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

Calculating the Fourier transform of shifted scaled unit step function

I have $x_1(t)$ here. To get $x_2(t)$, I need to differentiate $x_1(t)$. Express $x_2(t)$ as $2u(t+2)-4u(t)+2u(t-2)$. From Fourier transform definition integral, I got $X_2(j\omega)=\frac{2e^{j\omega ...
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1answer
29 views

Calculating the magnitude spectrum and phase spectrum

From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$. Then, I want to calculate its magnitude spectrum and phase spectrum. The ...
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0answers
18 views

Frequency response and corresponding magnitude response

I'm given this frequency response: And I want to find the corresponding magnitude response. My answer is $|H(e^{j\omega})|$ = 1 if $|\omega|$ is within $\frac{\pi}{2}$; 0 otherwise. Is this correct?
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1answer
37 views

How to match zero-pole diagrams to their frequency responses (Discrete Time)

I get confused when there are a lot of zeros/poles in the zero-pole diagram and I find difficulty understanding their frequency response. I know the following: 1. Complex conjugates cause double ...
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1answer
24 views

Adaptive equalization vs inverse of transfer function

I have the following equalization problem as shown in the figure below: Now I can compute the coefficients for my adaptive FIR filter c (dim(c) = N) the following: $\mathbf{c_{opt}} = (\mathbf{H}^T\...
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0answers
26 views

Adaptive interference calcellation

I've got a question regarding an adaptive filter for interference calcellation: Here, the interference is a periodic signal: $x[n] = \cos(\pi/4\cdot n + \varphi_1) + \cos(3\pi/4\cdot n + \varphi_2)$ ...
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1answer
43 views

Discrete Fourier Transform in Signal Processing - Interpreting graphs of transformed signals

Given above are the real parts of the signals I to IV. Which of the following statements are correct? (i): Signal III is the result of the discrete Fourier transform of signal I. The associated ...
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1answer
24 views

Change phase of the output of a buffer

I have a question about changing the phase of a buffer. Question - How to change the output phase of a buffer by 90 degrees, 180 degrees, and 270 degrees? I know to change the phase by 180 degrees, ...
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0answers
28 views

Explain if the following processes are stable or not

I have got a question about my homework and was wondering if anybody could help. In the picture below you can see the processes. I need to determine whether they are stable or not. Now I have only ...
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2answers
59 views

DFT frequency resolution exercise [closed]

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
32 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
31 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
39 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
43 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
27 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
34 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
269 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
80 views

Sampling period

I started it but didn't how to continue , any help ?
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1answer
61 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
60 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
79 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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2answers
131 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
66 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
447 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
66 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
279 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
27 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
68 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
199 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
134 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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1answer
68 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
76 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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1answer
269 views

Amplitude and Phase spectrum of a signal [closed]

Please help me to solve this question.
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2answers
41 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
117 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
134 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
82 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
86 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
59 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
46 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
1k 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 ...
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0answers
68 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
987 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
63 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 ...
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2answers
981 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
182 views

Block diagram of filter

Can you help me with this question. Can you explain where i should start to solve the problem.
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2answers
3k 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
157 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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