# 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
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### 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 ...
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 ...
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....
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
1answer
54 views

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 ...
1answer
98 views

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?
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 ...
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 ...
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'...
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 ...
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 ...
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 ...
2answers
197 views

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] =...
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 ...
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 ...
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 ...