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Questions tagged [self-study]

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1answer
14 views

Confusion regarding lacunarity of koch curves with same fractal dimension but different orders

I'm trying to use the concept of lacunarity to classify images, as per how a few research papers have done it. To verify whether my equations and implementation are correct, I'm trying to verify the ...
0
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1answer
41 views

Self study question about Padé Approximation and transfer functions

Given a signal $x[n] = [1, 2, 3, 4, 5]$. How many transfer functions can be found with Padé approximation which have a causal impulse response and start with those five samples. How many of them are ...
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2answers
99 views

Solving a Linear Mean-Square Estimation the easy way

I have an exercise which is quite trivial. However I got stuck and I'm not sure if this the end-result. I assume there has to be a way to get this result much quicker. Given are two randomly ...
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0answers
21 views

Burst Deblurring algorithm - Understanding the results

I've attempt to implement the algorithm from the paper "Burst Deblurring: Removing Camera Shake Through Fourier Burst Accumulation". The main idea is to take several frames of the same scene, each ...
1
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1answer
44 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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1answer
56 views

Covariance matrix associated with random DC level in Gaussian noise

Given a signal $x[n] = A + w[n]$ where $A$ is a Gaussian random variable and $w[n]$ is Gaussian white noise, then the covariance matrix of the signal is given by $[C(\sigma^2_A)]_{ij}=E[x[i-1]x[j-...
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2answers
52 views

Question About Kailath's Paper - An Innovations Approach to Least Squares Estimation Part I: Linear Filtering in Additive White Noise

I'm reading the paper at the link below and I was following it for about 2 pages until I hit a road block on the bottom of page 648 where the author says: putting together 9-11, we obtain and ...
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3answers
108 views

How to Improve Signal Processing Skills? [duplicate]

I've heard that signal processing is fundamental field that can be applied to many other fields (MRI, EEG, audio, speech recognition, communication even to economics) So, I want to contribute myself ...
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0answers
24 views

Estimating a Function from its Covariance Function

I am trying to solve this question: Suppose that $n(t)$, $−∞ < t < ∞$ is a stationary Gaussian random process with covariance function $E\{n(t)n(t-\tau)\} = \delta(\tau) + {5 \over 4}e^{-\left|\...
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2answers
60 views

MLE formulation — confusion regarding the terms in the equation (Part1)

If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model $$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
3
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1answer
138 views

Doubts on LMS derivation

I have been trying to follow the Least Mean Square(LMS) algorithm derivation given by Wikipedia here and have the following questions. Here I expected $y(n)$ is to be computed by convolving $x(n)$ ...
0
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1answer
139 views

Equalizer coefficients and channel coefficients

Blind channel equalization methods equalize the channel without using the source data and without knowing the impulse response of the channel. Consider the channel to be a single input single output ...
0
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1answer
40 views

Error plot between known and estimated data

The channel is an FIR model with input $u$. The input takes in values which are symbols from some constellation. Using an equalizer such as the Least Mean Squares (LMS), I estimate the input to the ...
1
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2answers
69 views

Why use parametric based estimation methods - confusion regarding terms

Using the probability density function (pdf) we can estimate an unknown parameter using methods such as Maximum Likelihood estimation. If the pdf is not available, then Least Squares can be used. ...
0
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1answer
99 views

Unable to understand what notations to use in formulating and example of Maximum likelihood estimation

The received noisy signal $y_n \in \mathbb{R}$ is expressed as: \begin{align} y_n = \mathbf{h}^\mathsf{T}\mathbf{u}_n + w_n. \tag{1} \end{align} $\mathbf{h} = [h_0,h_1,\ldots,h_{p-1}]^\mathsf{T} \in \...
1
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1answer
5k views

Find the minimum sampling rate

As the signal $m(t)$ is Baseband signal after modulation it wil be bandpaas signal will look like this So I need to use the Baseband sampling Here $f_L=15kHz,f_H=25kHz,B=5kHz,$Now Undersampling ...
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2answers
99 views

which filters are these?

Location of poles are given in unity circle and 4 zeros are given at origin for every plot,How to check which plot shows which filters? For the Option (C) i am doing like this I can write the ...
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0answers
73 views

What is the difference between entropy and entropy rate and which one is important in information theory? [duplicate]

By entropy I understand the uncertainty or randomness. But if the uncertainty is high then what is its implication and advantage in transmitting information or as an information source or is high ...
0
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1answer
180 views

What is the significance of a spike like autocorrelation function

I have some questions and doubts to which the answers are difficult to extract from text books. Hence I have posted this question here. Help would be extremely beneficial. Thank you. (1) The ...
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1answer
250 views

Unable to understand the derivation of the update equation for LMS

I am trying to follow the derivation of the Least Mean Square https://en.wikipedia.org/wiki/Least_mean_squares_filter#Proof but I cannot get the update rule. I am stuck in the following steps and ...
1
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1answer
87 views

Performance of adaptive filters

Can somebody please provide an intuitive answer or reference for the following questions? Q1: Dependence of estimation performance on number of data points -- I could not find any information whether ...
1
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1answer
53 views

Doubts and some confusion on variance for complex rv

This question is in continuation of the one asked here. Let's say that the measurement noise $w$ or any random variable is circularly Gaussian complex. If the imaginary and real components each has ...
0
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1answer
149 views

Proper method for generating Channel coefficients in MATLAB

I am trying to estimate the coefficients of a Moving average model using popular estimation method such as Least Squares (LS). For educational purposes, I am trying to see if LS can work well when the ...
2
votes
1answer
256 views

How is the number of amplitude levels decided in modulation techniques?

For M-QAM modulation, where e.g. $M = 64$ there are 8 amplitude levels. Each level is represented by a symbol that is further represented by bits through the relation: $$b=\log_2(M)$$ This means ...
1
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1answer
74 views

Digital Signal Processing DSP Overview study documents

Well, I couldn't find better expression to say what I want :( I'm looking for a DSP study source, that doesn't dive too deep, and covers "all" or most of DSP topics, I just want to have an overview ...
0
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1answer
49 views

Is there a rule of thumb for selecting the variance of the input?

Considering an estimation problem, where I want to estimate the unknown input $x$ using the known channel parameters. This estimation problem can be solved by Least Squares. Thus, the model is $$\hat{...
1
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1answer
435 views

SNR for complex valued signal and when to use SNR and when to use Eb/N0?

This question is in continuation to the one asked earlier Help in understanding the formula of Signal-to-Noise-Ratio (SNR) - Part 1 Consider a model $$y[n] = x[n] + w[n]$$ Signal means the desired ...
2
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3answers
366 views

Computer exercises and solutions in signal processing

I am very interested in this question and can literally not find anywhere a simple answer, so apologize in advance if it does not fit well this community. I am looking for either an online resource ...
2
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1answer
86 views

What Makes a Signal Processing Book Good or Less Good? [closed]

I've recently been disappointed by a few books that have "using MATLAB" in their title, which makes me wonder why. I like MATLAB so it isn't MATLAB. There are other books that I will keep at ...
0
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1answer
97 views

Constant modulus algorithm - performance poor?

The question is based on a research article titled, "Novel Robust Blind Equalizer for QAM Signals Using Iterative Weighted-Least-Mean-Square Algorithm" The Authors have proposed an equalization ...
4
votes
1answer
357 views

Educational purpose - What is the correct way to simulate a multipath fading channel which has ISI

I am following the codes for rayleigh fading channel given in the webpage: http://www.raymaps.com/index.php/m-qam-bit-error-rate-in-rayleigh-fading/ I am confused and need help in clarifying some ...
1
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1answer
195 views

Why do digital modulation when the signal entering the channel is analog?

I am learning about digital filters and came across the link Why do digital filters work? In real world communications, I think the input to the channel is in analog after being modulated by digital ...
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1answer
68 views

Learner level information on Kalman filtering for different input kinds

I am learning Kalman filters and have seen example on data as state varaibles that have real values / numeric. However, in digital communication the information is in digital - bits. So, can Kalman ...
0
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1answer
260 views

Filtering White Noise to Generate Harmonic Signal

I have studied convolutions and filters a long time ago. Today, I am trying to review the basics using some notes of mine, but I am finding difficult to solve easy problems. Since I don't have ...
1
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2answers
53 views

What is the meaning of $l_p$ norm in this model for sparse channel estimation?

The signal $y(n)$ can be modeled in the time-domain as $$y(n) = \sum_{i=0}^{L-1}h(i) x(n-i) + v(t) \tag{1}$$ where $\mathbf{h} = [h_1,h_2,\ldots,h_L]^T$ is the coefficient of length $L-1$, and $v(t)$...
0
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1answer
32 views

Suggestions on how to use FIR model in sentence retrieval task

Estimating an impulse response from input-output measurements is called system identification. When the impulse response of the linear system $h(n)$, is of finite duration (M samples) or can be ...
0
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1answer
423 views

Confusion regarding pdf of circularly symmetric complex gaussian rv

Considering a random variable $x$ that takes in values from a complex domain. Its real and imaginary components are totally uncorrelated. I am following this link and also studying this document. In ...
2
votes
1answer
678 views

Difference between clustering and quantization : Part 2

The Lloyd-Max quantizer is a scalar quantizer which can be seen as a special case of a vector quantizer (VQ) designed with the Linde Buzo Gray (LBG) algorithm. In k-means clustering, we are given a ...
3
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1answer
747 views

Lloyd Max quantization and clustering : Part 1

The Lloyd-Max quantizer is a scalar quantizer which can be seen as a special case of a vector quantizer (VQ) designed with the Linde Buzo Gray (LBG) algorithm. In k-means clustering, we are given a ...
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3answers
275 views

Spectral window when FFT is not a power of 2

I am trying to better understand zero padding and the FFT. To do so, I am attempting to plot the spectrum of the Hann window function, i.e. $$ w(n) = \frac{1}{2}\left(1-\cos\left(\frac{2\pi (n+1/2)}{...
3
votes
1answer
193 views

Help in understanding from book expression of variance of an estimator : PRBS vs real valued input

The question is based on Book : Fundamentals of Statistical Signal Processing by Steven Kay, Chapter 4 : Eq(4.21). The expression for the variance of the estimated coefficients when the input is PRN ...
0
votes
1answer
94 views

Beginner level confusion regarding symbols used in modulation

For 4-QAM symbol sequence, each symbol can be represented by $k=\log_2(4) = 2$ bits. 4-QAM constellation can be generated using s = round(rand(1,T)*2 -1) For 16-QAM,...
0
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1answer
175 views

Shannon's entropy for non-equiprobable symbols

I am trying to understand the concept of Shannon's entropy and deciding the codelength. In first case, b is an array of 5 symbols. The symbol set is $\{1,2,...,8\}$....
0
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1answer
663 views

Entropy : do we prefer higher or lower entropy?

The entropy of a source $H(S)$ gives the average codeword length to encode a given source alphabet. i.e. it is the average number of bits per symbol required to encode the information in the source. ...
0
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1answer
253 views

Implication of Cramer Rao Lower bound and relation with SNR : non-technical overview

I need some clarifications on CRLB which has been bugging me for quite some time. Clarification: When computing the Fisher Information(FI), the mathematical expression contains $\theta$ and not $\...
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2answers
228 views

“Don't window a transient signal”

I'm a SP student and still a beginner in the field. When we were learning about window functions, my professor said "you're gonna almost always want to window your data but don't window a transient ...
1
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1answer
2k views

Matlab: What is the proper way to calculate mean square error for complex numbers

I am confused regarding the calculation of mean square error involving complex numbers. Considering, the true channel coefficients to be ...
1
vote
1answer
49 views

Help in understanding if the maximum likelhood estimation is working properly

I am learning estimation theory and need help in understanding for educational purpose how the concept of ML works with the help of a step by step implementation. I am trying to find out the ML ...
0
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2answers
134 views

Need help in understanding minimum variance estimator and CRLB concept using an example

I am reading the book, Fundamentals of Statistical Signal processing, Estimation Theory Volume 1 by Steven M. Kay. In Chapter 2, there is a Fig 2.5 which illustrates which estimator to select based ...
0
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1answer
202 views

Conceptual Question on equalization technique in rayleigh fading channel based on a paper

Question Link http://www.raymaps.com/index.php/theoretical-ber-of-m-qam-in-rayleigh-fading/ gives theoretical expressions for BER in Rayleigh fading channel. Can I use the expression for 64-QAM in ...