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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
37 views

Impulse response of a system from the input-output relation

I need to find out the recurrence relation and the impulse response of the following system. The relation seems to be $$y[n] = \frac{2}{16} x[n] + \frac{3}{16} x[n-1] + \frac{6}{16} x[n-2] + \frac{3}{...
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2answers
103 views

Linear Combination of Two Signals

In my signal processing class I have some basic tasks working with sinus signals in Matlab. I have two sinusoidal signals with 1kHz and 3kHz and sampling rate of 16kHz. The next task says 'Create a ...
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1answer
45 views

Cramér-Rao lower bound

I have been trying to implement the Cramér-Rao lower bound from the paper - A reference-free time difference of arrival source localization using a passive sensor array (eq. 6 and eq. 7). $$ \...
1
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1answer
33 views

What is exactly Power Spectrum Density? [closed]

In papers or textbooks, I have found several different definitions of PSD. I think I understand the meaning of PSD and all these papers or textbooks agrees that PSD and Fourier Series share a ...
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1answer
73 views

Upsampling signal using convolution-based interpolation filters

I am currently reading this paper which discusses several image interpolation methods, such as nearest neighbor and linear interpolation, using convolution filters. I first want to do this in 1D with ...
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2answers
51 views

Discrete signal testing for periodicity

How would one go about determining if the following discrete time signal x[n] is periodic, and if it is, determine its fundamental period? I understand that the ...
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1answer
69 views

Is there an example of an infinite signal? [closed]

In the real world, Is there an example of an infinite signal?
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1answer
19 views

What is the z-domain transfer function of variable delay?

Is it possible to obtain the transfer function of a signal that has a variable delay? For instance, I have a signal consisting of 10 samples: 0,1,1,1,1,0,0,0,0,1 If I would apply a unit delay to ...
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1answer
74 views

Octave - freqz strange results

I wrote octave code to find transmittance based on zeros and poles: ...
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2answers
217 views

What is the DFT of DFT of discrete signal [duplicate]

What is the discrete fourier transform of the discrete fourier transform of any discrete time signal. Is result same signal? How?
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1answer
70 views

State of the art algorithms for estimating noise variance

Suppose I have a signal $X[n]= f[n] + W[n]$, where $W$ is uncorrelated Gaussian white noise satisfying $E\{W[n]W[k]\} = \sigma^2 \delta[n-k]$. What are the state-of-the-art algorithms for determining ...
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1answer
62 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 ...
1
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1answer
90 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
183 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 ...
2
votes
1answer
43 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
33 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
99 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
120 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 ...
2
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1answer
45 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 ...
1
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1answer
62 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 ...
5
votes
1answer
79 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
37 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
142 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
45 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 ...
3
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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
40 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
75 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 ...
2
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1answer
95 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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votes
1answer
183 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....
3
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1answer
144 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
49 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
461 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 ...
4
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1answer
481 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}\...
4
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3answers
277 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
86 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
372 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
98 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
votes
1answer
126 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
60 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 ...
1
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2answers
40 views

Matlab frequency response

I'm trying to make a frequency response of that function: in matlab a made this: ...
0
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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 ...
0
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1answer
57 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 ...
2
votes
2answers
266 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[...
2
votes
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
146 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
56 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 ...
1
vote
2answers
290 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
48 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 ...