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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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 ...
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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 ...
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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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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 ...
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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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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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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 ...
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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 ...
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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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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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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 −...
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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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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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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 $y(n)$?
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1answer
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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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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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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. ...
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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: ...
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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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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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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 ...
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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
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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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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 $X_t = c\ \text{cos}(\omega t)$...
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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 ...
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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 ...
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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 ...
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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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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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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-...
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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: ...
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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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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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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 $\eta$...
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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 ...
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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 ...
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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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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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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?
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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 $...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...