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### 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 ...
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### 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 ...
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### 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 $F(:,:)$ ...
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### 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 ...
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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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### 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 – ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 pair of values, ...
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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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### 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.
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### 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?
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### 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 ...
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### Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
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### 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 ...
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### Find h[n] using DTFT properties

Using the DTFT property, find h[n] of a system where: Is it an FIR or IIR system?
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### 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 $$H_0(z) = 1+2z^{-1}+3z^{-2}+2z^{-3}+z^{-4}\quad\textrm{and}\quad H_1(z)=H_0(-z).$$...
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### 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 ...
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### 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 ...
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### 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 ...
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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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### 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 ...
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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 $$y[n] = w[n] + bw[n − ... • 35 3 votes 2 answers 482 views ### Extract approximation and detail coefficients I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)? 3 votes 1 answer 725 views ### Properties of DTFT to Infer the Inverse DTFT of Altered Data [closed] Given a signal  x \left[ n \right]  and its DTFT  X \left( {e}^{j \omega} \right) . Which property of the DTFT allows you to easily compute the inverse DTFT of  \frac{4 X \left( {e}^{j \omega} \... • 123 3 votes 1 answer 3k views ### Is this system invertible or not? Prove that the following system is invertible.$$y(t) = \mathcal{T}\{x(t)\} = \int_{-\infty}^{3t} x(\tau) \,\mathrm d \tau$$Answer: yes, the system is invertible. I need some hint here, not the full ... • 151 3 votes 2 answers 4k views ### How to plot magnitude response using \tt freqz in MATLAB if I have a transfer function without a denominator So I have the transfer function:$$H[z] = 1 + \sqrt{2}z^{-1} + z^{-2} $$And I have to evaluate H(e^{j\omega}) for \omega= 0, \pi/4, \pi/4 \ldots I have done the calculations manually using ... • 51 3 votes 1 answer 137 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 1 answer 526 views ### Understanding LTI systems graphically I'm currently working on this problem from Oppenheimer's book: Given x_{1}(t) and y_{1}(t) I should figure out y_{2}(t) and y_{3}(t) given that the system is LTI. My progress so far: I'm ... • 267 3 votes 3 answers 230 views ### 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 ... 3 votes 0 answers 112 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 ... • 31 3 votes 0 answers 511 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 0 answers 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 ... • 233 3 votes 0 answers 174 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[... • 403 3 votes 0 answers 143 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 \...
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 ...