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Questions tagged [discrete-signals]

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

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1answer
47 views

How to count the number of threads in a bolt or nut using image processing?

How can I count the number of threads in a Nut with image processing? I know that I need to find the place of threads and count them. Ok, But how can I find the place of threads? This is a sample ...
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0answers
19 views

How to count the up and downs [duplicate]

I want to count the threads of a bolt in an image. My solution is this: capture an image Find the bolt Get one dimentional data from it's top to bottom Find the thread count from signal This is the ...
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1answer
65 views

Limitation on the shift theorem of DFT due to frequency resolution?

The shift theorem states that shifting a sine wave in time domain by t is equivalent to multiplying the corresponding DFT coefficient of the signal by a complex exponential e^(-jwt). Described by the ...
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0answers
94 views

Linear Predictive Coding example in MATLAB

I have some data that is highly correlated and I wanted to see if I could try and encode it using linear predictive coding (LPC). Here is how I've been understanding the process: Encoding Generate ...
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1answer
37 views

IDFT of $Y[k]=2X[k]$ for even $k$

If the 16-point DFTs of $x[n]$ and $y[n]$ are given as $Y[k]=\begin{cases}2X[k], & k=0,2,4,...,14 \\ 0, & k=1,3,5,...,15\end{cases}$, where $x[n],y[n]=0, \forall n<0, n>15$, how can I ...
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1answer
28 views

Inverse DFT in terms of original signals for product of two DFTs

Given $x[n]$ and $h[n]$ that are zero for $n<0$ and $n>15$, their linear convolution being $y[n]=x[n]*h[n]$ and their discrete time Fourier transforms are $X(e^{j\omega})$ and $H(e^{j\omega})$, ...
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3answers
95 views

$e^{j\omega}$ on unit circle

I am new to DSP, and I'm self studying. I am confused about the magnitude of $e^{j\omega}$ - where $\omega$ is the normalized angular frequency - when we are on the unit circle. According to the ...
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4answers
109 views

Nyquist Theorem - Why unique frequencies upto Fs/2 and not Fs? f+Fs is start of Aliasing

If any frequency, f, displays an alias at f + Fs, This shows that unique frequencies have a range of Fs. Why does Nyquist theorem say that actually there is only half of this with unique frequencies ...
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1answer
39 views

Forward Linear Predictor

I just need some advice on a project. I have an unwanted sinusoid that has time-varying frequency (its not sinusoidally varying) which is relatively constant over a small section. I've been advised to ...
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1answer
45 views

Symbol Timing recovery for modulation producing ISI

I am interested in understanding why the common timing recovery algorithms function for modulation schemes which produce ISI. For example, suppose you are receiving at the output of a matched filter ...
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1answer
68 views

Is possible reach the DFT if I have the DTFT?

My teacher told me that DFT is DTFT sampled, i.e.: $$X[k] = X(e^{j \omega})\Bigg|_{\omega = \frac{2\pi k}{N}}$$ But, if I have the sine $$ x[n] = \sin(\omega_0 n) $$ the DTFT is: $$X(e^{j \...
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1answer
27 views

Interpolation of missing audio signal in a video sequence

Suppose there is a video sequence and there are some frames for which the audio data is missing. I want to interpolate the missing audio data on the basis of the correlation of the audio signal with ...
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1answer
75 views

How to determine fundamental frequencies (beats/minute) of heartbeat? (matlab)

read = matfile('ECG.mat'); [cor, lags] = xcorr(read.ecg, read.ecg); read.Fs; So i have read.ecg (signal) and ...
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0answers
38 views

Understanding linear predictive coding in MATLAB

I want to test my understanding of linear prediction by running it on some test data in MATLAB. The way I understand it is if I have some data that is correlated, I can encode the signal with linear ...
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1answer
48 views

Compare two signals, find times when they are affected by the same processes

I have two (noisy) signals $S_1(t)$ and $S_2(t)$. They contain information on three distinct events occurring in a physical system. Event $A$ affects only $S_1(t)$, event $B$ affects both $S_1(t)$ and ...
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1answer
37 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
72 views

Fourier transformations of discrete time signals [closed]

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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1answer
71 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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1answer
127 views

Add echo as described by difference equation to audio signal (in MATLAB) [closed]

A simple linear system is echo. It can be described by equation $$ y[n] = x[n]+ k\,x[n−d], $$ where $n$ represents sample index, $k$ represents an attenuation coefficient, and $d$ represents time lag....
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1answer
134 views

Discrete Harmonics - Why multiplying digital frequency by k does not get next harmonic

For continuous time $ e^{jk\Omega_0t} $ gives a complete set of orthogonal harmonics for fourier decomposition but for discrete $ e^{jk\omega_0n} $ does not form a complete set orthogonal basis set ...
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1answer
45 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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423 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 ...
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1answer
415 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
266 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
81 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
169 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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1answer
67 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
121 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
40 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
39 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
54 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
218 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
100 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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1answer
48 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
33 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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2answers
130 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
35 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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1answer
104 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
99 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
71 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
48 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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1answer
56 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
23 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
36 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
44 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
62 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
45 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
66 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 ...