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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1answer
223 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 ...
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2answers
194 views

Fourier series coefficient of signal when Time period is twice the fundamental period

My try: First of all I tried observing the symmetry but I did'nt find any.So I tried to calculate the fourier series coefficient of the signal like this First I differentiated the signal $x(t)$ so ...
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1answer
216 views

Finite moving average filter

I am trying to solve this problem but I need a lot of help. Below are my answers for the separate parts, please check and tell me where I am wrong because I am weak on the fundamental concepts of this....
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3answers
115 views

LTI system phase response given $z$-transform

I have been given this question \begin{equation} H\left(z\right)\:=\:\frac{1}{6}\left(1+z^{-2}\right)^6 \end{equation} (a) Compute and plot the phase response of the system. (b) Determine ...
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4answers
90 views

Signal periodicity in discrete-time

Let $x[n]$ be a discrete-time signal, and let $$y_1[n]=x[2n]$$ You have to show that if: $x[n]$ is periodic, then $y_1[n]$ is periodic. $y_1[n]$ is periodic, then x[n] is periodic. So for the ...
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1answer
38 views

Determine proper coefficients for the transfer function

The problem says that we have the information (actually a .mat file that contains the data) of 1 pixel from an IR camera from an object with 26° of temperature. Because of the noise, the output is ...
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1answer
6k views

Find the minimum sampling rate

As the signal $m(t)$ is Baseband signal after modulation it wil be bandpaas signal will look like this So I need to use the Baseband sampling Here $f_L=15kHz,f_H=25kHz,B=5kHz,$Now Undersampling ...
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2answers
142 views

which filters are these?

Location of poles are given in unity circle and 4 zeros are given at origin for every plot,How to check which plot shows which filters? For the Option (C) i am doing like this I can write the ...
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2answers
223 views

DT unit impulse function properties proof

How to prove the following properties of DT unit impulse function. If anyone got link to a proof please mention it. I have search on the web. But only found the properties, not a proper method of ...
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1answer
54 views

calculating estimate of a state for a system with two observations of the state from different times

I'm struggling with a problem that I just can't seem to get a grasp of. I'm supposed to calculate an estimate for state $x(k)$ at times $k=1,2,3$ from the state-space $ \begin{align} x(k+1) &= A ...
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1answer
2k views

Find the impulse response of an LTI system?

why there is a 3/2 in the (b) problem? Does the impulse response even exist?
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1answer
464 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 ...
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1answer
694 views

Linearity, Causality and Stability of a System

Consider a system: $$ y[n] = y[n-1] + u[n], $$ where $y[n]$ is the output and $u[n]$ is the unit step function. Is this system causal, linear, time-invariant and stable ? My attempt at the ...
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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?
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1answer
265 views

obtaning discrete-time system impulse response $h[n]$ from step response $s[n]$ [duplicate]

The discrete-time system of figure below a step response: $$s[n] = \left[ 5 - 4 \left( \frac{4}{5} \right)^n \right] u[n]$$ Find the impulse response of the system and verify it from the system ...
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1answer
863 views

Minimum number of Poles and zero of transfer function H(z)?

Suppose $G(z)=H(z)(1-\frac{1}{2}z^{-1})$ now in question its saying ROC of G(Z) is entire Z plane except Z=0,so here we need not to add anything because G(Z) already a right sided signal with ROC ...
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1answer
554 views

Find the nyquist sampling rate?

I have a signal $x(t)$ for which I want to find the Nyquist frequency : $$ x(t) = \frac{\sin{\pi t/2}}{\pi t/2} \ast \sum^\infty_{n=-\infty}\delta(t-10n)$$ I am trying to solve this in the time ...
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1answer
49 views

which of the analog sinusoidal frequency can not pass through the filter?

First time I am encountering this type of question so i just tried but not getting whether my logic correct or not. First let the sinusoidal signal be $X(t)=\cos(2\pi ft)$. After sampling this ...
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1answer
88 views

Deriving statistics of band limited Random Noise

The question is: Consider a continuous random number with a Gaussian distribution of mean $\mu$ and variance $\sigma$ . The RV is measured from time $t=-\infty$ to $t=\infty$. This time domain signal ...
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1answer
592 views

LTI system $y(t)=x(t-T)$ with or without memory

How can I verify if the LTI system ($T$ is a real number, $y(t)$ output, $x(t)$ input): $$y(t)=x(t-T)$$ is with or without memory? I know that, if $y(t)$ depends only on $x(t)$, the LTI system will ...
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3answers
1k views

Under what circumstances is a non-uniform quantizer preferable over a uniform quantizer? [closed]

I am studying btech ECE 3rd year. I want answer that question. Please tell me.
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1answer
2k views

How to add two signals?

If x(t) is the curve shown in the image how can I find (x(2t)+x(2t+2))? I know how to find the individual terms but don't know how to add them! And how can I express my answer in terms of the unit ...
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1answer
978 views

Convolution by differentiation property of convolution

This is the question when i am trying to do it by the deravative property of convolution https://en.wikipedia.org/wiki/Convolution#Differentiation like this Actual answer should come like this $...
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1answer
230 views

homework impulse response of system [closed]

Problem A student is given an unknown DT system. Upon entering a test signal x_tst[n] = [-1, 1] into the system, an output y_tst[n] = [0,-1,-1,2] is observed. Determine the impulse response of the ...
2
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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),\...
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2answers
119 views

Would anyone be able to help out with the following discrete convolution question?

I have been trying to attempt this question for quite a while and I am not sure how to approach it. Would anyone be able to help out with the working?
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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 – ...
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1answer
447 views

What are two different continuous-time signals when sampled at $10\textrm{ Hz}$ would produce the sequence $x(n)=\cos(n\pi/8)$?

The answer is: $\cos(1250\pi t)$ and $\cos(21250\pi t)$ I’m not able to verify. My understanding is that when you periodically increase $t$ by $1/10$ ($10$ here is the frequency, so $1/10$ is ...
2
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1answer
831 views

Signal to Quantization Noise Ratio (SQNR)

I have this problem in my homework (following picture). How do find the signal to quantization noise ratio at the output? I don't want the solution. I just want to know a better approach to tackle ...
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1answer
80 views

Tracking an object in a video with

I need to track an object in a video with MATLAB. There is an example frame from the video above. I need to track that car that carries the pendulum. But my problem is there is a bar behind the car ...
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1answer
174 views

Periodicity of signals

$$x(t) = \cos(2 \pi t) \cdot u(t)$$ $$y(t) = x(t) + x(-t)$$Is $y(t)$ periodic. If so, what is the $T$? $$x(t) = \sin(2 \pi t) \cdot u(t)$$ $$y(t)= x(t) + x(-t)$$ Is $y(t)$ periodic?
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1answer
65 views

Compute filter output with given values of $n$

\begin{align} x[n] &=\begin{cases} 1& \text{for}\quad n \ge 0\\ 0& \text{otherwise} \end{cases}\\ h[n] &= \delta[n] - \delta[n-1]\\ y[n] &= x[n]*h[n] \end{align} Find the ...
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1answer
561 views

Gravity center of a discrete signal

One of the problems of my home assignment was this. If i use the definition to solve this(I'm not seeing other way) i have an expression like $\sum\sum nx[n]e^{-j\omega n}$ on the numerator and $\sum\...
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2answers
2k views

Stability of a system

Is the system $y[n] = x[n] - x[n-1]$ stable or unstable ? If unstable, can you please give some examples of input signals for which the system becomes unstable?
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2answers
349 views

Fourier transform of $\sum_{n=-\infty }^\infty e^{-|t-2n|}$

I need to find Fourier transform of $$\sum_{n=-\infty }^\infty e^{-\lvert t-2n\rvert }$$ I found the solution online. But I think the choice of limits in equation (1) of the solution is wrong. It ...
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1answer
87 views

Does anyone can help me with signal processing problem?

(c)A linear time-invariant system with impulse response $h(t)=e^{-\alpha t} u(t)$ is driven by the input $x(t)=e^{-\beta t} u(t)$ . It is assumed that $\alpha, \beta > 0$. (i) Using ...
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2answers
1k views

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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2answers
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
69 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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2answers
197 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
233 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
77 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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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 ...
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2answers
143 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
308 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
426 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
261 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 ...
0
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1answer
52 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 ...