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33

My recommendation in terms of text books is Rick Lyons's Understanding DSP. My review of the latest edition is here. I, and many others from the ${\tt comp.dsp}$ community and elsewhere, have helped Rick revise parts of the text since the first edition. For self-study, I know of no better book. As an on-line, free resource, I recommend Steve Smith's ...


18

The below three are the best referred Text books on this subject. Discrete-Time Signal Processing, Prentice-Hall Signal Processing Series by Alan V. Oppenheim, Ronald W. Schafer, John R. Buck. Digital Signal Processing: Principles, Algorithms and Applications, Prentice Hall John G. Proakis, Dimitris K Manolakis Signals and Systems, Prentice Hall Alan V. ...


18

Paul Falstad's Java applets are a fantastic way to interact with systems and learn them intuitively. The Digital Filter applet is a revelation. Check out the rest at http://www.falstad.com/mathphysics.html. For a more informal introduction, I like A Digital Signal Processing Primer by Ken Steiglitz, which is exactly what it says it is. I TAed a class ...


10

Tips for DSP self-study huh. Well, ...studying 'signals and systems' is a great idea and having Matlab software means you have the tools to learn an awful lot. I think Dr. Steven Smith's book "The Scientist and Engineer's Guide to Digital Signal Processing", which you can read online for free, is a terrific source of fundamental DSP information. Dr. Smith is ...


10

For theoretical studies, Oppenheim is the god but if you're going to use it in practice, Mitra is one of the best: Digital Signal Processing: A Computer-Based Approach, Sanjit K. Mitra


7

Get, Read and Solve the following books: Signals and Systems. Discrete Time Signal Processing. Digital Signal Processing. Take the following courses: Coursera - Digital Signal Processing. edX - Discrete Time Signal Processing. edX - Signals and Systems: Part I, Part II. edx - Discrete Time Signals and Systems: Part 1: Time Domain, Part 2: Frequency Domain....


7

You can visit the MIT OpenCourseWare. A set of 20 video lectures by professor Alan V. Oppenheim.


7

You seem to have a number of misunderstandings, which I'll try to clarify while also trying to help with your questions. 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. While this is true, I think it's not ...


6

Lets say we want to transmit a sequence of discrete data $\left\lbrace x[n] \right\rbrace$. But because we are living in analog world, the sequence must be modulated. Call $T_s$ is symbol duration and use a set of orthonormal waveforms $\left\lbrace p_n(t) = p(t-nT_s), n \in \mathbb{Z} \right\rbrace$, (baseband) signal $x(t)$ can be written as \begin{...


6

Here I expected $y(n)$ is to be computed by convolving $x(n)$ with $h(n)$, but in the equation given by Wikipedia it is shown as a matrix multiplication $y(n) = h^H(n).x(n)$. Are these two operations(convolution and matrix multiplication) same here?. The system is an FIR system, so the vector multiplication here is equivalent to convolution --- for ...


5

In addition to the already mentioned books, if you are focused towards algorithm development, Proakis' Digital Signal Processing using MATLAB is an excellent resource for starters. The numerical recipes series is also an excellent resource regarding how to implement some core DSP algorithms (spectral decomposition, convolutions, interpolation and ...


5

The reason why almost all linear adaptive equalizers are implemented as FIR filters is that FIR filters are always stable and that there exist relatively simple and effective adaptation algorithms. Note that much work has been done on adaptive IIR filters (e.g., this book by Phillip Regalia), but in practice FIR filters are still the preferred option. Note ...


5

If you have two DFTs $A[k]$ and $B[k]$ (note the correct representation of a sinusoid at DFT bin number $1$) A = [0,-j,0,0,j]; B = [1,1,1,1,1]; with the corresponding time-domain sequences $a[n]$ and $b[n]$ a = ifft(A); % [0, 0.38042, 0.23511, -0.23511, -0.38042]; b = ifft(B); % [1,0,0,0,0]; then the multiplication of the time-domain sequences $c[n]...


5

There are, a few discrepancies that might be making a difference here. My suggestion would be to edit the question for clarity. There are quite a few assumptions that lead to non-straightforward thinking about the problem which I have tried to address to an extent and I would be happy to modify the response in light of more information. In machine ...


5

Complex channel coefficient is just a way to represent the independent real coefficients. You just need to generate h = [h_0, h_1, h_2] = [hR_0, hR_1, hR_2] + 1i * [hI_0, hI_1, hI_2]. The independence/correlation between coefficients depend on your model. And if I were not wrong, the number of element of h is the order of your MA model. The idea behind ...


4

Ok, there is some misconceptions in your question. I strongly recommend you to read a little more about the topics, but I will try to help you a little. My answers and some comments: ...linear equalizer is a filter that can undo these channel effects. When the channel coefficients w are unknown, we perform blind equalization. In this scenario, we ...


4

The book doesn't say that the impulse response must be zero for an ideal channel. It says that an ideal channel has exactly one, and not more than one, non-zero component, i.e. the ideal channel's impulse response is an impulse, which means that the signal is only delayed but not distorted.


4

"Digital Signal Processing: A Computer-Based Approach" by Sanjit Mitra is what you need I guess, especially the exercises at the end of each chapter. There is a booklet on the Internet again by Mitra, named Digital Signal Processing Laboratory Using MATLAB. The other option could be Practical Signals Theory with MATLAB Applications.


3

I would let them read the paper about the Non Local Means Filter: Antoni Buades, Bartomeu Coll, Jean Michel Morel - On image Denoising Methods. The paper is readable and it is a great introductory to the Denoising operation in the context of Image Processing. Also the Non Local Means is a very decent method (Result wise) even in our time.


3

I don't understand the subscript $n$ notation, however, in the least squares problem that is given by: \begin{equation} {\bf{y}}={\bf{H}}{\theta}+\bf{n}, \end{equation} where ${\bf{n}}\sim\mathcal{N}(\bf{0}, \sigma^2I_N)$ is a zero mean additive white Gaussian noise and $I_N$ is the $N \times N$ identity matrix, the maximum likelihood and the least squares ...


3

I would add to the list the book "Digital Filters", by Richard Hamming. A short classic, rather than a heavy tome.


3

I found this applet very helpful when understanding the nature of convolution in time. The Joy of Convolution. It lets you "draw" your time signals and convolve them so you get a picture of what's happening in the time domain.


3

Paul R is right: your system in not time-invariant, so the impulse response doesn't mean much. This could actually be a typing error o your site, more common is y(n) = k*y(n-1)+x(n). This being said, you can still calculate impulse response my simply starting at n = 0 and evaluate the difference equation one step at a time. For 1,2,3,4 ... so the impulse ...


3

The DSP neophyte who has some mathematical maturity may want to start with Martin Vetterli, Jelena Kovačević, Vivek Goyal, Foundations of Signal Processing, 2014. which is freely available online. The authors have also made their two other books freely available online: Jelena Kovačević, Vivek Goyal, Martin Vetterli, Fourier and Wavelet Signal Processing, ...


3

The fundamental idea to keep in mind is that in a wireless channels with reflections, if you transmit $s(t),$ you'll receive $$r(t)=\sum_{i=1}^Na_is(t-\tau_i).$$ Another important idea is that whether the channel is flat or not depends only on $s(t)$. For instance, let's say that the symbol time is $T_s$. Let's call the longest delay in the channel $\tau_{...


3

For question 1: apply the definition of time invariant: find the output as normal; find the output with the same input but delayed by $T$ $$ y_1(t) = \frac{dx(t)}{dt}\\ y_2(t) = \frac{dx(t-T)}{dt}\\ $$ Does $y_2(t) = y_1(t-T)$ ? For question 2: Find a definition of stability and apply it. For example, for a system to be BIBO stable it needs to have $$ \...


3

From the definition of the process you know that $$x_{n+1}=x_n-0.2x_{n-1}+w_{n+1}\tag{1}$$ Since $w_n$ is white you can't predict it, so the best linear predictor for the given process is the filter $$P(z)=1-0.2z^{-1}\tag{2}$$ which is a first order filter. It estimates the future sample $x_{n+1}$ by computing $$\hat{x}_{n+1}=x_n-0.2x_{n-1}\tag{3}$$ ...


3

To build on Laurent's answer, here is an example. Top frame shows an example transient signal: a damped sine wave. As the signal decays very quickly, the first 0.1s of the signal is the most interesting. Second frame shows hann window. Hann window is almost zero over that first 0.1s. Third frame shows what happens when you apply hann window to the ...


3

An M-QAM modulation contains M different constellation symbols. Hence, in one symbol you can encode $\mu=\log_2(M)$ bits. (i.e. 6 bits for 64-QAM for example). Now, the bits are equally distributed along the real and the imaginary part of the constellation, i.e. you have $\frac{\mu}{2}$ bits for the real and imaginary part. To encode $\frac{\mu}{2}$ bits, ...


3

A PRN sequence is a Pseudo-Random Noise sequence, often generated by using an Linear Feedback Shift Register (LFSR) with the feedback taps done by using a primitive irreducible polynomial in GF{2}, which is the Golois Field of 2 elements. When a primitive and irreducible polynomial in GF{2} is used, the LFSR will produce a "maximum length sequence", meaning ...


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