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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Help understanding quadrature sampling and effective bandwidth

Let me start off by saying I'm at least a little embarrassed that there's something simple that I'm fundamentally not understanding here. Not sure if the blame is on me, or the prof that taught me DSP ...
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2 votes
1 answer
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Combination of type I FIR linear-phase systems

Let $h_1[n]$ and $h_2[n]$ be impulse responses of type I FIR linear-phase systems with lengths $M$ and $N$. What can be said about the phase response of the following filters? $h_3[n] = h_1[n] + h_2[...
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Where is SNR and CNR calculated for LTE?

I read below that SNR and CNR are different and we have difference of post/pre modulation. In context of LTE which modulation do we refer to- Digital Data modulated using QAM/QPSK to IQ, or Baseband ...
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1 answer
50 views

How to detect a long deceleration phase in a signal?

Given the following signal, I would like to keep only the deceleration phase in orange. I have no idea whether there exists techniques to do that or not. I imagine that I can smooth the signal, ...
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How to interpret values of the autocorrelation sequence?

I know that (auto)correlation indicates the "degree of predictability" of a variable with respect of another. However, this is a vague notion. I know that a blank process should have an ...
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How to find segment with specific speed on the signal in comparison with reference signal?

How do I find a segment on the signal where the signal speed is 2 times the speed of the same segment on a reference signal? Which features describe this? On attached image can see "change of ...
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1 answer
91 views

Phase plot from impulse response function does not match that of the frequency response function

I have a first order linear filter $$ H(s) = \frac{1}{1+\tau\,s} $$ With the impulse response function, found using the inverse Laplace transform as $$ h(t) = \frac{1}{\tau}\,\exp\left({-\frac{t}{\tau}...
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113 views

Causality on an accumulator system

Can anybody explain why is this system not causal. $$T[x[n]] = \sum_{k=n_0}^{n} x[k]$$ How does it depend from future inputs when $n < n_0$. If $n < n_0$ then $T[x[n]]$ is zero because of ...
-1 votes
1 answer
112 views

Is there an order to apply time shifting and frequency shifting to signals in DTFT?

For instance in one question applying frequency shifting first and then applying time shifting yields a different answer wrt applying time shifting first. Please elaborate i am clueless. if i use ...
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1 answer
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How to choose the roots of 4 different Zadoff-Chu sequences? [closed]

I would like to generate 4 Zadoff-Chu sequences. The sequence length is 63. I need to properly choose the roots (r1, r2, r3, and r4) so that: Each root is relatively prime to the sequence length ...
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1 answer
58 views

Expression of output for discrete time causal filters

I have a question about the expression of the output of a discrete time filter described by its impulse response $h(k)$. Looking at the defintion of a discrete filter with input $u(k)$ and output $y(k)...
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2 answers
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Biexponential (double exponential) convolution of a function

Summary I am trying to run a convolution on some data that was originally calculated from a deconvolution (so the reverse). However I'm not getting the expected graph. Blue is expected, red is a ...
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2 votes
1 answer
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How could I do a Discrete Fourier Transform in Python if my data is non uniform?

I have been trying to find a way to transform my time series data in an equivalent manner to the discrete Fourier transform. What I wish to find is something like: ...
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Why is voice clipping happening after Dynamic Range Compressor (MATLAB) when applied in real time on chunks of data?

I have been working on real-time audio signals on smartphones (iOS and Android) and my goal is to make voice amplitude stable in a certain range even if a person is talking closer to the mic of the ...
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Inverse DCT4 by using Inverse DFT

Say I have an inverse DFT function ready for use. I am struggling to find online or mathematically deduce the additional steps needed to compute an inverse DCT4 by using said inverse DFT function. If ...
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2 answers
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Pulse-shaping FIR filter

I understand that pulse-shaping is performed to limit the bandwidth of the transmitted signal, but I would like to know how pulse-shaping can be implemented using an FIR filter.
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Convolution of a discrete continuous function for reconstruction

From chapter 9 page 198 of https://github.com/t4world/Computer-Graphics/blob/master/Fundamentals-of-Computer-Graphics-Fourth-Edition.pdf I am confused as to what this book's description is saying ...
2 votes
2 answers
368 views

Is it possible to calculate a 48-point FFT using a 32-point FFT and 16-point FFT?

I have to calculate a 48 point FFT using an N-point FFT library function which only supports lengths that are a power of 2. Is it possible to calculate a 48-point FFT using a 32-point FFT and 16-point ...
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1 answer
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Mapping a shifted and sequence to a given output axis

I have a sequence x1, which is the same length of an output vector (nx). However, the output vector goes from -12890:13975. I need to define the output (y[n]) of the system along the axis (nx). I ...
-1 votes
1 answer
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Defining a discrete sequence along an arbitrary time axis

I need to compute the output of the system y[n] = x[−n]. x[n] is of length 1 : 26866, and the y[n] output axis has the same length and goes from -12850 : 13975. variables: x[n] = x1, output axis y[n] ...
0 votes
1 answer
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converting complex sum of exponential signal to real signal

I have the following Signal model, that generates a discrete-time complex signal, where $a_k$ - amplitudes, $\phi_k$ - phases, $\alpha_k$ - damping factors and $f_k$ - frequencies are the parameters ...
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4 votes
1 answer
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How to linearize this state space model and write it in discrete form?

This might not be trivial nor short so in advance thank you all who read this in attempt to help. I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
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3 answers
66 views

Is this system time-invariant?

I have this system: $$y[k] = (1 + (-1)^k)x[k]$$ I would like to know if it is time-invariant or not. I've done some work and came out with this: $$y_1[k] = (1 + (-1)^k)x[k - k_0] = y_2[k] = (1 + (-1)^{...
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2 answers
140 views

What does it mean to calculate the FFT of an integer sequence?

The Fourier transform is used to map functions to and from time/frequency domains. I can make sense of what it means to calculate the Fourier transform of, say: $$y(t) = e^{j\omega_0t}$$ which is $$Y(\...
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1 answer
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State-space model and/or TF for a $K$-th order linear system given the signal sequence

The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential: \begin{equation} x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k} {\underbrace{e^{\{(- \...
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Sum of complex exponential signal in MATLAB

I want to create a sum of damped complex exponential signal with the known values of frequency $f$, damping $\alpha$, amplitude $a$ and phase $\phi$ for the $k = 1,2,...,K$ exponentials. Is there ...
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11 votes
6 answers
928 views

Do discrete-time series always have a continuous-time underlying?

Can one argue that discrete time-series coming from stocks or commodities (prices) are derived from a continuous-time process? One can probably argue that stocks or commodities at any time have a ...
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1 answer
30 views

$H(e^{j\omega})$ represented with a limited no of samples

I have a low pass filter defined as: $$ H_{lp}(e^{j\omega})=\left\{ \begin{aligned} &1 &|\omega|>\omega_c \\ &0 &\omega_c<|\omega|<\pi \end{aligned} \right. $$ and the ...
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1 answer
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Kay Statistical Signal Processing Estimation Theory Example 7.14

Example 7.14 from Kay Estimation Theory A common WSS random process has the ACF $$r_{xx}[k]= \begin{cases} 1+b[1]^{2}+b[2]^{2} & \text{k = 0}\\ b[1] +b[1]b[2] & \text{k=1}\\ ...
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1 answer
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How to remove or smooth the comb filter effect in real time audio signal mixing?

I have been working on a project where I have to mix multiple audio signals of the same source coming from different slave smartphones on one master smartphone in a distributed way. Now I have aligned ...
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1 answer
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How to rectify acceleration vibration signal?

I have acceleration vibration signal containing 2500 data points. What I need to do is rectifying the signal becomes no negative values but still has same mean and standard deviation as the original ...
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9 votes
3 answers
672 views

What is the definition of a "Symbol"

I’m looking for the simplest, precise definition of a Symbol e.g. The symbols found within a signal The signal has a N symbols per second I'm following this tutorial. The fellow defines the term ...
1 vote
2 answers
84 views

Encode bits in timing of signal

If you had two computers with two atomic clocks you could measure the time between signals at $10^{-16}\,\text{s}$. Can the time between signal pulses be used to encode additional bits of information ...
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1 answer
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Periodic signal detection algorithms?

I am currently working on pulsar signal periodicity detection. Most of the literature which i studied used traditional FFT (Fast Fourier Transform) or (Epoch Folding) techniques to find the ...
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1 vote
1 answer
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Prove Convolution Property for DFT using duality

If $x_1[n]$ and $x_2[n]$ are finite length sequences of length $N$ $$\mathcal{DFT}(x_1[n] \circledast x_2[n]) = X_1[k]X_2[k]$$ where $X_1[k]$ and $X_2[k]$ are the DFTs of$x_1[n]$ and $x_2[n]$, ...
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1 answer
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Prove Discrete Time Fourier Series Multiplication property

Note: This is not a homework problem. I'm just stalled at a point because I think I might be interpreting the duality property incorrectly. If $x_1[n]$ and $x_2[n]$ are periodic with period N, then if ...
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0 votes
2 answers
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Design of all pass filter with desired phase response

I want to design an all pass filter with a desired phase response in MATLAB. But in MATLAB, all pass filters are designed either by specifying the all pass filter coefficients or from a transfer ...
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1 answer
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n independent, normal, random variable distribution

There is 2 time-series signal and we have to compare the distribution of them. I have heard there is a theory that says for n independent, normal, random variables of a series with many members, the ...
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1 vote
1 answer
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On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies

It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
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1 answer
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Sampling frequency after aggregations

I have accelerometer signal, which is preprocessed by the actigraph on-device. Original sampling rate is 32 Hz, but activity count is summed for every minute, so I have a signal with 1 measurement per ...
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Introductory DSP Texts [duplicate]

I have an interview for a communication theory position and part of the interview requires basic knowledge of signal processing. What are good introductory texts that cover the basics of signal ...
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Why does the term "discrete" usually appear near the term "digital?"

Are these terms just parallel words? If not, why is it that when one reads about the first then one is very likely to come across the second? In such case, what would be a nice example to explain the ...
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3 votes
1 answer
427 views

How to alleviate the edging effect of the Hilbert transform?

I am trying to use Hilbert transform to extract the envelope of a residual signal. After implementing the Hilbert transform, I find that envelope jumps very high at its boundaries. May I ask the ...
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1 vote
5 answers
394 views

Why does twice the sampling rate (Nyquist Theorem) seem inadequate?

I was told in my electronics course that "to reproduce a wave, we need to sample it at least twice every period." If I take this to be literally true, then a sine wave with only 2-3 samples ...
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2 answers
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Are signals modeled either digitally or analogously or can signals modeled as both?

Are signals modeled either digitally or analogously or can signals modeled as both?
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Subspace decomposition

While reading the paper "Perturbation analysis for subspace decomposition with applications in subspace-based algorithms" by Zhengyuan Xu, I came across the decomposition technique called ...
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Symmetries of discrete analytic signals

Defining "analytic" as $x_a[n]$, where $X_a[k] = \text{DFT}(x_a[n])$, and $$ X_a[k < 0] = 0, \tag{1} \label{1} $$ what time-domain properties, such as symmetry or norm, are guaranteed for ...
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118 views

How to measure smoothness of a signal

Lets say I have two signals with a different number of data points - a step function and a smooth spline as you can see below. What is mathematical operation I can use to quantify the "smoothness&...
1 vote
1 answer
36 views

FInd the amplitude function to a system

I'm studying a course in signal analysis and have come across an exercise where I find the analytical part a bit tricky. I am to find the amplitude function $|H( f )|$ for a system with the impulse ...
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1 vote
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Properties of the Frequency Domain to Ensure a Periodic Inverse Discrete Fourier Transform

I've been working on a project to send data via sound waves. The way I've carried this out is by encoding the data in pulses in the frequency domain, and then creating a unique sound wave containing ...

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