Questions tagged [discrete-signals]
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.
1,435
questions
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Element-wise powering vs. discrete version of binomial theorem on a sum of Gaussians
I had recently posted a question on applying powers on a sum of Gaussians (here) to enhance signal resolution artificially. The discussion has given rise to another query. Consider this problem. We ...
1
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1answer
16 views
Having difficulty checking for time invariance of discrete system
A system is given with the following equation:
$$y(n) = 3y^2 (n-1) - nx(n) + 4x(n-1) - 2x(n+1)$$
I need to check for the linearity and time invariance of the system.
By just looking at the equation I ...
1
vote
2answers
46 views
Applying a Power on a Sum of Gaussians to Enhance Resolution
There is so-called Power Transform technique in signal processing where the unresolved signal is sharpened by raising each data to a constant positive power. The example shown below is a sum of two ...
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1answer
33 views
DTFT of even and odd samples
Here to find DTFT of $h(2n)$ they have scaled omega, while in RHS to find DTFT $x(2n+1)$ they didn't, why is that?
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3answers
47 views
Is $x[n]=(-1)^{n^2}$ periodic?
Is $x[n]=(-1)^{n^2}$ periodic? The answer said no, but when I draw it on a graph, it seems to be periodic, with fundamental period equal to $2$.
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1answer
40 views
Representing a continuous LTI system as a discrete one
I am aware that there are different ways to represent a continuous time system in discrete domain (e.g. bilinear transform, impulse invariance transform).
But my problem is as follows: Given an ...
0
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1answer
22 views
Inverse Discrete Time Fourier Transform of $1$
$\textrm{DTFT}(\delta[n]) =1$,
but $\textrm{IDTFT(1)} = \frac{\sin(\pi n)}{\pi n}$.
Why it is not equal to the unit impulse $\delta[n]$?
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0answers
60 views
Intuition behind using basis functions to optimize discretization of a 2D image obtained via projections
If I am not mistaken, the technique used to avoid a pixelated appearance of CAT scan images described as basis functions on page 4032 of this paper is not unique to CAT scan, and probably applied to ...
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0answers
19 views
Z transmittance from diffrence equation made out of diagram
I have a problem with getting Z transmittance out of a single block of diagram, when e(nT) is as an input, and u(nT) is as an output. Period of sampling is T = 0.5 s The diagram is:
My first thought ...
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1answer
35 views
DC Components and Frequency
I have started learning digital communication and was on line coding. I read there are certain characteristics that we need to keep in mind while choosing the right line coding method. One of these is ...
1
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1answer
27 views
Why zero padding the 2-d DFT interpolates images in spatial domain?
I was applying different image interpolation techniques and I came know to about interpolation in frequency domain. In this technique we first take 2d DFT of an image, padd it with zeros and take the ...
1
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1answer
42 views
Why the spectral coherence is unity for all frequencies between single-frequency time series and itself
In the example below, I am plotting the coherence between time series and itself. The time series do has one frequency.The coherence magnitude was one for all frequencies. I wonder why it is not zero ...
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2answers
61 views
Proof regarding the periodicity of a continuous-time sinusoid after sampling
Question
A continuous-time sinusoid $x_a(t)$ with fundamental period $T_p = \frac{1}{F_0}$ is sampled at a rate $F_s = \frac 1 T$ to produce a discrete-time sinusoid $x(n) = x_a(nT)$.
Show that $x(n)$...
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0answers
27 views
how many samples required? [closed]
A music song recorded in a studio is stored as a digital sequence on a CD. The analog signal representing the music is 2 minutes long and is sampled at a frequency f_s=44100\;s^{-1}f
s
=44100s
−...
1
vote
1answer
42 views
How to determine the phase of a time-sampled periodic signal?
I know this is a rather common and a rather simple problem, but somehow I can't find a solution that is equally simple to understand (and implement).
I have a signal that closely resembles a noisy ...
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0answers
26 views
Is it possible to get this type of periodic noise?
I got this current signal captured using Hall Effect sensor but was not sure if this is noise or actual informative signal (refer to the figure, the bottom plot is the magnified plot of the black box)....
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0answers
27 views
Finding the output y(N) [closed]
The impulse response is given:
$$
h(n)= 0.5^n u(n)\\
x(N)= 3^n u(n-1)
$$
How to calculate $y(n)$?
2
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1answer
55 views
Representation, Bandwidth and composition of Digital Signals
I have started learning data communication and I'm not able to grasp certain topics.
First
(i) I know that analog signals are continuous and digital signals are discrete. Analog signal are ...
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1answer
31 views
Bringing the signal into the same level [duplicate]
I have a signal, shown in the attachment (blue one). As you can see that the latter part of my signal has a higher dc offset. I want to bring the signal into the same level. I have tried eliminate the ...
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0answers
16 views
Detection time of a spur using FFT?
Say I have the following parameters,
NFFT=2^14
Fs= 50 MHz
main signal @ 22 MHz and its alias at 28 MHz at signal power -40 dbfs
and a spur @ 2 MHz and its alias at 48 MHz
Leave aside the alias's.
...
0
votes
2answers
144 views
Aliasing when interpolating with DFT?
I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me.
I have created a noiseless signal as:
...
1
vote
2answers
132 views
FFT of triangular wave
I am new in dsp.. so please bear with me.
I want to plot FFT of a triangular wave. I am using the code below to first generate the triangular wave and then take its FFT
...
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2answers
58 views
use of complex number in digital signal processing [closed]
how complex number used in digital signal processing.
detailed information about on how this method will be useful in radar technology.
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1answer
29 views
how do I derive the system equation for a simple delay with feedback?
I am a software engineer, and just learning digital signal processing formally, though I've hacked around before a fair amount.
I'm implementing a delay audio VST and I'm trying to wrap my head ...
0
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1answer
49 views
Prove that, in DFT ,interpolation in time domain is equal to replication in frequency domain
Given:
$x[n]$ is an $N$-point sequence whose DFT is $X[k]$
$$x[n]\xrightarrow{\mathcal{DFT}} X[k]$$
then,
Prove that: DFT of the same sequence after insertion of $(M-1)$ zeroes between successive ...
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3answers
55 views
Power of summed signals
Pretty much a newbie here, but would like to understand a pretty basic concept.
We all know that a quick and dirty way of calculating signal power of a part of a discrete sampled system (such as ...
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0answers
27 views
ACF of $X_t = a + bt$
I was able to prove the following convergence results. But how can we determine the theoretical autocorrelation function of the deterministic sequence $X_t = a + bt$ and $X_t = c\ \text{cos}(\omega t)$...
1
vote
1answer
54 views
Why would FFT interpolation using zero-padding undershoot the true frequency of a single tone sinusoid?
Why would FFT interpolation by zero-padding or using the Chirp Z-Transform produce a maximum at a bin that corresponds to a frequency less than the input frequency of a single tone sinusoid?
I am ...
0
votes
1answer
29 views
Discrete Real Sinusoid Formula
I have a basic question about the formulas represented for discrete sinusoids. In some textbooks we see this form
$$x[n]= A\cos (2\pi f nT + \phi ) $$
and in others we have
$$x[n]= A\cos (2\pi k/N ...
2
votes
4answers
69 views
LTI system and initial conditions
I suspect this is rather obvious once explained; I must be misunderstanding something.
From reading various answers here (such as this one), I understand that an LTI system must have zero output for ...
2
votes
1answer
27 views
Conflict with the properties of convolution
excuse me in advance for the lenghty question, consider the following signals:
$x_1[n]$, $x_2[n]$, $y[n]$ and
$z_1[n] = x_1[n] * y[n]$
$z_2[n] = x_2[n] * y[n]$
In addition, we know that:
$x_2[n] =...
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2answers
59 views
Determine the Given system is linear or nonlinear [closed]
Does the following define a linear or nonlinear system?
$$ y(n) -4 y(n)y(2n)=x(n) $$
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0answers
45 views
Position Kalman Filter fails to track a constant-acceleration path
I'm trying to build a discrete Kalman Filter that fuses accelerometer (acceleration) and GPS (position, velocity) measurements. However, I'm finding that my filter can't properly track a constant-...
1
vote
1answer
53 views
Proof of First Difference Property for Fourier Series
I am having trouble with deriving a proof for the first difference property for the Fourier Series.
Here is my attempt at the derivation:
$$
y[n] = x[n] - x[n-1]
$$
Fourier Series Representation:
...
1
vote
1answer
34 views
Is u[-n] defined from negative infinity to zero as it is folding of u[n] or from negative infinity to -1?
Folding of unit step function and definition of its boundaries.
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2answers
67 views
Why the following discrete type system,variable accumulator, is time invariant?
$y[n]=T{x[n]}=\displaystyle\sum_{k=n-n_{0}}^{n+n_{0}} x[k]$
it is some sort of moving summer which computes $n^{\text{th}}$ output sample by adding all samples lying within length $n_{0}$ around some ...
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0answers
27 views
what is the co-variance of system output cooresponding to a non-iid random variable
Consider the following system.$\DeclareMathOperator{\sign}{sign}$
$$
\begin{aligned}
&\dot{e_1}=c_1e_1+c_2e_2+\eta\\
&\dot{e_2}=c_3e_1+c_4e_2-c_5 \sign(e_1)+a \eta
\end{aligned}
$$
which $\eta$...
0
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1answer
148 views
How to remove striped noise from this image. Which filter or algorithm use better?
I need to process a gray scale image. The task is to remove the stripes, which constitute some noise.
I have next origin image:
This image received many channels ADC(Y) in moment of time (Xn) from ...
2
votes
2answers
70 views
How to apply discrete filters to a signal
Let's say I have a signal like x[k] = [-20 -50 -30 50 30 -60 60 -60 60 10 5 10 5 5], and I want to apply a lowpass and a highpass filter to this signal (separately). For example the impusle response ...
0
votes
1answer
49 views
Continuous-time vs Discrete-time Fourier transform
case 1) to calculate the Fourier transform of discrete-time signal(sampled signal) we use Discrete-time Fourier transform.
but my question is:
case 2) if I consider that discrete-time signal as ...
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0answers
22 views
Discrete vs Continuous Power Spectrum Analysis
Let's suppose we have a time signal of watt units which in the frequency domain transforms into a sinc-like spectrum. The amplitude of that spectrum will likely be also of watt units. In order to find ...
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2answers
926 views
How do I explain a complex exponential intuitively?
What is a complex exponential, explained intuitively?
How do I explain to an adolescent a complex exponential function?
3
votes
1answer
53 views
analog-to-discrete-to-analog system sampling problem
This is not a homework problem, I am solving practice problems for my exam.
Consider the analog-to-discrete-to-analog system shown in figure 1. The CT signal $x_a(t)$
is sampled at a frequency of $...
1
vote
1answer
107 views
Why Wiener filter not IIR
I would like to limit discussion to discrete time causal Wiener filter.
By definition it is an FIR filter, and it also has optimality under Mean Square Error criterion within the class of linear ...
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0answers
18 views
Should PSD be smoothed for SNR computation in frequency domain?
When taking the Power Spectral Density of a short duration signal (say 1 second, sampled at 4096 Hz), should it be smoothed to compute SNR? I want to computed the matched filter SNR, perfectly knowing ...
1
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2answers
56 views
Building periodic sequences from finite-support sequences
Given a discrete-time finite-support signal x[n]
$$x[n] = \left\{ {\begin{array}{*{20}{l}}
{{{( - 1)}^n}n}&{{\rm{ }}n = 1,2,3}\\
0&{{\rm{otherwise}}}
\end{array}} \right.$$
And consider also ...
0
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1answer
28 views
Polyphase components Spectrum formula in Discrete time
I am trying to understand the meaning behind some of the components of the formula for polyphase components in discrete time. Note that $\Omega$ indicates discrete in this notation and the formula is ...
0
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1answer
33 views
How to sketch this multirate system spectrum?
In the following system:
The signal x(n) is upsampled by 2 and then filtered. The signal and the filter have the following spectrum:
After upsampling the spectrum of X would look the same except ...
1
vote
1answer
25 views
Method to rescale signals to mean length
I have a set of signals of varying lengths. I have provided an example of the same below -
Their lengths vary between 186 to 202, with a mean length of 197. I am looking to rescale them to the mean ...
0
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0answers
35 views
How to remove sum and difference terms while computing frequency from fft?
I am currently operating in vhf band AND trying to detect frequencies using Fast Fourier transform thresholding method. While detection of multiple frequencies , i received spurs(May not appropriate ...
