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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How to draw a finite-duration sequence

On page $359$ of the 2nd edition of the book "Signals & Systems", by Oppenheim and Willsky, the authors wrote the following words: "Consider a general sequence $x[n]$ that is of finite duration. ...
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29 views

IID noise assumption at Matched Filter sample time

I read that at the correct sample times of a matched filter output the noise is independent assuming a Nyquist pulse. Can someone provide a proof of this or explain it more? Assuming your matched ...
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Applying Wavelet on energy disaggregation as denoising technique to remove uncertainties

I would like to apply Wavelet in MATLAB as a denoising technique on Non-Intrusive load Monitoring data. The data was captured by sensors on each appliance and one sensor on the smart meter (Normally ...
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39 views

Deep Learning based NDA Channel Estimation

I was wondering if it is possible to use Deep Learning to estimate the Channel Impulse Response for NDA synchronization? I understand Deep Learning is not normally used for regression problems but I ...
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1answer
356 views

How to convert from Laplace Domain to Time Domain?

I want to convert the following equation from Laplace domain to continuous time domain: $F(s) = \frac{-2 m k v R}{2 m R s^{2} + m k s + 2 k R}$ m, k, v, R are all constants. If I can factor or put ...
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Are discrete time functions expected to be this inaccurate?

I am attempting to test some discrete time functions against their continuous counterparts and I am surprised by how inaccurate the discrete versions are coming out. I am modeling the displacement, ...
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1answer
107 views

inverse discrete FFT in python, multiple times?

I was wondering what really happens when taking the inverse discrete FFT on some set of numbers, for 3 times? Because looking at it, it looks like we're getting an output that is identically with the ...
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1answer
84 views

Reconstruction of sampled band-pass signal

I am pretty new to signal processing. I am currently trying to reconstruct a sampled band-pass signal created with the filtfilt and ...
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0answers
22 views

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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1answer
61 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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45 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 ...
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1answer
88 views

Ways to differentiate three respiratory signals

I have three 1-min respiratory signals I derived from ECG signals. I am wondering if you guys have any suggestion on differentiating those three? The red line represents the experimental signals and ...
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127 views

DFT truncation of signals

How can I calculate 8 point DFT of signals whose length is less then 8 ( say 2,4) then what will I assume other members in formulae "0" or rotation or keep repeating the same two numbers Consider I ...
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22 views

Detecting changes in signal due to server delay

I'm currently working on an application that can be used to determine when a signal changes due to a server delay. Essentially, I have an API that is used to output data to a UI. However, for reasons ...
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67 views

How to calculate Eb/N0 for a digital BPSK modulated multicarrier waveform

Suppose that I have a BPSK modulated multicarrier carrier waveform $L$ samples long at a sampling rate of $f_{s}$: $$ x_{tx}[l] = \sum\limits_{n=0}^{N-1} A \cdot \cos\left(2 \pi \frac{f_{n}}{f_{s}} ...
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Finding the differences(using features, not subtraction) in order to find differences in signals

I have a question. Let’s say I have two signals (discretely represented as arrays), $S_1$ and $S_2$ as shown below. $S_1$ has a similar form to $S_2$. If the signals are subtracted, $S_2-S_1$, they ...
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36 views

Discrete Frequency Equation and Relation

I think I am looking at conflicting equations from a few sources, or maybe I just dont understand it. $ \Omega $ is Discrete frequency $ N $ is Discrete Period in number of samples $ \omega $ is ...
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70 views

Python FFT outptut

I have a (real) array of data and am trying to analyze its frequency components. I've been using NumPy's FFT routines, but I realized there is something I don't quite understand: why does the output ...
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45 views

How to crop a song and mantain the same values in the sample vector?

Does anyone know how can I crop an audio signal and maintain the same values in the sample vector? I am working on a audio signal processing project for song recognition in Python and I wanted to ...
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66 views

why we use time step only in continuous convolution in MATLAB? But not in discrete convolution?

I am studying convolution from book of alex palamides but i am confused because he uses time step(in this case 0.01) in his code for continuous convolution as shown highlighted in attached photo but ...
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51 views

Mathematical expression for a system

I have a system that delays the input with k samples and concatenates the new input with delayed one so that y = [x(n) x(n-k)] so if the input comes with n samples the output should be k+n samples. ...
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1answer
192 views

Inverse FFT of complex exponential with time delay - window leakage?

I am working in MATLAB with a frequency domain signal that is a sum of complex exponentials, e.g. $X(\omega) = \sum_i e^{-j\omega t_i} $ where $t_i > 0$ $ \forall $ $ i $ I expect the output to ...
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51 views

PLL carrier recovery: intermediate versus baseband

When looking at carrier recovery, a PLL is often applied to correct the frequency offset between the local oscillator and the transmitter after down conversion. I'm wondering what happens to the PLL ...
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1answer
164 views

Please help me understand this paper about Discrete Wavelet Transform!

I am trying to understand this paper says. I have found this paragraph to be vague: (a) Preprocessing Stage. The first step in this stage was to apply the Discrete Wavelet Transform (DWT). This ...
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102 views

Chirp resolution as a function of bandwidth

My question concerns about the Chirp resolution during the crosscorrelation as a function of the sampling rate and available bandwidth. Suppose at a transmitter a chirp signal is transmitted (ranging ...
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45 views

What is the error rate in compressed sensing?

Let $x \in \mathbb{R}^n$ be a $k$-sparse vector. Given $A \in \mathbb{R}^{m \times n}$, we have a measurement vector $y$ given by $$y=Ax$$ Let $\hat{x}$ be defined as follows $$\hat{x}:=\arg\min_{z\...
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1answer
213 views

Discrete-time, second-order section, direct-form II filter

I found dfilt.df2sos in Matlab and trying to figure it out how do I do that in Python? Is there any function that works similarly with the Matlab function? I also ...
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510 views

Please explain Multiplication property in Z transform?

I am having problem visualizing contour any example will be great help. As far as as where I need it I was trying to find Z transform of a contracted signal by first multiplication by impulse train.
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46 views

Interpreting Auto correlation results

I used xcorr function in Matlab to compute the autocorrelation of my signal. I obtained a graph, which is shown below. How to interpret this? I read that autocorrelation helps in finding the patterns ...
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52 views

How to low pass very few samples

I'm asking myself what is the best way to low pass a signal which only has a few hundred samples? Or is there a proper way at all? It must not be a sound signal but I used Audacity to display the ...
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1answer
88 views

About the variance of the coefficient of narrowband noise when using signal-space representation

Assume that n(t) is a white Gaussian noise process with zero-mean and power spectrum density $N_0/2$. By using the signal-space representation, it can be expressed as: $$n(t) =\sum_{j=1}^N n_j \phi_j(...
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21 views

How can we do finite-step signal sampling in practical?

The signal has infinite length. We cannot sample it with a whole length. How can we truncate a infinite signal and sample it in finite step? And then how can we analyze it.
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46 views

Correct way to calibrate RX into a measuring receiver

While playing with my SDR (Software Defined Radio) Board, I was interested in performing a TX output power table at different center frequencies and TX antenna gains. I have an RF frequency generator....
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1answer
577 views

Power Spectral Density of discrete White Gaussian Noise defined with variance and sampling interval

From Creighton and Anderson Chapter 7 on Gravitational Wave data analysis: Please explain where the delta t and the limit came from in this derivation.
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46 views

Removing outlier data points from frequency-domain signal

Hello signal processing stack exchange, I have a complex frequency-domain signal representing the impulse response of a physical system over some range of frequency space. As an artifact of the ...
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2answers
52 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
168 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 ...
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54 views

Can we sample the signal with any period as long as the Nyquist rate is respected

I have a question regarding the sampling rate. Suppose that we transmitted a signal $m(t)$ then at receiver side, we received the continuous signal $x(t)$, which is time varying and sampled with a ...
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1answer
67 views

Meaning of a formula about transient frequency bins

I'm trying to understand the following formula in this paper: Sadly, the paper does not define most of the symbols it is using, so my guesses so far are: $T_{tr}$ refers to the sampling interval i....
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191 views

State Space conversion of Sinusoidal model

i would like to learn how to convert sinusoidal model into state space form which has following equation our model consist of sum of periodic components with additive of white noise, given by ...
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23 views

Is there a criterion that says at what point you can distinguish 2 partially overlapping Lorentzian peaks?

If you have 2 Lorentzian peaks that partially overlap and you have some frequency resolution df (your points in frequency space are separated by df) and both Lorentzian peaks have FWHM $\Gamma$ is ...
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1answer
97 views

Harmonics in Quantal Histogram

I'm studying what I believe to be a system that produces a (noisy) quantal response (i.e. there should be a minimum increment of response). To do this, I've plotted a histogram of some ~6000 amplitude ...
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1answer
246 views

How to choose the right segment length for a given signal?

Im working on plotting the power spectral density of a random time series measured. I know the target spectrum.The idea is check the measurement vis-a-vis the target spectrum. However, I get slightly ...
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1answer
57 views

Measure 3-D length using smart-phone's accelerometer

I'm wondering if we can measure 3-D length only by our smart-phone's accelerometer. And we all know these low cost IMUs are not accurate. You can model accelerometer's error this way: $$ a = f*a' + g ...
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68 views

How can I find a relation between the input and output of the overall system?

I have system for filtering a continuous-time signal using a discrete-time filter where sampling is performed by multiplication with the impulse train. The frequency response of the discrete-time ...
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37 views

Sampling Process Question

This is what I know about the basic sampling process I am told that fbar(t) (i.e the sampled signal) is defined for all t. I don't understand that. If n is a finite integer (..,-3, -2, -1, 0, 1...), ...
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22 views

Find which groups of ants are coexisted in the location from their signal profiles using NMF

I try to solve biological problem to tell which groups of ants are co-existed at this location by their sounds in specific time frame. My chosen framework is Non-negative Matrix Factorisation (NMF) ...
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1answer
136 views

Amplitude problem by puting 5 FIR in a row

I'm trying to use 5 FIR in a row to improve the S/N ratio on my signal, but I have some difficulties doing it. In fact I have 2 signals, let's call them sig_I and sig_Q. I want to apply my 5 filter ...
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19 views

Join 2 NMF models where dictionaries has hierarchical structure

I have two NMF models $A = W_1A_{dict}$ and $B = W_2B_{dict}$ (where the $W$ represents weight coefficient matrix). What is a good way to join two NMFs if I know each column of $B_{dict}$ is summed up ...
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65 views

How do I improve the SNR of my signal given a noise profile (additive noise)?

From an iPhone microphone, I have a background recording of 5s(fs = 44.1 Khz), and immediately after that, I have a voice recording of a person saying 'aaa...' for 10s(fs = 44.1 Khz). How can I use ...

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