Questions tagged [discrete-signals]
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.
2,110
questions
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1answer
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Can we apply CZT after FFT?
I want to improve the frequency resolution of the FFT algorithm. Can CZT (Chirp z transform) be better to use after FFT. Because i read in some articles that CZT has better frequency resolution than ...
2
votes
1answer
48 views
Hankel Matrix SVD Denoising
I have performed Hankel Matrix Singular Value Decomposition de-noising to smooth out my univariate time series. It is the close price of EUR/USD exchange rate. Here is a picture:
The problem I have is ...
0
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0answers
36 views
Frequencies calculation of discrete signal in frequency domain
I have some misunderstanding in definition of frequency resolution of the signal. Here it is assumed that the resolution is: $$\hat{f_k}=f_{signal}\cdot T_{sampling}$$ (which is just relation of ...
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0answers
17 views
How can I generate X Axis componant in R_xy in MATLAB?
Let's say I have cross-correlated $x(n)$ and $y(n)$ and got the $R_{xy}(n)$.
Now if I want to generate the x-axis component of $R_{xy}(n)$ in the command window of MATLAB. How can I do that? is there ...
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0answers
15 views
Fourier transform of x[n] = e^(jn/8)*u[n]? [closed]
Fourier transform of x[n] = e^(jn/8) is non-zero for only w=w0, w0=1/8 here. It is an impulse at w=w0.
But what is the Fourier transform of x[n] = e^(jn/8)*u[n] ? I couldn't find out.
2
votes
2answers
68 views
zero-centered and causal zero padding
I have followed the link below to simulate two different zero-padding methods (zero-centered and causal)
https://ccrma.stanford.edu/~jos/mdft/Zero_Padding.html
Sample code
...
0
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2answers
48 views
How would one solve this question if no initial conditions are given? Which assumption can I make?
This was a question on our test, I know it can be easily solved by Z-transforms but there are no initial conditions specified. In this case, what would be the right approach?
Assume all initial ...
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0answers
12 views
How can we divide our long-time domain signal into equal segments and then apply Wavelet transform?
I have a time-domain signal and the samples size is 80000. I want to divide these samples into equal sizes of segments and want to apply wavelet transform to them. How I can do this step. please guide ...
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1answer
52 views
Causal inverse of $h[n]=\delta[n]-\alpha\delta[n-1]$
Find the causal inverse of $$h[n]=\delta[n]-\alpha\delta[n-1]$$
we have
$h[0]=1$ and $h[1]=-\alpha$ also $h[n]=0$ for $n>1$
From the formula $$
h_i[n]=\sum_{i=1}^n\frac{h[n]h_i[n-i]}{h[0]}
$$
we ...
0
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1answer
74 views
Implementing basic high pass filter using difference equation
For the following signal, I am trying to remove the gradual positive drift but retain the spikes using a high pass filter.
I am aware that I can use implement a high pass filter using difference ...
1
vote
1answer
63 views
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 ...
2
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1answer
78 views
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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0answers
17 views
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 ...
0
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1answer
47 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, ...
1
vote
2answers
86 views
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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0answers
22 views
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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1answer
71 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
$$
h(t) = \frac{1}{\tau}\,\exp\left({-\frac{t}{\tau}...
0
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1answer
37 views
Causality on an accumulator system
Can anybody explain why is this system not causal.
$$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 ...
0
votes
1answer
60 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 ...
0
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1answer
48 views
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 ...
1
vote
1answer
50 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)...
4
votes
2answers
91 views
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 ...
2
votes
1answer
81 views
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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0answers
63 views
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 ...
0
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0answers
16 views
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 ...
0
votes
2answers
94 views
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.
0
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1answer
36 views
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
2answers
309 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 ...
0
votes
1answer
21 views
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 ...
0
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1answer
23 views
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
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1answer
43 views
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 ...
4
votes
1answer
74 views
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 ...
0
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2answers
35 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)^{...
0
votes
2answers
81 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
$$Y(\...
0
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1answer
56 views
State-space model and/or TF for a $K$-th order linear system given the signal sequence
The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential:
\begin{equation}
x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k}
{\underbrace{e^{\{(- \...
0
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1answer
54 views
Sum of complex exponential signal in MATLAB
I want to create a sum of damped complex exponential signal with the known values of frequency $f$, damping $\alpha$, amplitude $a$ and phase $\phi$ for the $k = 1,2,...,K$ exponentials. Is there ...
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6answers
836 views
Do discrete-time series always have a continuous-time underlying?
Can one argue that discrete time-series coming from stocks or commodities (prices) are derived from a continuous-time process?
One can probably argue that stocks or commodities at any time have a ...
0
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1answer
25 views
$H(e^{j\omega})$ represented with a limited no of samples
I have a low pass filter defined as:
$$ H_{lp}(e^{j\omega})=\left\{
\begin{aligned}
&1 &|\omega|>\omega_c \\
&0 &\omega_c<|\omega|<\pi
\end{aligned}
\right.
$$
and the ...
4
votes
1answer
74 views
Kay Statistical Signal Processing Estimation Theory Example 7.14
Example 7.14 from Kay Estimation Theory
A common WSS random process has the ACF
$$r_{xx}[k]=
\begin{cases}
1+b[1]^{2}+b[2]^{2} & \text{k = 0}\\
b[1] +b[1]b[2] & \text{k=1}\\
...
0
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1answer
43 views
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 ...
0
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1answer
16 views
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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0answers
9 views
Efficient Method to match vector time series where the vector entries may not line up
Asking here because I couldn’t find or didn’t have the right words to search for the answers online. Also sorry for no examples—gotta maintain my NDA for work.
I have two N-dimensional vector time ...
8
votes
3answers
565 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
2answers
79 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 ...
0
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1answer
95 views
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 ...
1
vote
1answer
67 views
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 $x_2[n]$, ...
0
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1answer
56 views
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 ...
0
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0answers
31 views
How to effectively stationarise non-periodic wave signals?
I am pre-processing a non-periodic signal for further implementation of autoregressive modelling on the signal. The signal is shown in the following figure. However, when I applied the Augmented ...
0
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2answers
73 views
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 ...
0
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1answer
32 views
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 ...
