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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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162 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
135 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
97 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
60 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
25 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
37 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
49 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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94 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
50 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
69 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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1answer
66 views

Moving average algorithm that conserves integral

Suppose I have point array $y_i$ of size $N$. How to implement moving average algorithm that conserves quantity $$ I = \sum_{i=1}^{N}y_i $$ NOTE: I don't want time shift so I would prefer to use ...
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1answer
39 views

How to solve this question by using convolution?

I had previously posted this question but my method was wrong in it. Two signals are given: $$x[n]=2^nu[n]$$ $$h[n]=u[n]$$ I have to find $y[n]$. I have spent hours on this question but I am unable ...
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3answers
90 views

Maximum Magnitude Deviation between DFT and DTFT

Let $x[n]$ be a finite-length discrete-time signal with length $N$. The continuous DTFT $X(\omega)$ is then $$ X(\omega) = \sum_{n = 0}^{N-1} x[n] e^{-j \omega n}. $$ The length-$N$ DFT of $x[n]$ is $...
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1answer
28 views

What is the value of last sample of a discrete sinewave

I have a simple question. If I compute N sample values of a single cycle of a discrete sinewave (whose initial phase is zero radians), will the value of the last sample be equal to zero?
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2answers
88 views

Conversion from stationarity to non-stationarity

Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
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1answer
40 views

Finding the transfer function of a discrete signal described by two equations

A discrete time system is described by the following system of equations. $$q[n] = \big(x[n]-\frac k4q[n-1]\big)$$ $$y[n] = \big(q[n]-\frac k3q[n-1]\big)$$ Find the systen function and then find the ...
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1answer
37 views

Convolution of discrete time signal

I'm given a discrete time signal which is as follows: $$ x[n] = \alpha^n u[n],\\$$ $$ h[n] = u[n],\\$$ Why is unit function neglected in the following step: $$ y[n] = \sum_{k=0}^{n} \alpha^{k}\\$$
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1answer
54 views

How does an IIR system affect magnitude and phase of a sinusoidal signal

Consider an IIR system with impulse response $h[n]=\left( \frac{1}{\sqrt{3}} \right)^n u[n]$. If I apply $x[n]=\cos(n \frac{\pi}{2} + \varphi)$ at the input, how can I determine the change in ...
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1answer
97 views

Are two jointly stationary white noise processes independent?

I am currently dealing with a problem concerning beamforming, where two "jointly stationary zero-mean white noise processes" form the input of an adaptive system. One of those processes resembles the ...
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1answer
101 views

Difference between these two integrators

I am an electrical engineering student but new to digital signal processing. However while searching references for my senior project I came across following two different discrete integrator blocks ...
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3answers
80 views

Why must the angle contain $\pi$ for $\cos$ be periodic?

The $\cos(\frac{n}{6})$ is aperiodic, and $\cos(\frac{n\pi}{6})$ is periodic, why? What role does the $\pi$ play? By the way, $n$ must be integer I have seen this question,Why is cos(n/6) aperiodic? ...
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2answers
128 views

What is a memory less system?

As far as I have grasped the concept is that if we are given the expression $$y[n]=(2x[n]-x^2[n])^2\,,$$ it is a memory less system because even if we give negative values of $n$, we still get the ...
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0answers
16 views

artifact identification in irregular-samped data

There is a dataset combined by different datasets a,b,c,d,e. The time intervals are irregular(i1, i2, i3:intervals between a and b, b and c...), but the sampling rate SR in every single dataset is the ...
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3answers
59 views

How do I know if the given signal is discrete?

If I am given an expression of a signal then how do I know if it is a discrete signal or not? If this signal is given how do I know if it's a discrete or continuous? $$x(n) = e^{j (n \pi/2 + \pi/8) ...
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1answer
23 views

Optimising an input signal for a system to minimise distortion of output signal

I have a discrete time-series signal which I am able to process before passing it through a system which distorts said signal. This system cannot be altered and is non-linear, but a signal can be ...
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1answer
47 views

What does it mean that the normalized power of a received equals one?

I have read in that lecture, page 2, here that, the symbols are independent, and normalized to have power 1, which means $E(x x^H) = I$ .. what does that mean? could you please explain that for me?
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1answer
117 views

How does a digital filter work?

To introduce my situation: I'm developing a digital synthesizer in a form of a C++ library, working with low level APIs like WASAPI, ASIO, ALSA etc. It's probably not very practical and I'm mostly "...
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1answer
187 views

Reconstruction of a signal from non-uniform samples [duplicate]

So I'm having some troubles with a signal that's been sampled but where the samples don't have consistent intervals. I've been looking into the NFFT (in python) as a starting point but I'm a complete ...
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2answers
163 views

Carrier Frequency Offset, Rotating Constellation and Correlator

I have been further reading up on carrier recovery methods and something is not clear to me: It's written that a carrier frequency offset results in a rotating constellation diagram but if you are ...
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2answers
220 views

Quantization level versus bandwidth [closed]

Why is it that increasing the number of quantization levels $L$ results in an increase in the signal's bandwidth?
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1answer
70 views

Using the compressive sensing mathematical concept in signal processing

I am new in the field of compressive sensing, I've read many papers explaining that compressive sensing is used widely in sparse signal reconstruction. I've tried to understand how compressive sensing ...
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1answer
73 views

Linear combination of DT unit impulse

Came across this example in class but I'm not sure how the expression $x(n)$ was derived.
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1answer
98 views

Impulse response from Frequency response: why using $e^{j\omega}$ as an input?

Every resource that I can find uses this identity when deriving impulse response: $h[n] = IDTFT \Big\{H(e^{j\omega}) \Big\}$ Suggesting that the input signal was $e^{j\omega}$. But by definition ...
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1answer
330 views

How to Check Separability of 2D Signal / Matrix

suppose x(n1,n2) = {1 ,n1=0,n2=0 ; 2 ,n1=1,n2=0 ; 3 ,n1=0,n2=1 ; 6 ,n1=1,n2=1 } then, how do i prove it is separable.
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1answer
68 views

A general conceptual understanding of moving average

I have a conceptual question here. I understood how to calculate a Moving Average(MA). For example : x(n) = 0, 1, 2, 3, 4, 5 MA = 0, 1/2, 3/2, 5/2,7/2, 9/2, where for calculation of the MA we only ...
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2answers
622 views

How to get around the circular shift property of Discrete Fourier Transform?

I understand that when we introduce a linear time shift using DFT on a finite sequence, the algorithm assumes that the signal repeats itself outside of the given range. Here is an example explaining ...
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1answer
53 views

Band limited signals that are sparse

I am looking for examples of signals that are band limited but also sparse. For instance, the spiking of the neurons can be modeled as banded in frequency domain and sparse in time domain. What other ...
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0answers
13 views

graph display problem [closed]

I have a problem with the end of my code. I would like to display the last two curves, the problem is that at the beginning the size of YY is 288 and then after the equality with diff, my size goes to ...
2
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4answers
65 views

Bandlimiting and OFDM spectrum - what is considered “bandlimited”?

I have been reading about OFDM modulation, it's not clear to me how you can have band-limited OFDM but given its prevalence in wireless communication there must be some designation of approximately ...
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1answer
62 views

Extracting positive frequencies of discrete-time signal

Convolution in the time domain is the same as multiplication in the frequency domain. My data is sampled at 200 Hz, which means that the Nyquist frequency is 100 Hz, and all frequency content is <=...
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1answer
189 views

How to measure acoustic pressure level under water with a hydrophone?

this is my first post here and I am also new in signal processing. Let's say I have a hydrophone with amplifier which is connected to a sound card plugged in to a computer. I gather the sounds to a ...
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1answer
409 views

Discrete Fourier transform of an exponential decay

I have a vector with an exponential decay, using Numpy: t=np.arange(128) k=0.1 decay=np.exp(-k*t) I would like to compute the discrete Fourier transform (DFT) of ...
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1answer
60 views

What's the difference between Channel shortening and time-domain equalizer

I'm asking about the difference about channel shortening and time-domain equalization. I have checked on-line and tried to get something clear but I couldn't. What I found is that channel shortening ...
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1answer
26 views

Equation Derivation: Help with intermediate steps

As per the attached image above, I don't know how the equation in the first line transformed to the form in second line. I tried solving it by multiplication but the result was different.
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0answers
45 views

Implementing Fractionally Spaced Equalizer

I have been searching for robust algorithm that can be implemented for avoiding the ISI (Inter-Symbol interference), I came across two types of channel equalizations are there. One is data Aided (...
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2answers
170 views

Software PLL tracking of carrier frequency in bandlimited transmission

My understanding is that a PLL(either in hardware or software) can recover the carrier frequency(or be used to correct the frequency offset) of a system. My question is how does this work when the ...
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0answers
78 views

What is the relationship between FFT size and demodulation in OFDM

As I mentioned in the title of the question, how can we demodulate the data in order to get the same number of subcarriers with different FFT size. For example, 10 MHz LTE can be sampled with 15.36 ...
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0answers
76 views

How can I oversample OFDM received signal in MATLAB

I need to oversample a received signal in OFDM by MATLAB, according to the below diagram, but when I oversample, I finally get the same number of samples however that should be double. !! The ...
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1answer
68 views

transfer function and 'causal' signal - evaluate transfer function or use z-transform of input?

From my studying difference equations and transfer functions, I understand that when a complex exponential input $x[n]=z_1^n$ is applied to an LTI system with transfer function $H(z)$, determining the ...