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A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.

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Apply the DTFT transform to calculate the magnitude of the spectrum [on hold]

Assume you are given the following discrete signal, which has an amplitude x(0)=8 and x(1)=3: Apply the DTFT transform to calculate the magnitude of the spectrum, if = 3,1 radians. You need to ...
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1answer
23 views

Confussion on roll-off factor, sampling time and Raised Cosine pulses.

I am reviewing some bandlimited communications theory and something is bothering me - My book says increasing the roll-off factor makes the received sequence more tolerant to timing recovery errors ...
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1answer
53 views

Fourier transformations of discrete time signals [on hold]

How does one Fourier transform the following signals? $$x[n]=[0,9,0]$$ and $$y[n]=[9,0,19,0,9]$$ I've tried to get it along the way of $$X[\omega]=e^{-i\omega n}$$ but this seems incorrect. I'm not ...
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0answers
20 views

Why can't I directly apply difference property on this Fourier Series question?

I am given a discrete time signal, with fundamental period 10 and coefficients $a_k$, which is as follows: $$ x[n] = \left\{ \begin{array}{ll} 1 & \quad 0 \leq n \leq7 \\ ...
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0answers
23 views

Linear Predictive Coding for general signals

I have a signal that's monotonic and roughly linear and have been looking at using Linear Predictive Coding to encode information and compress my signal. I guess my first general question is if this ...
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0answers
12 views

How does Praat perform framing of signals?

I am new to Praat and I am trying to find the intensity of a .wav file. When I try to create an intensity object the popup window asks for the minimum pitch and time step. The praat documentation ...
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0answers
22 views

modify main sound with second sound (matlab)

So i have 2 sounds. Main sound and second sound which represents "parking garage" effect. So i want to modify main sound that sounds like it's playing in parking garage. ...
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0answers
31 views

add echo described by equation to audio signal (matlab)

A simple linear system is echo. It can be described by equation $$y[n] = x[n]+ k\,x[n−d]$$, where $n$ represents sample, $k$ attenuation coefficient and $d$ lag. How can I add echo to an input signal ...
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1answer
31 views

Confusion about frequency illustration of FMCW in matlab

I am currently working through the FMCW radar example in the Matlab Docs and have a question concerning the following plot Why is the frequency of the signal apparently decreasing if I have a linear ...
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1answer
72 views

Discrete Harmonics Concepts

If we add $2 \pi $ to the discrete frequency $ e^{j(\omega_0+2\pi k)n} $ it gives the next frequency, why is this true? For continuous domains $ e^{jk\Omega_0n} $ gives a complete set of orthogonal ...
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0answers
58 views

Recursive signal output using linear algebra and initial conditions

I am messing around with signal processing, and I figured out the equation of a delay feedback loop, but I want to write it out in linear algebra. The problem is that I'm not quite sure how to format ...
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1answer
40 views

Where in the signal chain is Channel Equalization applied?

I am reading about channel equalization and I am somewhat confused on where in the signal chain channel equalization is normally applied and if it's before or after a correlator detector or matched ...
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7answers
359 views

Intuition behind commutativity of convolution in LTI systems

Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system? If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
3
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1answer
376 views

Associative Property of Convolution:

Consider the following sequences: $x_{1}(n) = A$ (a constant), $x_{2}(n) = u(n)$, $x_{3}(n) =\delta(n)-\delta(n-1)$. ($\circledast$ stands for linear convolution) If I perform the operation $x_{2}\...
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3answers
228 views

Is Linear Prediction ever exact?

I'm just learning about linear prediction and was wondering whether or not there are any signals that would produce no error if run through a linear prediction algorithm. I was thinking (maybe naively)...
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1answer
67 views

Spectrogram of 493 signals at a time [closed]

I have been working with some seismic data and recently submitted a paper to a journal. My seismic data has 493 traces: each trace are 8300 seconds long with sampling frequency of 2000 Hz. One of ...
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2answers
79 views

Choosing sampling frequency and base interval to eliminate leakage

I'm studying for an exam and have some trouble with an exercise. So I have a continuous-time signal that is $$s(t)=\sin(2\pi f_{s1} t) + \sin(2\pi f_{s2}t)$$ with $f_{s1} = 1.4\text{ kHz}$ and $f_{s2}...
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0answers
23 views

Characteristics of the process noise and measurement noise in dynamic system

I have a set of time series of biological origin. I managed to model these with the following 2nd order difference equation: $y(k) = a_1 y(k-1) + a_2 y(k-2) + b_1u(k) + b_2u(k-1),$ where $y(k)$ is ...
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1answer
38 views

Partial Fraction Expansion for Inverse Fourier Transform

In many textbooks, I've seen the application of Partial Fraction Expansion (PFE) to find an inverse Fourier Transform. Let's stick to the discrete time case, and let me give you an example. Let's say ...
5
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1answer
114 views

Bounds of the difference of a bounded band-limited function

For a continuous signal (function), we have Bernstein inequality : $$ |{df(t)}/dt| \le 2AB\pi $$ where $A=\sup|f(t)|$ and $B$ is the bandwidth of $f(t)$. The question is: is there a relationship ...
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1answer
29 views

edge detection of 1-D signals

Would you please introduce me to some methods (or references) to do edge detection on some pulses (rectangular pulses embedded in noise). At first I apply some filters to smooth the signals, then I ...
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2answers
35 views

Matlab frequency response

I'm trying to make a frequency response of that function: in matlab a made this: ...
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1answer
31 views

Design a Discrete-Time System

Could you help me with this theoretical question. The purpose is to design a discrete-time system. What it does is, it finds the maximum value in a one-dimensional sequence whose elements consist ...
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1answer
48 views

Energy of compressed signals

I have tried a code to compress a signal using Compressed Sensing(CS). The input signal is $x$ and the compressed signal $y$ is given by : $y=Φ*x$ where $Φ$ is the sensing matrix. I have used ...
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2answers
194 views

How to compute autocorrelation of signal defined by difference equations?

I have no experience with difference equations and I want to learn how to compute the following, but I found no resource online. Any help would be greatly appreciated. Find: $$\mathbb{E}\left[d[n]d[...
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0answers
48 views

Explicit formulation of the role of eigenvectors of the matrix of a linear time-invariant filter

At this point in a lecture by MIT Professor Strang the idea of gaining insight into a filter by studying its eigenvectors is introduced. The idea is clear with the example chosen in the lecture: an ...
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1answer
66 views

White noise and entropy confusion about concepts

The spectral entropy (SE) of a signal is a measure of its spectral power distribution. The concept is based on the Shannon entropy, or information entropy, in information theory. The SE treats the ...
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0answers
23 views

Frequency Response, dB for aliasing control, Sampling frequencies and attenuations, and sketches

There are 3 issues here. A. This is a diagram of a high fidelity application that uses the following sampling system (shown in the picture). If the bandwidth interest for this application is +/- 20 ...
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0answers
25 views

Frequency Response of Discrete and Continuous time systems

Are the following two equations true for the frequency response of Discrete and Continuous Time systems respectively: $$H(jw)= \int_{-\infty}^{\infty} h(\tau) e^{-jw\tau} d\tau $$ $$H(e^{jw})= \sum_{...
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0answers
21 views

Good reference to study graduate-level DSP course

I'm looking for a textbook on discrete-time signal processing, that has solution in the back of the book, so I can work on practice problems, and validate the result, so that I can study on where I'm ...
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0answers
26 views

what are the hot area of searching in FMBC and Massive MIMO

I'd like to ask about Massive MIMO, and FBMC. What are the hot areas of searching in these two topics? I mean for example in OFDM, it's needed to check the ISI, ICI and channel estimation and so on. ...
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1answer
42 views

Signal reconstruction from sampled signal? [closed]

Can we construct exact analog signal at receiver as same as the source from the sampled signal?
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1answer
32 views

Frequency component not filtered properly

Are frequency components other than wanted signal present in the output? If yes then why does it not disturb the original signal? I think all practical filter responses are not ideal, so all frequency ...
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0answers
38 views

Stability in evaluating real part of a Fourier transform

I posted this on maths stack exchange but realised it might be more appropriate here. So forgive the cross posting! I have a signal $S$ and want to evaluate the magnitude of the real part of it as ...
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2answers
52 views

What are the Even and Odd Components of a 2D Signal

A signal $x$ can be decomposed into its even, $x_e$, and odd, $x_o$, parts. By, $$ x_e(t) = \frac{1}{2} [x(t) + x(-t)] $$ $$ x_o(t) = \frac{1}{2} [x(t) - x(-t)] $$ What would be the equivalent for ...
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1answer
30 views

3-tap FIR filter: simple expression for $H(e^{j\omega})$ using trigonometric identities

We have a linear time-invariant system described by the input-output relation $$y[n] = x[n] + 2x[n - 1] + x[n - 2]$$ Below is my approach to analyze this system. The impulse response of this system ...
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0answers
15 views

Question about Down-sampling a Scale Space Representation

Quick version: Given a discrete input signal f we can compute a scale space representation by repeatedly blurring and downsampling. I've lost the source for ...
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1answer
61 views

Applying Nyquist's sampling theorem to a real signal

I'm struggling to fully understand the Nyquist-Shannon sampling theorem. For some message input signal $m(t)$ that is infinite in time (i.e. is not identically $0$ for any interval $t_1<t<\...
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1answer
66 views

How to find the impulse response of this system with complex roots?

I've been working trying to analyze a causal stable system. Hopefully a numeric example such as the one I am working on, and the problems I face during it could be useful to others. I have this ...
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1answer
60 views

Damped sinusoidal form FFT of signal

I'm doing an assignment for the course Signal analysis where I have to analyse a signal. I've tried quite some things now but it's still bothering me that the FFT is looking weird, and not looks like ...
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1answer
47 views

Counting blinks of a LED

I'm working on an algorithm that counts blinks of a LED. I have series of non-neagtive integers. They represent brightness of a LED in time. I give you two examples of these integer series below. ...
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0answers
43 views

Depending on how a system function is written, will it always have the same zeros and poles?

There are many ways to write a system function. In terms of direct forms, cascade, parallel, transposed. Also the system function depends on if you write the poles and zeros in terms of $1+az^{-1}$ or ...
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1answer
47 views

How was this result on discrete Fourier series achieved?

I was trying to do the question 10, part b of the following document (https://ocw.mit.edu/resources/res-6-007-signals-and-systems-spring-2011/assignments/MITRES_6_007S11_hw10.pdf) I was going through ...
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1answer
21 views

Causality of the given system

I am given the following discrete system $$y[n]=x[-n]$$ where $$x[n]=n+3$$. Now from what I understand, since $$y[n]=x[-n]$$ therefor the system is causal as the output is depending on the ...
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1answer
31 views

Discrete Fourier Series of square of a signal

I am having trouble in deriving a result, which asks me to find a relation between $X_{1}(k)$ and $X_{2}(k)$ where $X_{1}(k)$ are the DFS coefficients of single period of signal $x(n)$ and $X_{2}(k)$ ...
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1answer
41 views

Why are binary signals drawn continuous in time despite being a digital signal

The conventional definiton of a Digital signal is as follows: A digital signal is a signal that is discrete in time and quantized in amplitude. Almost all resources (textbooks, online sources,etc) ...
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1answer
35 views

Why must the Region Of Convergence (ROC) contain infinity and the system function be a right-sided sequence for it to be causal?

I need the simple logic on the condition a system becomes causal. We know that causal contains only past values. I can't relate this with the Region Of Convergence (ROC) concept.
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0answers
41 views

How general are adaptive-filtering techniques? [closed]

How often do problems arise that let you use adaptive filters? Unless I am understanding something incorrectly it seems the requirement that the input signal be stationary(or even WSS) is too strong ...
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2answers
58 views

Is it possible to discretely sample the function

I had a few questions on sampling(I'm quite new witht his), I tried to answer them, I think that I did the first one correct , but not sure about the 2 other: . given the next functions,Is it possible ...
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0answers
18 views

N point sum of a periodic complex exponential [duplicate]

I am having trouble verifying this identity $$\frac{1}{N} \sum_{n=0}^{N-1}e^{j\frac{2\pi}{N}rn} = 1$$ if $r=mN$ where $m \in I$, otherwise this summation turns out to be 0. I am not able to prove the ...