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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45 views

DFT frequency resolution exercise

I have a discrete signal that goes as follows: $$x[n]=[-1,4,-1,0]$$ I have already done the DFT for the signal, with the following result: $$X[0] = 2, X[1]=-4i,X[2]=-6,X[3]=4i$$ But for some reason, I ...
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1answer
26 views

To find the impulse repsonse using the difference equation

A causal linear time-invariant filter has transfer function a) Denote the input signal by x[n] and the output signal by y[n]. Find the difference equations for the filter. f) Find the impulse ...
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0answers
29 views

Signal to Quantization noise problem

a full scale signal of bandwidth 5 khz is sampled by an 10-bit ADC at a sampling rate of 2 Msa/sec calculate the Signal to Quantization noise of the resulting DT signal repeat for a 14-bit ADC at ...
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1answer
25 views

KL (Karhunen-Loève) transform of images

I know how to implement the Karhunen-Loève (KLT) for one 2D image. Which we first find the covariance matrix of the image vectors of length N along the column and the row dimension and etc. When we ...
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1answer
31 views

How can I obtain the response signal for this question?

In particular I am having trouble with 6b). From what I understand, we can split a difference LTI equation into two sums, the sum of the previous responses, and the sum of the previous inputs. ...
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1answer
42 views

Fourier Series representation of a signal

Use the defining equation for the Fourier Series coefficients to evaluate the Fourier Series representation of the following signal: $$x(t)=\sum_{m=-\infty}^{+\infty}=(\delta(t-m/3)+\delta(t-2m/3))$$...
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1answer
22 views

ROC and impulse response

For the LTI system given below, there are three regions of convergence. $$H(z)=\frac{5-3z^{-1}}{1-\frac53z^{-1}-\frac23z^{-2}}$$ a) Find all possible regions of convergence for this filter. b) For ...
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1answer
33 views

To find the filter Co-efficients of the following equation

Given $y[n]=h_1[n]x[n]+h_2[n]x[n-1]+h_3[n]x[n-2]$ is an LTI system with unity gain at $\omega =0$ and zero gain at $\omega =\pi$. $h[n]\neq0$ .Also given that the system has a linear phase. Compute $...
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2answers
144 views

Finite impulse response FIR filters

If H(Z) is linear phase FIR filter, then what can 1/H(Z) represent? Can it be causal and stable? Can it be stable if it is not required to be causal? I think it represents non linear phase FIR ...
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1answer
53 views

Sampling period

I started it but didn't how to continue , any help ?
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1answer
46 views

Derive DFT of $x((n+1)/2)$

If $X(k)$ is the $N$-point DFT of $x(n)$, and $y(n)= x\left(\frac {n+1}{2}\right)$ for odd $n$, and $0$ for even $n$. What is the $2N$ point DFT of $y(n)$ in terms of $X(k)$? So far, I've ...
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1answer
39 views

Which of these signals have same Nyquist rate as $x(t)$?

The options are: $x^2(t)$ $x(2t)$ Time derivative of $x(t)$ Convolution of $x(t)$ with itself I guess, the Nyquist rate remains the same as long as bandwidth of $X(w)$ remains the same, as Nyquist ...
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1answer
73 views

Recovering a signal after filtering

A signal $x[n]$ is to be transmitted over a communication channel. The communication channel is described by an FIR filter of length $M$ such that the received signal is given by $$r[n]=\sum_{k=0}^...
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0answers
53 views

Calculating output of a digital system signal with a filter that introduces delay

We have a step function at the entrance that goes through the following system. The $D(z)$ digital filter introduces a 0.25s delay. Output as $y(kT)$ must be calculated. How can we tackle this problem?...
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2answers
67 views

Determine the Given system is linear or nonlinear [closed]

Does the following define a linear or nonlinear system? $$ y(n) -4 y(n)y(2n)=x(n) $$
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0answers
31 views

Calculating the number of MACs in a system

I want to calculate the number of MACs. I am looking for the method. How would I do it if I know the domain equations from a biquadratic digital filter. I have already calculated the Z domain ...
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1answer
57 views

Computing response of LTI system in terms of its step response

I have solved a problem, Kindly help me in determing if I solved it correctly. I will post the question and my own working below. Problem My working
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1answer
219 views

How to prove a filter has linear phase response?

I have designed an FIR filter to have linear phase response using odd-symmetry design. The coefficients of this filter are {2,1,3,1,0,-1,-3,-1,-2}. I am now being asked to prove it has linear phase ...
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0answers
30 views

FIR Kaiser Window Discrete Time Filter Design

Please look at Part (c) of the question. How do we know that the Filter is a Low-pass or High-pass and is the filter designed in C a multi-band-pass filter.
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2answers
138 views

Question About Sampling White Noise

Assuming that we have a continuous signal $v(t)$ $$v(t) = \int_0^t g(u)\, \mathrm du\tag1$$ where $g(t)$ is white noise.Then take the derivative of it. $$\frac{\mathrm d}{\,\mathrm dt} v(t) = g(t)\...
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1answer
24 views

Equivalence of difference equation with system of difference equations

I have this system and tried to write down its difference equation as follows $$ y[n] = b_0v[n] + b_1v[n-1]\\ v[n] = x[n] - a_1v[n-1] $$ I was asked to prove that the system can be ...
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1answer
45 views

Consider the integrator and check for time invariance

I'm trying to check the following system for for time-invariance. $$ y(t) = \int_0^t x(\lambda) d\lambda$$ Please explain me why it is time-invariant.
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1answer
132 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)?
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1answer
81 views

Inverse Fourier Transform From Plots (2019 edition) [closed]

Hello I borrowed the title for another post. I cannot figure out how to find the inverse fourier transform from this spectrum. I know what the transform is I'm sorry for the plot being hard to ...
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0answers
55 views

OFDM system with cyclic prefix

I have: Bit rate $ R_b = 25.6 [Mbit/s]$ Sampling frequency at the input of the receiver: $ f_p = 8 [MHz]$ Protective spacing between successive OFDM symbols: $ τ = 16 [µs] $ The combined length of ...
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1answer
66 views

QAM constellation coder - transmitting a file

The file with size 6 MB is transmitted in 100 seconds using a constellation coder QAM with a constellation of 6 bit/symbol $ { M = 10^6, B = 8} $ Tasks: 1. What is the signal bandwidth if the band ...
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0answers
59 views

OFDM modulator: Transmission time calculation

I have a problem with a certain task. The frequency of the signal sampling at the OFDM modulator output is 20 MHz. The length of the protection period is 2 microseconds and it is 20% of the ...
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0answers
30 views

Synthesizing a function from a fourier transform

So I have this question in a homework and cannot seem to solve it no matter what I try. Question: Use Matlab to find out what function in time x(t) resulted in the Fourier Series ...
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1answer
173 views

Amplitude and Phase spectrum of a signal [closed]

Please help me to solve this question.
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2answers
32 views

Is this calculation of inverse z-transform proper

I wonder whether my calculation of inverse z transform are correct. My IIR system is described as follows in Z-domain $H(z) = \frac{z^{-2}}{1-0.5z^{-2}}$ After using partial fraction decomposition I ...
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3answers
107 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 ...
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2answers
104 views

Trouble with inverse Z-transform and calculating of samples

I have a little problem. I have to solve this task but I can't. Z-transform of sequence $\{x(k)\}$ describe by the formula: $$X(z) = \frac{2.5 -3.15z^{-1} + 1.2 z^{-2}}{1-2.3z^{-1} + 1.2z^{-2}...
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1answer
75 views

Sketch the following Signal: $x(t)=3\sin(\frac{\pi t}{4})$ [closed]

I feel kind of overwhelmed by it, and would like someone to walk me through the steps of sketching the signal.
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1answer
75 views

How do I know what is causing the noise in my signal

I have a noisy audio file, available here (It is safe to download if you wish to) https://ufile.io/pstrt Now, I inspect it in matlab: And then i plot it on normalised frequency: Now I need to ...
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1answer
23 views

Implementing echo on adsp 21262 [closed]

I'm working on an echo implementation on the board adsp 21262. I've added a buffer to have more samples to work with. I end up then with 4 buffers of size 2048 each. The problem is that I need to ...
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0answers
49 views

How to calculate the magnitude of rounding error in N-bit signed fixed-point arithmetic?

In example take into consideration 11-bit <11,5> signed fixed-point arithmetic. 000000.11111 - 0.96875 000001.00000 - 1 so the error magnitude will ...
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1answer
45 views

Transfer function: from poles and zeros to polynomial coefficients

I understand how this transfer function was solved except I don't know how to get the 0.87. Any help would be appreciated.
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2answers
704 views

Using Fast Fourier Transform to determine musical notes

Hi guys i am doing a course in Digital Filters and Spectral analysis. We are given a coursework/homework, and I have absolutely no idea what to do with it. I come from Maths background, never done any ...
3
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0answers
59 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 ...
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2answers
564 views

Calculating N-point DFT of a signal based on another signal's DFT

Recently I have asked this answer. Now I would like to know a little bit more about expressing N-point DFT's of signals in terms of one another. Having N-point DFT X(k) of a certain signal x(n), ...
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1answer
60 views

State space equations

I am stuck on this exercise. I don't know how to deal with this squared y in the denominator. What am I supposed to do to obtain state space equations? ex.1 Simplified dynamic model of the steel ball ...
4
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2answers
669 views

Determine whether the system is linear?

$T(x[n]) = ax[n] + b$ $ T(\alpha_{1}x_{1}[n] + \alpha_{2}x_{2}[n]) = \alpha_{1}ax_{1}[n]+ \alpha_{2}ax_{2} [n] +b $ $ \alpha_{1}T(x_{1}[n] ) + \alpha_{2}T(x_{2}[n]) = \alpha_{1}(ax[n]+b) + \alpha_{...
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1answer
74 views

Block diagram of filter

Can you help me with this question. Can you explain where i should start to solve the problem.
4
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2answers
2k views

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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1answer
76 views

Calculating an output of a system (Z- transform question)

I have a following question to answer: An LTI system is described by its impulse response h[n]. For input x[n] it gives output y[n]. $$h[n] = u(n) - u(n-N) $$ $$x[n] = u(n) - u(n-M)$$ I want to ...
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1answer
538 views

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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1answer
278 views

partial fractions expansion inverse Z-transform, help

I have the correct solution from teacher's solution guide, but I was slightly confused by some algebra about the partial fractions expansion evidently difference equation is as follows $ y[n] = \...
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1answer
44 views

How to find period of signal, when spectrum is known?

Here is signal in frequency domain .Division of frequencies does not give an integer number or real number. May it can be here another method of finding period for ths signal.
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1answer
43 views

solving recurrence relation with Z-transform (LTI and causal)

I just wanted to doublecheck answers for my sanity's sake (exam next week) problem statement recurrence relation, solve it $y[n+1]= 35 + y[n]*0.5$ according to my teacher it will be such that the ...
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1answer
208 views

finding inverse Z transform with usage of tables (LTI and causal sequences)

problem is as follows try to find the inverse Z $Z^{-1} (\frac{3}{z+2}) = ???$ with the usage of z-transform tables Ok, so in order to find something from the table, I thought that we expand with ...