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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DFT exercise in the book Understanding digital signal processing 3 Ed
I am trying to solve exercises from the book Understanding digital signal processing 3 Ed - Richard Lyons.
I will repeat the question as it is in the book:
3.3 We want to calculate an N-point DFT ...
6
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1
answer
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Filtering $ n \times n $ Images by Separable $ m \times m $ Filters. Computation Time for Filtering Using FFT, 2D Convolution and Two 1D Convolutions
Consider filtering square $n\times n$ images by square, separable $m\times m$ filters.
Give general equations for the computation time for the following approaches to this:
Filtering using FFT
2-D ...
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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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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.
$$\frac{\mathrm d}{\,\mathrm dt} v(t) = g(t)\...
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Why is $A\cos(2\pi f_ct)$ a non-stationary process?
I am studying analog communication and having Communication system - Simon Hykin as one of the reference.
There is a question
Consider the sinusoidal process$$X(t) = A\cos(2\pi f_ct)$$where the ...
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When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?
Heads up, this is for homework. I never took a signals and systems course, so I'm behind on this stuff.
I want to compute the convolution of two rectangular regions. I know the standard equation ...
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Signal Processing using Fourier Transform
How can I derive the fourier transform of
...
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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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1
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Unit step function symbol
I've been studying communications and i see that the book used the symbol $u_{-1}(t)$ for unit step function , why ?
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Filtering voice signal from randomly added frequencies
I have this assignment that I can't figure how to solve.
I have a sound.wav human-voice file, and use matlab add-random-noise (monotonic)
Goal: to remove the noise from the sound (and the sound from ...
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The error probability of 16QAM
The signal constellation for a communication system with 16 equiprobable symbols is shown as below. The channel is AWGN with noise power spectral density of $N_ 0/2.$Using the union bound, find a bound ...
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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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How to find frequency response, stability, and causality of a linear system?
I have the following transfer function:
$$H(s)=\frac{s}{(s+1)(s+2)}$$
How can I find the gain and phase response of the above system? I know the first step has something to do with substituting $s = ...
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Determine whether the system is linear?
$T(x[n]) = ax[n] + b$
$ T(\alpha_{1}x_{1}[n] + \alpha_{2}x_{2}[n]) = \alpha_{1}ax_{1}[n]+ \alpha_{2}ax_{2} [n] +b $
$ \alpha_{1}T(x_{1}[n] ) + \alpha_{2}T(x_{2}[n]) = \alpha_{1}(ax[n]+b) + \alpha_{...
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Understanding LTI systems graphically
I'm currently working on this problem from Oppenheimer's book:
Given $x_{1}(t)$ and $y_{1}(t)$ I should figure out $y_{2}(t)$ and $y_{3}(t)$ given that the system is LTI.
My progress so far:
I'm ...
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Inverse z-transform. Where is mistake?
I've already wrote about that trouble (link here), but I don't understand where I've made a mistake.
Full description of the task is as follows:
Z-transform of sequence {x(k)} describe by the ...
3
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Extract approximation and detail coefficients
I am a student and would like to know how to extract the approximation and detail coefficients (A5, D5, D4, D3, D2 and D1) after an applied DWT decomposition dB5 (Daubechies 5, level = 5)?
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Use polyphase representation to construct a perfect reconstruction filter bank
I'm posting this question in response to Question about zero-phase filter bank
This is a homework question for which I found an answer, but I didn't do it the way I was supposed to. I'm wondering ...
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Question about zero-phase filter bank
I found what I believe is a valid solution to the following assignment problem but the answer is bothering me.
Let $$H_0(z) = 1+2z^{-1}+3z^{-2}+2z^{-3}+z^{-4}\quad\textrm{and}\quad H_1(z)=H_0(-z).$$...
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Polyphase Decomposition in Matlab
I created the lowpass filter
h = firls(100, [0 .2 .25 1], [ 1 1 0 0],[.001 60]);
My goal is to get four filters $H_{k}(z) = H(W_{4}^{k}z) k =0,1,2,3$
From my ...
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2
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Minimum number of Poles and zero of transfer function H(z)?
Suppose $G(z)=H(z)(1-\frac{1}{2}z^{-1})$ now in question its saying ROC of G(Z) is entire Z plane except Z=0,so here we need not to add anything because G(Z) already a right sided signal with ROC ...
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LTI systems inverse of each other
So my question looks like this:
Suppose that we have two LTI systems with impulse responses
$$h_1(t) = \frac 12\delta(t-1)\quad\text{and}\quad h_2(t)=2\delta(t+1).$$
Determine whether these ...
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Calculate the Output of Linear Time Invariant System Given it Impulse Response [closed]
A filter is defined as $ h \left[ n \right] = \delta \left[ n \right] - \delta \left[ n - 1 \right] $.
Given a signal $ h \left[ n \right] $ defined as:
$$ x \left [ n \right ] = \begin{cases}
1 &...
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Relating transfer functions with step responses
Relate the transfer function to its' corresponding step response.
First, I tried setting up the poles and zeros of the transfer functions. This helped a bit since I know that $G_A (s)$, $G_B(s)$ and $...
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1
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How to compute the 2N-Point DFT in terms of N-Point DFT with other properties involved
Let's say the N-Point DFT of $x[n]$ is $X(k)$.
Now from this question, I know how to compute the 2N-Point DFT of the same $x[n]$ in terms of $X(k)$
However, this idea doesn't translate well if I have ...
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Trouble with subtracting a signal by a unit impulse
For my homework I was given the signal by the illustration:
I was asked to draw the illustration for $$x_1(t) = 3x(-1+0.5t) - \delta(-t+3)$$
I have figured out how to draw the $3x(-1+0.5t)$ part, but ...
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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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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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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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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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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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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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Expression to represent alternating pulse train?
I have a question regarding an alternating pulse train signal, $p(t)$, and a system which looks like this:
Immediately, I'm supposed to be able to extrapolate that
$$
P_t = P_1(t)-P_1(t-\Delta)
$$
...
1
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1
answer
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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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Impulse response of non-causal system
Suppose I have the following equation, where $x[n]$ is the input and $y[n]$ is the output: $$x[n]-x[n-1]=-10y[n-1]+2y[n]+2y[n+1].$$
The question asks me to compute the impulse response from this ...
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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 ...
0
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1
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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:
$$X(z) = \frac{2.5 -3.15z^{-1} + 1.2 z^{-2}}{1-2.3z^{-1} + 1.2z^{-2}}$$
...