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 Transform of shifted Impulse

I'm new here and I hope you can help me. I started studying the Fourier Transform now at University and I have a lot of doubts about this subject. My teacher sent to us one list of exercises and I don'...
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57 views

Poles and Zeroes - Z Domain

2nd order Butterworth transfer function: $$H(z) = \frac{ 0.0201z^2 + 0.0402z + 0.0201 } { z^2 - 1.5609z + 0.6413 }$$ I'm a bit uncertain about the factorization at the denominator. Here's what I ...
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1answer
71 views

$\mathcal Z$-transform of an equation [Exam question]: Verifying the solution

I'm studying for exams at the moment and I'm trying to reproduce a solution from my professor (I have the solutions). The following signal is given: The excercise says: Calculate the Fourier ...
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2answers
111 views

Simplification after sampling an analog signal [closed]

$80\textrm{ Hz}$ Sampling rate produces the $x[n] = 3\cos(5\pi n/4)$ signal, the original analog signal is $x(t) = 3\ cos(100\ π t)$. This is a solved problem used as an example. In the solution ...
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220 views

Showing linear-phase frequency response when only real part is known

I'm studying for an exam, and this particular practice problem is missing the solution: Given a causal LTI system where only the real part of the frequency response is known, $$\Re\left\{H(j\...
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1answer
253 views

A property of all-pass filters

Let $G(z)$ be a real coefficient stable all-pass transfer-function with degree greater than zero. Then it can be shown that $|G(z)| < 1$ for $|z| > 1$: Given that the poles occur in complex ...
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1answer
78 views

Analogue filter analysis (band-pass)

The transfer-function: $$G(s) = \frac{\beta s}{s^2 + \beta s + \omega_0^2}$$ is to be used in an application that requires the magnitude of the frequency response to be of the band-pass form. ...
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395 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 ...
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147 views

Fourier transform of the product

I'm new at signal processing. I also don't know if this is the right section to post. I have this problem: I must calculate the Fourier transform of the signal shown in the image below I have ...
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1answer
325 views

How to solve this entropy integral?

I am having the entropy integral below where $\mathbf x$ is a $N$ dimensional Gaussian vector having variance as $\mathbf P$ and mean zero, $$ -\int\frac {\exp\left(\frac{1}{2}\mathbf x^T\mathbf P^{-...
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1answer
448 views

First order Wiener–Hopf filter design

Consider a random process with auto-correlation function: $$r_{\rm dd} [k] = \beta^{\lvert k \rvert}\quad\text{where}\quad 0 < \beta < 1. $$ Suppose also that the observation is: $$ x[n] =...
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2answers
282 views

Median filter problems about the output image

An image has an isolated cluster of dark pixels on a light background. The area of the cluster is $(n - 1)/2$ pixels where $n$ is an odd positive integer. What happens to the cluster when it is ...
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1answer
54 views

Harmonic oscillation and Fourier

I am back to college after 6 years of professional life and I need help with the following problem [...] The standard form of the function is $S_{E}(t) = e^{j2\pi f_k t}$, whose derivation ...
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1answer
3k views

Fourier-series odd vs even square wave?

I really need to know the difference when doing a fourier seires between even and odd square waves. I've been trying to understand but I just get the same results and the same spectrums... Is the ...
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1answer
243 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
2k 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
61 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
116 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
76 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
80 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
135 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
421 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
325 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
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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
280 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
322 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
302 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
702 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
681 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
569 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
63 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
835 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
507 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
366 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
43 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
156 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
460 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
373 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
378 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
436 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
165 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
219 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
177 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
192 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
153 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
180 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
1k 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\...