Questions tagged [discrete-signals]
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.
1,915
questions
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How can i read .edf.seizures format in MATLAB?
I need to read chb01_03.edf.seizures file from CHB MIT database in MATLAB for seizure detection
2
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0answers
22 views
transfer function of a sampler in the s domain
I would like to modelize my whole system into the S-domain. This is a mixed system, there a numerical part (corrector, ADC, DAC) and an analogic part (plant transfer function, sensors, etc...). I know ...
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2answers
208 views
Problems computing the DFT of finite length sequence
I am having trouble finding the same answer as the solution manual for this sequence.
The problem asks to compute the DFT of
$$
x[n] = \begin{cases}
1 & \text{for even } n \in \{0\...
0
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1answer
22 views
What is impulse response in simple AWGN channel?
Assume a sender and receiver communicate through an AWGN channel. Let $x(t)$ be a transmitted signal and $y(t)$ be a received signal and $z(t)$ be the Gaussian noise. It is known that $y(t) = kx(t-\...
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2answers
79 views
Convolution of two sets
In my systems and signals course I had been asked a question about finding the convolution of two sets.
I was given:
\begin{align}
x[n] &= \{3,2,1\}\\
h[n] &= \{1,-2,3\}\\
\text{Find}\quad ...
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1answer
58 views
How to correctly use sinc interpolation in Matlab?
What is the right way to use sinc interpolation for a given discrete signal $x[n]$? Following is the sinc interpolation formula:
$$x(t) = \sum_{n=-\infty}^\infty x[n] \mathrm{sinc}\left(\frac{t-nT}{T}\...
4
votes
1answer
81 views
Autocorrelation function of a triangular wave
I am interested to find the analytical expression for the autocorrelation function of a signal that comprises triangular pulses. I have followed the derivation in "Statistical Theory of ...
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0answers
20 views
How to handle cross products in feedback loop?
I'm trying to simplify the following block diagram from
to the following block diagram
However, h(t), H(s) in time domain, has a cross product in it (gyroscopic torque). How can I represent the ...
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22 views
An example of a signal that neither have a $z$-transform nor a DTFT? [closed]
What is an example of a signal that do not have a $z$-transform or a DTFT? With explanation.
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31 views
Check vanishing moment property of db4 wavelets
I am reading the book "a primer on wavelets and their scientific applications" by James S. Walker. In chapter 3, Property I on page 46 says that if a signal $f$ is linear, then the $k$-level ...
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0answers
23 views
The effect of time increment $\Delta t$, frequency resolution $\Delta f$ and Gibbs phenomenon on the amplitude of the signal in the frequency domain?
Experiment: Vibration analysis (i.e.: major concern is on transfer function or frequency response).
The input is an impulse (imagine as a knocking effect or knocking force), defined as a half sine ...
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2answers
130 views
In the context of DFT, Where Does the Nyquist Frequency Sample Belong In a Double Sided Frequency Spectrum (Positive / Negative Side)?
If we have an even number of data points $N$, after DFT in MATLAB, the output has the order:
$$(\text{DC}, f_1, f_2, \ldots, f_{N/2-1}, f_\text{Nyq}, -f_{N/2-1}, -f_{N/2-2}, \ldots, -f_1)$$
For real ...
1
vote
1answer
23 views
Is Kalman Filter for LTV systems applicable on Hybrid systems?
As all of us know Kalman Filter is designed for LTV (Linear Time Variant) systems. But nobody in the literature applies that on Hybrid systems. In my opinion Linear Hybrid systems are a subset of ...
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0answers
33 views
Variance of AWGN in BFSK system
I am trying to compute the variance of AWGN in the system for finding the BER with $Q$ function.
The PSD of the AWGN is $N_0/2$, my answer was $N_0T$ but it was incorrect.
This is my calculation (...
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1answer
66 views
Calculating the output of a pole eigen signal in a difference equation
Let an IAR system be defined by the following difference equation:
$$y[n]-\frac{1}{4} y[n-2]=x[n]+3x[n-1]$$
and an input signal $x[n]=(-0.5)^n$.
The transfer function is defined as $H^z(z)=\frac{1+3z^{...
2
votes
1answer
71 views
Super Resolution in Frequency Domain Using Compressed Sensing
To be noted that I'm very new to this topic, I would like to understand the fundamentals of how to get Super Resolution in Frequency Domain estimation using the Compressed Sensing Model.
I am also ...
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2answers
76 views
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2answers
46 views
voltage current analysis in time
I am looking at the transmembrane voltage of a neuron model and would like to investigate this in more detail. The applied current is divided into a deterministic and a noisy component - if I set the ...
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3answers
176 views
Discrete-time signals increase in frequency and period
I am studying Discrete-Time Signal Processing by Alan V. Oppenheim and Ronald W. Schafer. I am confused when it says
periodic discrete signal oscillates more rapidly when its frequency is increased ...
5
votes
1answer
86 views
Circular Convolution as Cyclic Shift Operator
Given the following signal vectors:
$$ Ī³=[Ļ_0,0,Ļ_1,0,Ļ_2,0,ā¦,Ļ_{N-1},0]^T\in \mathbb{R}^{2N}, Ļ=[1,\frac{1}{2},0,ā¦,0,\frac{1}{2}]^T \in \mathbb{R}^{2N}$$
I want to show that the convolution of $Ī³$ ...
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1answer
43 views
Is it possible to specify number of taps and cutoff frequency independently?
When specifying the properties of a moving average filter, is it possible to specify the number of taps and the cutoff frequency?
My guess is no since taps (the number of samples in a moving average ...
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2answers
49 views
How to interpret frequency response of moving average system in discrete time signal processing?
Excerpt from Discrete Time Signal Processing by Alan Oppenheim:
The text says this can be considered as an approximation of a Low Pass Filter. A low pass filter in continuous signal system is ...
2
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0answers
77 views
Aliasing below $f_s/2$
phi = exp(linspace(0, log(511), 1024)) - 1
x = cos(2 * pi * phi)
Above will alias, despite peak instantaneous frequency evaluating to ...
1
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0answers
37 views
Detecting periodic components in discrete-time signals [closed]
I am looking for real data examples where it is of interest to detect the presence of a periodic component of some discrete-time signal when the period of the periodic component is not known.
Suppose ...
1
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1answer
28 views
Evaluate expressions without computing DTFT
Let $X(\omega)$ be the DTFT of the sequence $x[n]$ given by:
$$
x[n] = \{4, 2, -1, 5, -3, 1, -2, 4, 2\},\quad\text{for}\quad n \in [-6, 2]
$$
I do want to compute
$X(0)$
$X(\pi)$
$\displaystyle\int_{-...
2
votes
1answer
24 views
confusion related to finding inverse Z-Transform using Complex Integral Method
I am facing problems related to evaluation of inverse Z-Transform using Complex Integral Method;
Consider $X(z)=\frac{z}{z-2} $ and $ROC: |z|>2$
then, $$x(n)= \frac{1}{2\pi j}\oint_c X(z) z^{n-1} \...
0
votes
2answers
37 views
Convert complex valued sinusoid to real valued sinusoid
This is the homework problem: convert $x[n]=je^{j\pi n/8}-je^{-j\pi n/8}$ to a real valued sinusoid.
I understand that $\sin\theta=\dfrac{e^{j\theta}-e^{-j\theta}}{2j}$
In the solution, the answers ...
2
votes
1answer
35 views
A basic question regarding frequency analysis of an EEG signal
Assume that an EEG signal is sampled at $f_s = 300$ Hz then a 10000-point segment of it is selected, called $x[n]$. The corresponding 10000-point DFT is then computed and called $X[k]$.
Assume further ...
0
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1answer
39 views
DFT Signal DFT Length N , FFT
If We sample an Signal let say sine(2 * pi * f) with f=1Hz and a sampling Frequecy of Fs = 8Hz, is it right that the length of the data schoul be N = Fs/f or multiple of Fs/f like N= d*(Fs/f) with d=...
2
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1answer
53 views
Fourier coefficients of discrete difference of a square wave
I have a discrete square wave $f(t)$ where $t \in \mathbb{N}$, of amplitude $A$, period $T$ and duty cycle $1/T$
$$
f(t) = \left\{\begin{matrix}
A, & \mathrm{if}\;t=Tn\\
0, & \mathrm{if}\;t\...
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2answers
52 views
Converting Audacity Filter Curve EQ into transfer function and applying it to a signal via python
First of I am very new to Signal Processing and to python in general. I am trying to write a script where I would feed a voice recording into it, internally apply an eq and have the modified signal ...
2
votes
5answers
200 views
How is the DTFT of a periodic, sampled signal linked to the DFT?
I am trying to understand the connection between FT, DTFT and ultimately the DFT. But I am failing to link the DTFT to the DFT.
This is how far I am getting: Say I have a function $f(t)$, and its ...
2
votes
2answers
82 views
Inaccurate phase returned by np.angle
I am generating 2 sine waves, first one has fundamental frequency = 50 Hz, amplitude=10, phase=0, the second one has fundamental frequency = 100 Hz, amplitude = 5 and phase = np.pi/6 (which is ...
0
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1answer
34 views
What is a “jump response” of a filter?
I know how to determine if a filter is FIR or IIR, but I don't understand the question. What is a "jump response"?
0
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1answer
36 views
Sampling interval $T$ as a multiplier in digital processing of a continuous-time signals
[from: Discrete-Time Signal Processing, Oppenheim and Schafer, p.224]
Q: Why do we have $T$ as multiplier in $TY_a(j\Omega)$ in Eq.155?
5
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1answer
74 views
Why not use the same “standard” exponentials for both continuous and discrete time
In continuous time the standard exponential signal is usually defined as
$$
e^{st}, \quad\text{with}\quad s = \sigma+j \omega
$$
In discrete time the standard exponential signal is usually defined as
...
0
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1answer
27 views
In pulse code modulation what is pulse word represent?
we study lot of things in PCM we do sampling quantization encoding etc but we never come across pulse so what is pulse word represent in PCM
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2answers
19 views
Impulse response of forward difference cascaded with one sample delay
Below is the excerpt from Discrete Time Signal Processing by Alan Oppenheim.
I don't get how $(\delta[n+1] - \delta[n]) * \delta[n-1])$ becomes $\delta[n] - \delta[n-1]$. The convolution sum operator ...
0
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1answer
18 views
Discrete Fourier transform of a finite length signal which saturates at non-zero value
I am performing spectral analysis of a finite length signal that saturates to a non-zero value. The signal ($s(t)$) can, practically, be write as
$s(t) = f(t) \big(1-H(t-t_0)\big) $, where $t_0$ is ...
1
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2answers
56 views
Is this piecewise-defined system time-invariant?
\begin{equation}
G_c \qquad y[n] =
\begin{cases}
u[n] & \text{if} & n<0\\
2u[n] & \text{if} & n\ge 0
\end{cases}
\end{equation}
I found this question in ...
0
votes
1answer
51 views
Interpolated FIR filter (from Oppenheim and Schafer's Discrete-Time Signal Processing, 3rd ed)
[from Discrete-time Signal Processing by Oppenheim and Schafer, 3rd ed., p.196]
Two questions:
In this context, the filter with system function represented by Eq. (103) is called an interpolated FIR ...
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1answer
27 views
Discrete-time Fourier transform of $a^{|n|} u[n]$
I have a problem calculating the DTFT of this pair:
Could anyone tell me why the DTFT for $a^{|n|} u[n]$ is different from $a^{n} u[n]$'s?
3
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1answer
54 views
Prove that a specific auto-correlation function is even
Background (from digital signal processing):
The $\delta$ function is defined as below:
$$\delta[n]=\begin{cases}
1 \quad \mbox{if} \hspace{.4em} n=0\\
0 \quad \mbox{o.w.}
\end{cases}$$
In an LTI (...
0
votes
1answer
31 views
Transform lowpass filter to highpass filter, what happened to unit sample response and difference equation?
I know that multiple a lowpass filter signal by $(-1)^n$ can transform it to a highpass filter.
$$
s_{hp}[n]=(-1)^n s_{lp}[n]
$$
But exactly what happened to the unit sample response and difference ...
0
votes
1answer
55 views
If a time-series has odd number of samples does it have no energy at Nyquist frequency?
Suppose I have real time series A with n samples and time-spacing dt and I want to analyze ...
0
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2answers
45 views
Problem with applying elliptic filter to ecg signal
I'm currently working on an article for ECG classification which it says that it has used elliptic bandpass filter with 0.5Hz and 50Hz critical frequencies to eliminate base-line and interference etc. ...
0
votes
1answer
54 views
How can you perform echo cancellation on features of audio signals?
I am working on a project that takes some features of audio signals and classify them with a neural network. However, the audio signals are added with their own echo with the environment. What would ...
3
votes
2answers
3k views
Why do we need DFT when we already have DTFT?
We already have DTFT so why do we need DFT?
Please don't write DTFT is used for discrete, aperiodic signal which transfers in the frequency domain to periodic and continuous, but in DFT is discrete ...
1
vote
1answer
42 views
The shift-invariance operator
I am reading the paper "Algebraic Signal Processing Theory: Foundation and 1-D Time". In page one, the first paragraph of second column, I did not get why shift invariance forces the ...
0
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4answers
47 views
Filtering Angular Measurements
I am trying to apply a filter to reduce noise in angular measurements. Since the data comes with noise, the filter needs to be able to handle measurements that are not smoothly progressing; for ...
