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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194 views

order of fir filter

Assume we want to filter the audio signal from a digital video disc (DVD) player as shown in Figure P5–3. The filtered audio signal drives, by way of a digital-to-analog (D/A) converter, a speaker. ...
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1answer
2k views

Finding system stability

LTI system with impulse response: $h(t) = e^t \sin(-3t) \text{u}(-t)$ I know the rule and formula , but I am lost in how to do this because of the absolute. Please help. Sorry if I posted in the ...
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1answer
1k views

How to plot magnitude response using 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 ...
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1answer
49 views

Discrete time signals connected in series

Two discrete-time systems are connected in series. Their input-output difference equations are: \begin{align} w[k]&=0.25x[k-2]\\ y[k]&=0.5w[k-1]+0.5w[k-2]. \end{align} Determine ...
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1answer
108 views

How to find the Fourier transfer function of a Laplacian operation?

My practice exam question is: A discrete Laplacian operation on an image $f(x,y)$ results in the following output image: $$g(x,y) = 4f(x,y) - f(x+1,y)-f(x-1,y)-f(x,y+1)-f(x,y-1)$$ Find ...
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0answers
74 views

Using matlab (or some other tool) to perform convolution? [closed]

I have an homework assignment in my signals and systems class involving various tasks having to do with signal analysis, but my main question is this: I am given a system described by the differential ...
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1answer
75 views

Finding frequency respone of a differential/integral LTI system

So suppose that we have an LTI system defined by the differential/integral equation below, where $x(t)$ and $y(t)$ denote the system input and output, respectively. How would I find the frequency ...
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1answer
129 views

Gaussian noise definitions

I have an exercise that asks for us to determine the model for a system that goes like this: A battery manufacturer for cars is studying how their batteries behave. The measurements are influenced ...
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1answer
384 views

Samples per second in a row vector in Matlab?

I wrote two functions in MATLAB, function called half that removes every other element from an arbitrary length vector, creating a shorter vector made of only the ...
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1answer
297 views

Discrete time Signal Transformation

I have a discrete-time system defined by $y[ n]=x[5n+2]$. And an input $x_1[n]=\delta[n-5]$. Is the output $y_1[n]=\delta[25n-5+2]$?
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3answers
990 views

LTI systems inverse of each other

So my question looks like this: Suppose that we have two LTI systems with impulse responses $$h_1(t) = \frac 12\delta(t-1)\quad\text{and}\quad h_2(t)=2\delta(t+1).$$ Determine whether these ...
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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 ...
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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 $$H_0(z) = 1+2z^{-1}+3z^{-2}+2z^{-3}+z^{-4}\quad\textrm{and}\quad H_1(z)=H_0(-z).$$...
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1answer
220 views

BIBO stability of $1/x(t)$

I realize this is quite basic stuff but I am having trouble with the following question: Determine whether the following system with input $x(t)$ and output $y(t)$ is BIBO stable: $$y(t) = \frac{1}{...
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1answer
584 views

Signal generation: random noise

I have attempted question 1 a) below in MATLAB 6.5, but I need my answer to be checked. How do I do question 1 b) below ? What does it mean to have a zero mean? Generate the following signals ...
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1answer
629 views

How do I identify a notch filter given the transfer function?

I am studying for an exam, and a problem that my professor gave produces a transfer function that looks like the following: $$H(z)=\frac{z^2-j}{z^2-\frac{1}{4}j} = \frac{\left(z-e^{j\frac{\pi}{4}}\...
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1answer
59 views

Discrete entropies

I've been given a problem where I need to find the entropy of two random variables. I can find part of the answer, but not all of it. I am given the following: $X$ is a uniformly distributed random ...
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1answer
470 views

Find the difference equation and draw the simulation diagram

Calculate the difference equation and then draw the simulation diagram of the below transfer function. $$ H(z) = \frac{Y(z)}{X(z)} = \frac{0.4142 + 0.4142z^{-1}}{1.4142 - 0.5858z^{-1}} $$ I ...
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1answer
59 views

Finding the stability of the system [closed]

Determine whether the system $h(n)=nu(n)$ is BIBO stable or not. I have solved it and got it as unstable as $\displaystyle\sum_{n=-\infty}^\infty \lvert h(n)\rvert = \infty$. But the book ¹ is saying ...
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2answers
670 views

Textbook question regarding LTI System

I was posed the following homework problem: 2.10 The following input-output pairs have been observed during the operation of a time-invariant system: \begin{align} x_1(n)&=\{\underset{\...
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1answer
440 views

Magnitude spectrum for discrete-time signals

I am doing the following question (it is not homework, I am preparing for an exam). The time discrete signals $x_1(n)$ and $x_2(n)$ is created by sampling the continuous signal $x_a(t) = \cos (2 \...
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1answer
317 views

Designing observer with non-observable system

I have this state-space system \begin{align} \dot{x}&=\begin{bmatrix}1 & 0\\3 & -2\end{bmatrix}x+\begin{bmatrix}10\\0 \end{bmatrix}u\\ y&=\begin{bmatrix}1 & 0\end{bmatrix}x \end{...
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1answer
42 views

Inverse $\mathcal Z$-transform problem

$B(z)+B(-z) = 2c$, explain the structure of $b[n]$ and find the constraint of its length given that $c$ cannot be $0$. This is a homework problem. "Explain the structure" means that $b[n]$ is zero ...
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1answer
144 views

Output of lowpass filter with damped sine wave input

The random process $$Y(t)=\cos(\omega_0t)\cos(\omega_0t+\pi N(t))$$where $N(t)$ is a Poisson process of parameter $\lambda$ enters a lowpass filter with transfer function $$H(j\omega) = \left\{ \...
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1answer
1k views

DTFT and Inverse DTFT Homework Problem

I'm trying to solve this signals homework problem: So for part a, since multiplication in the time domain is convolution in the frequency domain, I just used a DTFT table, found the DTFT for $\left(\...
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1answer
407 views

Solving for frequency deviation, $\Delta f $ (FM modulation)

I'm sorry if I posted this in the wrong section. I solved the question and got $50\textrm{kHz}$, but the solution says it is $100\textrm{kHz}$ without any proof. Im asking for someone to tell me ...
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1answer
339 views

Demodulating upper sideband (USB) signals

A modulating signal $m(t)= \sin(2 \pi \nu_m t)$ is transmitted via a carrier of frequency $\nu_c$ using upper sideband (USB) modulation. Show that the USB modulated signal can be demodulated using a ...
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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 ...
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1answer
383 views

How to do this root locus by hand?

I have an open-loop system function $$L(s)=6\frac{(s-2)^2}{s(s-20)^2}$$ and I wanted to to the root locus diagram for it. I did it in MATLAB and got the following graph What I don't know how to do ...
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2answers
150 views

Impulse response of a continuous time system

Question The impulse response of a continuous time system is $h(t) = e^{-t}u(t)$. When $x(t) = u(t - 1)$ is input to this system what is the value of the output signal $y(t)$ at $t = 2.34$. My ...
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1answer
217 views

Signal equation using signal waveform and Fourier series?

Part A: Obtain signal waveform from mathematical equation of the signal Let a sinusoidal periodical signal is represented by an equation $$y=f(t)=10+10\cos\left(\frac{2\pi f_1t}{T} +\frac{\pi}{6}\...
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1answer
150 views

Response of cascading FIR filters

I can't seem to get the right answer for this. Could someone show me the procedure? As shown in the figure a system is constructed by cascading four FIR filters having the following frequency ...
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1answer
190 views

How to calculate transmission capacity?

My textbook doesn't explain how they got the answer to this question: "If a transmission channel uses an analog carrier wave that is modulated by eight amplitudes and sixteen frequencies per bit ...
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1answer
146 views

Are these Linear and Time Invariant Systems?

We were given the above systems and we were asked to tell whether they are linear (or not) and time invariant(or not). $y(m,n)=x(m,n)+c,\quad c>0$ $ y(m,n)=x(m,n)+x(m,-n)$ $y(m,n)=x(m,n+m)$ $y(m,n)...
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1answer
139 views

Linear Time-Invariant system frequency response and impulse response given input and output in time domain

I am having difficulty with this question specifically with the $\sin()$ part. So here goes nothing: Consider a Linear Time-Invariant system with input $x[n]$ and output $y[n]$. When the input to the ...
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2answers
821 views

How to find Fourier Series Coefficients

I saw many solved examples about this topic but again I coudn't come up with any solutions about this question. How can I find the Fourier Series coefficients of the following signal ? $x(t)=2 \cos(3\...
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2answers
64 views

What is the phase of the Fourier Transform of $h(n)={\frac13,\frac13,\frac13}$ (zero position is at 2nd element)

I am using Digital Signal Processing Principles, Algorithm and Applications, 4th edition written by Proakis and Manolakis. Here is s a part that I don't understand. $h(n)={\frac13,\frac13,\frac13}$. ...
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2answers
69 views

Unable to obtain correct correct fourier transform for homework

Okay so I have this question for my homework which I am asked to find the fourier transform of a signal. However I am unable to obtain the correct answer, the question and my working is shown below. ...
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1answer
361 views

How does both shifting and scaling a function affect the Fourier Transform?

I understand how shifting and scaling work separately, but I'm unsure how to put them together. That is to say, I understand if $x(t) = X(\omega)$, $x(at) = \frac{1}{|a|}X(\frac{\omega}{a})$ and $x(t-...
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1answer
2k views

Impulse response of non-causal system

Suppose I have the following equation, where $x[n]$ is the input and $y[n]$ is the output: $$x[n]-x[n-1]=-10y[n-1]+2y[n]+2y[n+1].$$ The question asks me to compute the impulse response from this ...
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1answer
115 views

properties of System

I am studying Signals and Systems. Anyone, please help me to answer the problems. $y(t)=dx(t)/dt$ is time invariant: True or False ? $h(t)$ is the impulse response of an LTI system. If $h(t)$ is ...
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2answers
88 views

How to represent half of equilateral triangle signal?

How to represent the signal in above image ? I know a ramp signal can be represented by $$x(t) = t\cdot u(t)$$ but here amplitude of that signal is not same with $t$
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1answer
36 views

Artificial Neural Network Example Problem

I was looking at an example of a NN but I dont understand in the Answer i where the .68 come from or .6637 This is the link of the tutorial
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1answer
3k views

Question on sketching the amplitude spectrum of signals

I can't seem to understand the sketches of the amplitude spectrums provided in my tutorial solutions. For this part , I understand that X(f) is basically sampling (T/Tp)sinc(Tf). But from what I ...
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1answer
65 views

Working out integration of basic signal functions

As the title suggests , I'm having problems working out the integration of some basic signal functions. Shown below are the questions and my workings. For some reason I'm just unable to get the answer....
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1answer
115 views

What happens at the edges in fft2 filtering?

I am doing a fairly simple homework assignment in MATLAB that is to filter an image in the frequency domain. So my code looks something like this: ...
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1answer
324 views

Example exercise - Shannon's law on PCM-digitized signal

I am studying for a Digital Communications course in my university, and I am presented with the following example exercise. You have a sound signal with spectral components in the 300-3000 Hz range....
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1answer
1k views

Circular Convolution of h(n)*x(n)

So I understand how Convolution works but Circular convolution seems a bit messy to me, all the examples seems to have even series of number like h(n)={1,2,3,4} & x(n)={1,2,3,4} and they are all ...
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2answers
90 views

How to simplify this sequence

So I had this question (f) at my last exam that I failed and I'm now studying for my re-exam, the problem is that I still don't know what the answer is supposed to be in this question (f): Do you ...
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2answers
386 views

Filtering of complex exponential functions

In my problem the signals $x(t), h(t), w(t), y(t)$ and $y_w(t)$ are defined as follows: \begin{align} x(t)&=\sum_{i=1}^M a_i\delta(t-\tau_i) \\ h(t)&=e^t\exp\left(-e^t\right) \\ w(t)&=\...