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.

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Filter away INT_MIN when doing DSP since -INT_MIN is undefined(?)

My problem is that I have a mic that delivers 24 bits 2's complement signed. There is nothing in that data sheet that hints at it not also delivering INT_MIN. The 8 ...
Øyvind Teig's user avatar
1 vote
2 answers
143 views

How can I apply a filter to remove reverberation with python?

I am developing an algorithm that automates the processing of audio files for the assembly of datasets of machine learning models. Among the steps to be followed for the processing of the files is to ...
JouseJG's user avatar
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0 answers
21 views

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 ...
Simple's user avatar
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1 answer
56 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. ...
Illia Zakharov's user avatar
1 vote
1 answer
54 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. ...
Tam's user avatar
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1 answer
61 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 ...
Tam's user avatar
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-1 votes
1 answer
81 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 ...
A couple of three things's user avatar
2 votes
1 answer
116 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] =...
Insipiddrew's user avatar
0 votes
2 answers
174 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 ...
Irmantas Želionis's user avatar
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, ...
Yalçın Cenik's user avatar
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1 answer
85 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_{\...
nashynash's user avatar
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1 answer
38 views

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 $|h|^2$ ...
nashynash's user avatar
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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}...
Aedrha's user avatar
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1 vote
1 answer
75 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 ...
Aedrha's user avatar
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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 ...
Aedrha's user avatar
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1 vote
1 answer
340 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 ?
Elias's user avatar
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2 votes
2 answers
636 views

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 ...
Matthias La's user avatar
1 vote
1 answer
896 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 ...
tir_nor's user avatar
  • 67
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1 answer
125 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 ...
FafaDog's user avatar
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1 vote
1 answer
224 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 ...
fac120's user avatar
  • 11
2 votes
2 answers
3k 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 ...
Hokkyokusei's user avatar
5 votes
1 answer
680 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 $\...
k_gelloch's user avatar
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 ...
StuartBingham's user avatar
0 votes
1 answer
371 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 ...
Chen Huang's user avatar
2 votes
2 answers
605 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 ...
tir_nor's user avatar
  • 67
1 vote
1 answer
139 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_{-...
Anonymous's user avatar
0 votes
2 answers
90 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 ...
Idr's user avatar
  • 143
0 votes
1 answer
278 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(|\...
thnghh's user avatar
  • 13
0 votes
0 answers
213 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 ...
thnghh's user avatar
  • 13
2 votes
2 answers
64 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 ...
Lionel Iceberg's user avatar
2 votes
2 answers
527 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 ...
S.H.W's user avatar
  • 726
-1 votes
1 answer
459 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 ...
Princy Angelina's user avatar
1 vote
1 answer
167 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 ...
megasplash's user avatar
0 votes
1 answer
88 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.
I KALPANA's user avatar
2 votes
1 answer
288 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 ...
Orpheus's user avatar
  • 211
1 vote
1 answer
98 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 ...
Orpheus's user avatar
  • 211
1 vote
2 answers
63 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 &=...
thnghh's user avatar
  • 13
1 vote
1 answer
145 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 < \...
Giovanni Cerciello's user avatar
0 votes
1 answer
162 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 ...
calveeen's user avatar
  • 283
0 votes
0 answers
93 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 ...
luan.votrong.gpronet's user avatar
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 ...
tir_nor's user avatar
  • 67
1 vote
1 answer
159 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? ...
megasplash's user avatar
1 vote
1 answer
199 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 ...
S.H.W's user avatar
  • 726
0 votes
1 answer
91 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 ...
amn_suryansh's user avatar
1 vote
1 answer
53 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. ...
Razor's user avatar
  • 121
1 vote
1 answer
369 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 ...
achatief's user avatar
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 ...
Saurabh Jadon's user avatar
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 ...
Sm1's user avatar
  • 291
0 votes
0 answers
31 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 ...
vvm32812's user avatar
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 } ...
Sylvain Leroux's user avatar