Questions tagged [self-study]
This tag means the asker is new to the DSP field and is requesting extra guidance. It has similar connotations to the homework tag, but this lets potential answerers know they should probably do more than guide the self-studier compared with the homework requester.
158
questions
1
vote
0
answers
18
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implement gradient descent with sparsification algorithm
I am trying to implement the algorithm in this paper for finding a sparse vector x that minimizes the square error $\lVert y − \Phi x\rVert_2^2$ where $\Phi$ need to satisfy the restricted isometry ...
- 145
0
votes
0
answers
73
views
Prove the following [closed]
If $$x_1[n]=A$$ where $A$ is a constant, $$x_2[n]=u[n]$$ and $$x_3[n]= \left \{ \begin{array}{l} 1, \mbox{for n=0}\\-1, \mbox{for n=1}\\ 0, \mbox{otherwise} \end{array}\right.$$
Prove that $$x_3[n]\...
- 21
0
votes
1
answer
48
views
Magnitude spectrum of LTI system output signal
First year student so please excuse my lack of knowledge.
As i understand i need to use convolution which is:
$$ y^{out}(t) = u^{in}(t) * h(t) $$
Or maybe my thoughts are wrong so please correct me.
...
1
vote
1
answer
51
views
Plotting the amplitude and angle spectre of this signal
I am looking clarification that I have the appropriate solution to this question, thoughts and tips to improve my understanding are also welcome!
f(n) is a discrete sample of the following signal. ...
- 17
0
votes
1
answer
57
views
Determining the full DFT values of X(k) given a partial sample [closed]
I have a sample of a signal lets say 8 values of a 16 value sequence. I am trying to obtain the full DFT from the partial.
I am thinking that I am going to work back, I read the matlab documentation ...
- 17
-1
votes
1
answer
68
views
Expected value and autocorrelation
I have a wide sense stationary stochastic process ${{X_t;t\in \Re}}$ with mean 0 and autocorrelation function $R_x(\tau)=1-\frac{1}{4}|\tau|$ for $|\tau|=0,1,2,3;$ and zero anywhere else. I'm supposed ...
2
votes
1
answer
99
views
Expressing the frequency response in a more 'compact' form
I've just been working through the questions in Discrete-Time Signal Processing (Oppenheim and Schafer) and I came across this (Q33):
Consider an LTI system defined by the difference equation $$y[n] =...
- 23
0
votes
2
answers
154
views
Calculating connected component's central moments
I am learning about image's moments. As an exercise I got this:
For x̄ value I get 5 from this formula:
$$= \frac{\sum_{x=1}^{X} \sum_{y=1}^{Y} xf(x,y)}{\sum_{x=1}^{X} \sum_{y=1}^{Y} f(x,y)}$$
As ...
1
vote
1
answer
70
views
How to learn image processing in an applicational way?
My question is for image processing and computer vision "practitioner" who study on a company. Since I have an degree on electrical engineering and mathematics, I have signal processing, ...
- 33
0
votes
1
answer
81
views
Probability of achievable data rate greater than target data rate $\Pr\left[\frac{1}{2}\log_2\left(1+\text{SINR}\right)>R_{\text{target}}\right]$?
I came across this formulation of the probability that the achievable data rate is greater than the target data rate for the NOMA system.
$$\Pr\left[\frac{1}{2}\log_2\left(1+\text{SINR}\right)>R_{\...
- 105
0
votes
1
answer
37
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What does $\mathcal{ E}(|h|^2)$, where $|h|^2$ is power of the channel gain $h$ represent?
I came across this notation of $\mathcal{E}(|h|^2)$ in a research article.
$h$ is the channel gain of a wireless communication channel. In particular, a Rayleigh fading channel.
I know that $|h|^2$ ...
- 105
0
votes
1
answer
33
views
Running a signal through a circuit with some odd components
I am studying a course in signal analysis and systems. Currently we are looking at aliiasing, samplig,DTFT and reconstruction.
I got stuck on an excercise.
For the in signal $x_{a}(t)=2\cos(2\pi F_{0}...
- 53
1
vote
1
answer
59
views
FInd the amplitude function to a system
I'm studying a course in signal analysis and have come across an exercise where I find the analytical part a bit tricky.
I am to find the amplitude function $|H( f )|$ for a system with the impulse ...
- 53
0
votes
1
answer
33
views
Zeroes and poles for a system
I have run into some issues on an exercise for the course in signal analysis and systems I am currently studying.
We are to create an echo effect and are using the system below:
I am to find the ...
- 53
1
vote
1
answer
266
views
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 ?
- 47
2
votes
2
answers
463
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Recommendation for courses / studies on digital signal processing
I hold a master's degree in mechanical engineering. However at my job I am more and more diving into topics of signal processing and data science. I find it great to discover about new topics and to ...
- 380
1
vote
1
answer
737
views
Finding optimal decision threshold for binary comm system
I'm trying to solve the following exercise: Given a system that transmits bit $b$ with probability $p_b$ and $-b$ with $p_{-b}$ and the transmission is degraded by AWGN $N(0,\sigma^2)$. What is the ...
- 67
0
votes
1
answer
114
views
Finding the discrete time fourier coefficients to this problem
I'm trying to find the fourier series to this discrete time signal.
$$x_1[n] =\begin{cases}
+\frac72&\text{if }0\le n \le 4\\
-\frac72&\text{if }5\le n \le 9
\end{cases}$$
My approach:
We see ...
- 149
1
vote
1
answer
133
views
The Math of Histogram Matching
Please help solve the problem in the picture. I am confused due to the piecewise nature of the density functions. If it was a simple curved PDF, I would simply integrate over full range and use the ...
- 11
2
votes
2
answers
2k
views
Find power of a sum of sinusoids
We got this question to solve:
Calculate the power of the signal:
$$s(t) = 8\cos\left(20\pi t-\frac \pi4\right) + 4\sin(15\pi t)$$
Now, I thought of two approaches :
Use Parseval theorem, so first ...
- 125
5
votes
1
answer
594
views
LMS Convergence and the Step Size ($ \mu $) Parameter
I am running the LMS algorithm based on Haykin's Adaptive filter theory.
I aim to plot the cost function $\mathbf{J}$ and calculate $\mathbf{J}_{\tt min}$ and the simulation
excess mean square error $\...
- 51
0
votes
0
answers
25
views
Best way to compare audible alarms
I'm working on an alarm recognition program in MATLAB in which multiple reference audio samples of different alarms would be recorded. Afterwards, the program would sample every so often and compare ...
0
votes
1
answer
340
views
Simulate butterworth filter with initial condition of state vector in R
I'm working in R with the packages signal and control (don't know wether these are even the best for my use case).
I have a high ...
- 109
2
votes
2
answers
541
views
Inverse system of sinc?
I'm doing some self-study for an important exam I'll have in late March and came across the following question:
So, using the convolution properties, if I want to find an identity system so that the ...
- 67
1
vote
1
answer
131
views
Evaluate expressions without computing DTFT
Let $X(\omega)$ be the DTFT of the sequence $x[n]$ given by:
$$
x[n] = \{4, 2, -1, 5, -3, 1, -2, 4, 2\},\quad\text{for}\quad n \in [-6, 2]
$$
I do want to compute
$X(0)$
$X(\pi)$
$\displaystyle\int_{-...
- 11
0
votes
2
answers
76
views
Convert complex valued sinusoid to real valued sinusoid
This is the homework problem: convert $x[n]=je^{j\pi n/8}-je^{-j\pi n/8}$ to a real valued sinusoid.
I understand that $\sin\theta=\dfrac{e^{j\theta}-e^{-j\theta}}{2j}$
In the solution, the answers ...
- 143
0
votes
1
answer
230
views
Coefficients of a Zero Forcing linear equalizer for infinite length input
Given a discrete-time white noise model:
$$y_k = \sum_{i=0}^{\infty} \alpha^{-i}a_{k-i} + \eta_k$$
where $E(|a_k|^2)=2$, $|\alpha|>1$, $\eta_k$ are uncorrelated zero mean random variables with $E(|\...
- 13
0
votes
0
answers
195
views
Degradation of BPSK system using matched filter with a timing error
Given a BPSK system with:
\begin{align*}
s_1(t) &= Au_T(t) \\
s_2(t) &= -Au_T(t) \\
\end{align*}
where $u_T(t)=1$ for $0<t<T$, and zero otherwise. Given $A > 0$, and Gaussian white ...
- 13
2
votes
2
answers
60
views
Clarification on eigenfunction property from Oppenheim's Discrete-time signal processing, 3rd ed
Could anybody explain what is meant by the following statement on page 50 of Oppenheim and Schafer's book Discrete-Time Signal Processing (third edition)?
The eigenfunction property of complex ...
2
votes
2
answers
458
views
Power of an angle-modulated wave
Let $$\phi(t) = A\cos(\omega_c t + km(t)) \tag{1}$$ be an angle-modulated wave(FM or PM). What's the power of $\phi(t)$? Intuitively, it seems that the answer is $$P = \frac{A^2}{2} \tag{2}$$ since ...
- 726
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votes
1
answer
410
views
How can I find expansion coefficients of the a vector in a given basis?
How can I find the coefficient of the vector $\mathbf y$? And how can the inner product be done on these vectors?
Let $\mathbf y = \begin{bmatrix}1\\2\\0\\1\end{bmatrix}$
What are the expansion ...
1
vote
1
answer
157
views
How to choose a fixed adaptation step for decision feedback equalizer
How do I choose $\mu$ - a value of a step size for adaptation in a decision feedback equalizer (DFE) with adaptive reference control (ARC)? For a regular adaptive FIR filter an adaptation step depends ...
- 396
0
votes
1
answer
87
views
Even and odd components of a constant function [closed]
Let $x(t)= 1$ for all values of $t$. The even and odd components of $x(t)$ are ____ , _____
respectively.
2
votes
1
answer
273
views
Discrete Time Convolution Evaluation
I'm trying to solve a problem on convolution from Alan V.Oppenheim:
Find the convolution output $y[n]$ for the following signals:
$$x[n]= u[n]\quad\text{and}\quad h[n]=a^{n}u[-n-1], \ a>1 $$
I ...
- 211
1
vote
1
answer
92
views
Discrete-time Convolution Convergence Issue
I'm trying to solve a problem on convolution from Alan V.Oppenheim:
Find the convolution output $y[n]$ for the following signals:
$$x[n]= u[n]\quad\text{and}\quad h[n]=a^{-n}u[-n-1], \ a>1 $$
I ...
- 211
1
vote
2
answers
62
views
Optimal receiver for a binary system employing waveform $s=A\cos^{2}(\pi f_c t \pm \alpha)$
I want to design an optimal (minimizing error probability) receiver for system of two waveforms (with $0<\alpha<\frac{\pi}{2}$):
\begin{align}
s_1 &=A\cos^{2}(\pi f_c t + \alpha)\\
s_2 &=...
- 13
1
vote
1
answer
136
views
What is the average of $\DeclareMathOperator{\rect}{rect} \rect(\cos(\pi t/2)) $?
We have this signal:
$$\operatorname{rect}\left(\cos\left(\frac{\pi t} {2}\right)\right) $$
I must find the average power , how can i get there ?
My solution:
I have seen that
$$-\frac 12 < \...
0
votes
1
answer
144
views
Should we use all $N$ correspondence points to compute Homography or just $4$ points?
Given correspondences of $(x,x')$, we want to find a Homography matrix $H$ that maps $x' = Hx$. If we use 4 corresponding non - collinear points and the matrix $H$ has rank $n-1$, then the homogenous ...
- 283
0
votes
0
answers
74
views
Newbie want to self-study to make guitar effect/amp plugin
I am a senior Game developer want to self-study how to create electric guitar amp/effect plugin.
I read around and managed to made a simple distortion plugin using JUCE. But because of lacking in ...
0
votes
1
answer
89
views
Inverting a sampled system
I'm doing some self-study for an upcoming exam and came across the following question:
My first idea to solve it was using the bilinear transform to get some approximation of $H(Z)$ (or just using ...
- 67
1
vote
1
answer
150
views
What is a correct approach to baud-rate digital timing recovery for self-equalized line code
In particular, I have a signal coming from a twisted pair of arbitrary length with a differential encoded
biphase line code. What should be a correct approach to timing recovery in this case?
...
- 396
1
vote
1
answer
188
views
Prove a property using shift theorem and duality
I'm reading Lectures on the Fourier Transform and Its Applications and I'm going to prove shift theorem for the inverse Fourier transform using duality. According to the mentioned source, the duality ...
- 726
0
votes
1
answer
86
views
Inverse discrete time Fourier transform with differentiation
Consider a signal x[n] and its DTFT $X(e^{jω})$ . Assume $X(e^{jω})$ is differentiable. Compute the inverse DTFT of
$j\frac{dX(e^{jω})}{d\omega}$
You should write your answer in terms of $x[n]$ and ...
1
vote
1
answer
50
views
How to construct Neyman Pearson statistic to detect discrete signal in AWGN with unknown location?
I have a discrete datastream of length $10^5$ samples. Somewhere embedded in it is a rectangular pulse of unknown amplitude (prior probability of data containing signal is 0.5) and width 100 samples. ...
- 121
1
vote
1
answer
327
views
Effect of sampling rate on BER simulation
I am trying to build a bit error rate simulation for a digital baseband signal
(specifically using Manchester coding). The simulator generates a digital waveform from random symbols at a sample rate ...
- 13
1
vote
3
answers
2k
views
How do the magnitude and phase spectrum of an imaginary function look like?
Say I have the function
$$x(t)=j \operatorname{rect}(t)$$
Is the phase spectrum even or odd?
I am confused whether the phase spectrum is an odd/even function of $\omega$ (angular frequency, Fourier ...
0
votes
1
answer
2k
views
How to find out the noise level of a signal
Is it possible to find the amount of noise or SNR of a signal from its time series output? For example; let x = randn(100,1) and ...
- 291
0
votes
0
answers
30
views
Use Cases of FFT in Signal Processing [duplicate]
I am trying to learn about signal processing and fft's applications within it. My understanding is that a classical use case for fft is to remove "noise" (ex. high frequencies that are not supposed to ...
- 1
2
votes
2
answers
4k
views
What is the meaning of the DTFT of the unit impulse sequence?
In an exercice, I'm asked to draw the $X_{imp}(\omega)$ Discrete-Time Fourier Transform (DTFT) of the $x_{imp}(n)$ unit impulse sequence defined as:
$$
x_{imp}(n) = \begin{cases}
1 & \text{if } ...
- 315
7
votes
2
answers
841
views
Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)
I'm experimenting with the Inverse Discrete Fourier Transform. Starting from the two-cycles continuous $x(t)$ signal below:
I have the discrete signal $x(n) = \{ 1, 0, -1, 0, 1, 0, -1, 0 \}$ leading ...
- 315