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

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13 views

steady state - calculate [on hold]

$$x[n]=10 \cos⁡(0.4nπ+45°)+20 \cos⁡(0.5nπ+30°)$$ That is a steady state input. I think that to solve and join them in one, we must apply this formula: $$cos⁡(x)+cos⁡(y)=2cos((x+y)/2)cos((x-y)/2)$$ ...
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1answer
17 views

Relating phase shift to the ROL/ROR operations

Is phase-shifting in continuous-time analogous to the rotate-left (ROL) and rotate-right (ROR) operations in discrete-time?
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1answer
14 views

Stability of the summation function

Stability of the below function was asked. $$ T(x[n]) = \sum_{k=n_0}^n x[n] $$ I understand that $x[n]$ shouldn't exceed $M$ value. $x[n]\le M$. I mean, we are looking for if the input is bounded, ...
1
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1answer
30 views

Simple discrete time transformation $x[(n-1)^2]$

If I want to do the following transform $$x[(n-1)^2]$$ I have thought about substituting each value of $n$ in $x[n]$ according to $x[(n-1)^2]$ i.e at $n=0, x[0]=1$ to put it in $x[(n-1)^2]$ ...
0
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2answers
41 views

Very simple question about signal periodicity

$$x[n] = u[n]+u[-n]$$ Is it periodic or not? My answer is $$u[n] = {1 , n\geqslant0}$$ $$u[-n] = {1 , n\leqslant0}$$ which means that the signal $x[n]$ is always equal to $1$ from ...
0
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0answers
14 views

Inverse Discrete Wavelet Transform - partial reconstruction

I'm pretending to approximate a time series/vector usind dwt , with haar filter, in R. I can apply the full ...
0
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0answers
22 views

How to implement PLL blocks in MATLAB

I want to implement a PLL in MATLAB with individual components as Phase Detector, LPF and VCO. My problem is in implementing the LPF. I have determined the values of the pole and zero for the Laplace ...
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1answer
20 views

Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT

I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
0
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0answers
57 views

DFT of a continuous quasi-periodic signal

If I have a continuous quasi-periodic signal and I want to do a DFT of signal then what could be appropriate length of continuous signal that I should consider for sampling? I want to do DFT of the ...
1
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1answer
35 views

Wavelet transform in MATLAB

Suppose I have a wave with $20 \textrm{ kHz}$, $100 \textrm{ kHz}$ and $300 \textrm{ kHz}$. Sampling frequency used is $1000 \textrm{ kHz}$. I apply the discrete wavelet transform on the wave like ...
2
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1answer
32 views

Implementing Welch's method for Power Spectral Density

I want to implement Welch's method for PSD calculation in MATLAB. I do not want to use built in MATLAB cpsd function, such that I can change the FFT implementation ...
1
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1answer
35 views

MATLAB and sampling rate

I have a question about sammpling rate in MATLAB. I read a .wav file using audioread(). It give me sampled data called ...
0
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1answer
16 views

How is the matrix $\mathbf R_x$ not Toeplitz in case of a signal missing one term?

I am solving a question that says if we have sequence $x(n)$ of a signal missing one term then we have to find autocorrelation matrix $R_x$ as follows: $$R_x = E\{\mathbf {xx^H}\}$$ Now if I take ...
1
vote
1answer
25 views

Difference in following random proccess

Let just say I understand the first process that is white noise, Process 1: If $x(n)$ is a Gaussian random variable and a process is formed from a sequence of $x(n)$ and all random variables ...
0
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0answers
18 views

concerning the usable frequency band of signal

The spectrum amplitude of the response of instruments is generally trapezoid-shaped, with a flat portion in the middle and decaying at higher and lower frequencies. By deconvolving with the ...
0
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2answers
31 views

Measuring amplitude of a spectral component

I'm trying to measure the amplitude of a spectral component in a signal. The component's frequency is always known beforehand. I take a given number of samples, apply the flattop window to reduce ...
3
votes
1answer
49 views

Envelop detection with low sample rate?

I have a signal up to $3\textrm{ MHz}$. The ADC that sample it has a rate of $1.5\mu s$. So a full $T$ of the signal is $0.3\mu s$, and I can only sample each $1.5\mu s$. It sounds not enough, but I ...
2
votes
2answers
126 views

Features of a non-periodic signal for comparison

I am looking for comparing a signal (256 / 512 point discrete | non-periodic ) (obtained after extracting some features from the captured image) with a database of around 5000 signals (256 /512 point ...
1
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1answer
32 views

Problems calculating Z-transform

I am trying to solve a class exercise in which I am given the following, in Laplace domain: $$G(s)=\dfrac{e^{-Ts}}{s+3}$$ $$H(s)=\dfrac{1}{s}$$ And I need to calculate $\dfrac{C(z)}{R(z)}$, which is ...
0
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1answer
42 views

Output a sine wave from samples-limits?

Using a micro-processor of 48MHz, I am trying to output a sine wave from the DAC (digital to analog ), and I am not sure if my ...
0
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1answer
25 views

Behaviour of the poles in transfer function $H(s)$, given system properties

If a linear system is causal and its impulse response is an energy signal. What's the behaviour of the poles of $s$-domain transfer function $H(s)$?
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0answers
26 views

Unique signal extraction from a cumulated signal

I'd like to start off by saying that I am not very experienced at signal processing, so I apologise in advance if I do not explain everything properly the first time. I would like to analyse the ...
0
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2answers
34 views

A question about the concept of the time

$\delta[n+1]$ equals to one only $n+1 = 0$ ? If the 1. is true, so what does a signal $x[n+1] $ stand for? Is this signal causal or anticausal? I mean, if 1. is true, $n = -1$, so is this signal ...
1
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1answer
40 views

Real Time Goertzel Algorithm

Why is Goertzel Algorithm considered a block algorithm? Given that my input is bounded, couldn't I just run it forever (taking every sample that comes out after some length N) given a big enough word ...
0
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0answers
23 views

Simple sample and reconstruction code - MATLAB

I am trying to go from theory to code. I take x (let say 16KHz is continuous time) then I sample it in 2Khz So I do ...
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0answers
18 views

Is adding zeros part of the Hermitian Symmetry process?

I have been reading about DMT/OFDM and every source I find defines their system differently. I simply want to know if zero insertion is part of the Hermitian symmetry process that produces real OFDM ...
1
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1answer
42 views

Why does Fourier zero-fill interpolation pad the middle frequencies?

In this: http://dspguru.com/dsp/howtos/how-to-interpolate-in-time-domain-by-zero-padding-in-frequency-domain the author says that we can interpolate a signal by zero-padding the middle frequencies in ...
3
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2answers
66 views

what is nyquist rate of $h(t)\cdot h(t)$ and $h(t)\circledast h(t)$

Let's say we have $h_c(t)$ as a continuous-time signal with bandwidth $B$ and we would like to sample it. To be able to reconstruct it correctly, the sampling rate must be greater than $2B$. Now ...
0
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0answers
13 views

How can i plot the power spectrum in terms of time history representation of a signal?

I have a signal and How to plot the power spectrum in terms of time history representation as shown in the below figure in MATLAB. and also i would like to plot the spectrogram as shown in the ...
0
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1answer
38 views

Filter Design near Nyquist frequency (complex curve fitting)

I'm fitting IIR filters to a complex transfer function with Matlab's invfreqz.m. My fitting results are very good, but when I come very close to the Nyquist frequency the phase response runs to 0 and ...
7
votes
2answers
293 views

What really means stationary and non-stationary?

I really struggle to find out what really means stationary signal. There are some nice definitions in textbooks and wikipedia. But what that means in practice? To understand what is it, please answer ...
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1answer
41 views

Importance of Discrete Cosine Transform over High Pass filter?

I have recently studied few work where the low and high frequency components of an image is accessed using the discrete cosine transform (one such example is presented here). Low and High frequency ...
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2answers
42 views

How to interpret output of matched filter with complex input?

I have implemented a matched filter based on the Fourier Transform approach. In the real numbers domain that means that I use as the coefficients of my filter (B) the inverted time-samples of the ...
3
votes
2answers
156 views

Special case: Band-limited in time domain and band-limited in frequency domain

I know except for some special cases, aliasing is unavoidable. Assume we time-limit a function, $f(t)$, so that it is zero outside an interval say $[0,T]$ to form $y(t)$. Then, in the frequency ...
1
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0answers
13 views

Power Spectral Density Via Rank 1 Update

I know that I can find the autocorrelation matrix of a series of finite length sequences via rank-1 updates using the relation: $\mathbf{R}[k] = \frac{1}{k}\mathbf{R}[k-1] + ...
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1answer
28 views

Calculate Energy and Power infinite signal (math)

So we have example: $$x[n]=\left(\frac{1}{2}\right)^nu[n]$$ and I want to find $E_\infty$. So I found by wild search that this can be solved using this: $$E_\infty = ...
0
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0answers
42 views

Choosing correct filter parameters for IMU sensor datas

I have a IMU sensor breakoutboard using ITG3701, LSM303D LinkProduct. This involves accelerometer, gyroscope and magnetometer. I have connected the sensors to a Arduino and sending the datas to ...
0
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1answer
40 views

How many non-zeros samples in convolution

If I have $b[n]$ of length 30 (30 non-zero samples) and $c[n]$ of length 40 (40 non-zero samples). How many non-zero samples will $a[n]=b[n] * c[n]$ have? (Note '$*$' is a convolution). I think ...
4
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2answers
202 views

What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
3
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2answers
69 views

Adding “realistic” noise to signals of different amplitudes

I have a question regarding basic signal processing, which I have to start using since I have started studying fault isolation. The thing is, I have three computed signals, which are gathered in the ...
0
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2answers
32 views

How do we actually obtain samples to form discrete time samples? [closed]

I'm in my second week of an online DSP class and I'm still kinda lost on some of the concepts of what we are actually doing. I'm hoping you guys can help clear up my understanding. Please forgive me ...
2
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1answer
65 views

Why is the signum function $=2u(t) - 1$?

Basically I couldnt find proof for this anywhere though it's a very simple and basic equation.
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1answer
69 views

Combination of accelation signals from two devices

I have $x_A$, $y_A$, and $z_A$ acceleration signals collected from a smartphone and I call it: set $A$ and I also have $x_B$, $y_B$, and $z_B$ same acceleration signals from smartwatch: let's call ...
2
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2answers
93 views

Signal correlation vs Pearson correlation between signals

I have some data which are the sets of values uniformly distributed along some measure (simple example - along the time intervals). I tested both the coefficients and found the difference, some times ...
0
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1answer
87 views

Why does this reconstruction produce a phase shift from the original signal?

After an FFT of a signal is done, it is plotted as in the image below, with the original signal is on the first subplot. Using the magnitude and phase data of each frequency, it's reconstructed, ...
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2answers
67 views

Causal system, order of numerator and denominator [duplicate]

Is it true that if the order of numerator of a system function is larger than its denominator, then we can say that the system is causal? (Without finding R.O.C.) Is there similar thing for ...
0
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2answers
57 views

Synthesis DFT Filter Bank

I have a DFT bank analyzer with N channels, but the the bandwidth of the signal occupies only the first 2 channels, therefore I'll reconstruct only these and not entire full bandwidth. I'd like to ...
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4answers
103 views

What is the real difference between DSP and AI/data science?

I am very much into DSP, but lately everybody is talking about "Data science" and ...
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1answer
27 views

Cost function for adaptive algorithms

I am having little difficulty to understand that why most of the adaptive algorithms use error power or addition of error power as cost function/minimization criterion. I have read that minimization ...
5
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2answers
124 views

Eigenfunctions of discrete-time LTI systems

Given a discrete-time signal x[n], how does one determine if it is an eigenfunction of a stable, discrete-time LTI system? For example, consider $5^nu[n]$ ...