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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Mathematical Approach to Detect If a 2D Signal Is Separable

In the Special 2-D Sequences page the following examples are demonstrated, 2D dirac 2D diagonals 2D unit step function Is there a more defined method or series of steps for determining if a ...
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Sampling period

I started it but didn't how to continue , any help ?
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When to Apply Circular Convolution Formulas?

Context I am studying the family of Discrete Trignometric Transforms (DTT): Discrete Cosine Transforms (DCT) and Discrete Sine Transforms (DST). And trying to understanding more their properties, I ...
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Effect of filtering on Energy of a Digital Signal

I am trying to detect (not remove) noise from the digital signal to get meaningful information out of it. The signal I need is in the frequency range of 0.1 Hz to 10 Hz. Anything beyond this is just ...
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replace input signal with δ will have the impulse response of the function?

Is my impulse response right? By definition,the impulse response is the output when the input is a impulse signal,so $y[n]=\sum\limits ^{n}_{k=-\infty}\frac{1}{2^{n-k}}\ x[k]$,the impulse response ...
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39 views

The effect of upsampling on DFT coefficients

I am learning DSP by myself and I encountered a problem that bewilders me. If I have a sequence of length N, and I upsample it by a factor of 3. How would the DFT change or related? For example: <...
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32 views

$x[n]$ after sampling of $cos(16\pi t+\phi)$ at 12kHz

I'm not sure what the question really means, so this is just guesswork. I think options 1 and 4 can be ruled out as $w_0<\pi$. The CTFT of $cos(16\pi t+\phi)$ has two spikes at $16\pi$ and $-16\...
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Find integral of DTFT after sampling (Graph of CTFT given)

So for the first question: If this is sampled at 10kHz, then the amplitude is scaled by 10000. In the DTFT, the frequency 3.5kHz gets mapped to 3.5/10* 2pi=0.7pi. So this point lies outside the range ...
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Which frequency bins give the best interpolation for the derivative of a function?

A function $u:[0,2\pi]\to\mathbb R$ sampled over $N$ equidistant points $\theta_j=(2\pi/N)j,\, j = 0, \dots, N-1,$ can be interpolated by a set of functions $\{u_{k_0}\}$ enumerated by integers $k_0\...
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How to compute the energy of a NON-STATIONARY (transient) random discrete-time signal

When computing the energy of a NON-STATIONARY (transient) random discrete-time signal $x(n)$, does it make more sense to compute the energy as $ E=\sum_1^N{x^2(n)}$ over all the $N$ samples or does ...
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Find $X(j\omega)$ after sampling of $2\cos(2000\pi t)+\sin(5000\pi t)$ at 5 kHz sampling rate

The Fourier transform of the first term has two spikes at -2000pi and 2000pi of magnitudes 2pi for both. The Fourier transform of the second term has two spikes at 5000pi and -5000pi having ...
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How to calculate auto-covariance for a discrete-time symmetric block-wave?

I am newbie to this field, so this question seems difficult to me. I'd appreciate your help. For a discrete-time symmetric block-wave u(t), ...
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Passing a sampled signal through a filter

I was wondering why is it wrong to use a band-pass filter on a sampled signal? If the signal we want to sample has frequencies up to fmax, we sample it with frequency fs = 2fmax (so that Nyquist ...
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79 views

Recovering a signal after filtering

A signal $x[n]$ is to be transmitted over a communication channel. The communication channel is described by an FIR filter of length $M$ such that the received signal is given by $$r[n]=\sum_{k=0}^...
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Derivation of Nyquist Frequency and Sampling Theorem [closed]

I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
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64 views

How to filter out noise in high frequency signal?

I am trying to filter this signal (download-zip): ...
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146 views

DC Spur in DAC output

I have a design in which a signal from ADC is filtered and then played by DAC. In FPGA the real signal is converted to quadrature using DDS with 70 MHz frequency. After filtering, the baseband signal ...
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How to remove non-periodical high frequency noise from signal in python3?

I am trying to get rid of the noise in my data. You can find the python file and signal.csv here ...
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Digital Spectrum Analyzer: Video Bandwidth

I am currently working on a Digital Spectrum Analyzer. We are trying to imitate a hardware Spectrum Analyzer by capturing I/Q data and performing an FFT on it. I am a bit stuck on how to imitate the ...
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1answer
83 views

Low pass filter output showing instability

I am fairly new to DSP, and I'm trying to implement the Pan Tompkins algorithm for QRS detection of ECG signals in MATLAB. The first stage of the algorithm consists of a second-order low-pass filter. ...
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Determining if a 2D system is LSI

After a long time away from school, I'm a bit rusty and struggling with this question: Determine if the following discrete system is LSI: $y(m,n) = mn*x(m+n) + mn*x(m-n)$ So here's what I've done ...
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1answer
27 views

Impulse coefficient when it does not match the bin index

Assume that I have a N=10 samples with Fs=10. assume in the time domain an unit impulse event happens which should be placed at 3.425 index in time domain. Assume that I could not change Fs or ...
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1answer
29 views

Invariance of $T[x[n]]=\sum_{k=n-1}^{n+2}x[k]$

I have to test whether the following system is invariant or not: $T[x[n]]=\sum_{k=n-1}^{n+2}x[k]$, so I want to verify that, if $y[n]=T[x[n]]$, then $y[n-N]=T[x[n-N]]$. $$T[x[n-N]]=\sum_{k=n-1}^{n+2}x[...
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Filtering in the Frequency Domain - DIP [closed]

I am trying to do some filtering with a gray scale image in the frequency domain. I am just getting into matlab after some time away from any signal processing or coding and can't quite seem to get my ...
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As of 2019, which discrete nonlinear, time-invariant systems with memory are considered “easy” to model and identify?

There are several types of discrete nonlinear time-invariant systems with memory ("NTIM") which are considered "easy" to model and identify. Any such system can be represented using a Volterra series, ...
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Why does knowing the impulse response allow you to determine the output for any LTI system?

Going over some notes on LTI systems and I’m quite confused about how knowing the impulse response of a system allows us to recover the systems’ response to any signal. In the textbook screenshot ...
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1answer
61 views

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
56 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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72 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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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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149 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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48 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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70 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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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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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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206 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
95 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, pad it with zeros and take the ...
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1answer
83 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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170 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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1answer
59 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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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
35 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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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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230 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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377 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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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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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
141 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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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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