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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Convolution of a non-symmetrical window function by a cosine signal in the frequency domain
A have a time signal:
The associated DFT spectrum of this signal:
The time signal can be considered as a non-symmetrical rectangular window function multiplied by a cosine signal with a frequency $...
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0answers
20 views
decouple signal from environmental effect
Sensor signal depends on environmental factors such as temperature, relative humidity. Temperature compensation is relatively straightforward. But I am not entirely sure how to model the effect of ...
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1answer
26 views
To find the impulse repsonse using the difference equation
A causal linear time-invariant filter has transfer function
a) Denote the input signal by x[n] and the output signal by y[n]. Find the difference
equations for the filter.
f) Find the impulse ...
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14 views
Cross-correlation, spreading out the error
I'm looking for a method to determine the most likely offset of a measured 1-dimensional signal to a reference signal. The reference signal does not need to be generalized and always has a similar ...
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1answer
34 views
Where can I read up on zero state and zero input response for Discrete Time LTIs?
There seems to be something I'm just not understanding about this topic.
Every question I work out that asks for zero state or input I get wrong.
Hence I think I am just not understanding the ...
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21 views
Motion Control Implementation for Robotic Arm [on hold]
I am interested in learning about motion controller for the 5 axis robotic arm. So the system is engineered with Host as the provider of the G-CODE and the motion controller (MC) as parser of the G-...
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1answer
64 views
Is it impossible to determine the inverse Z-transform without any other information?
Suppose I give you this as my transfer function $H(z)$:
$$ H(z) = \frac{1} { 1 - az^{-1}}$$
With no other information given, is it even possible to determine the inverse Z-transform?
The reason I'...
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1answer
21 views
Shifted output of input vs output of shifted input
As I understand it, shifted output means first getting the output and then shifting it. We feed in $x[n]$, and get our output as $x[2n]$. Then we shift it by $k$ to get $x[2n-k]$. This is the shifted ...
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1answer
46 views
What is the time reversal convolution
Given a signal $r(t)$ which is a result of convolution between signal $x(t)$ and a channel $h(t)$ as below :
$r(t) = h(t)*x(t); $
what I know, the time reversal convolution can be process as ...
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1answer
40 views
How to describe correlated noise after the signal is oversampled?
The Gaussian noise in discrete signal models is usually assumed to be independent and identically distributed variables (i.i.d.). Does this mean that the signal must be sampled with the sampling rate ...
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17 views
Some confusion about calculating spectrogram
I am new to DSP and i have a question because it is not the same as theory.
I need to get spectrogram of wav file and feed it to CNN. I have used scipy.signal to get spectrogram.
I know spectrogram ...
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2answers
60 views
The sum part of the formula for a signals power
$$P_x=\lim_{M\rightarrow \infty }\frac{1}{2M+1}\sum_{n=-M}^{M}\left | x[n] \right |^2$$
I have used this formula to find out the powers for different signals, but the sum part of the formula still ...
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1answer
31 views
Steady-State Output from Transfer Function
The progress I have made is as follows:
$\sin(t)$ is our signal therefore $\omega = 1 = 2\pi f$ and $f$ = $\frac{1}{2 \pi}$
Also, $f_s$ = 10Hz therefore T = $\frac{1}{f_s}$ = 0.1s
$H(z) = \frac{z}{...
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1answer
56 views
Reconstruction of sampled band-pass signal
I am pretty new to signal processing. I am currently trying to reconstruct a sampled band-pass signal created with the filtfilt and ...
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0answers
16 views
DTFT based Frequency Sampling
H($e^{jw}$)= 1, |w| < $\pi/2$ and 0, $\pi/2$ <= |w| <= $\pi$
I took M equally spaced frequencies from 0 to $2\pi$. If we assume h[n] to be causal, $H(e^{jw})$ should have some phase and it'...
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1answer
20 views
Peak to Average Power Ratio of an exponentially increasing signal
I am having an exponentially increasing sinusoidal signal.
After sampling, I am dividing the signal into frames of length 128 and doing windowing operation with a hanning window of length 128. Then ...
2
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1answer
35 views
finding the output of these three systems when connected in series?
I have just started to study Oppenheim's "Signals & Systems, Second Edition" and there is this easy-looking problem that has evaded me its solution for the past 48 hours:
consider systems $S1$, $...
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1answer
21 views
Simulating multipath channel
I'm trying to simulate a multipath channel to see how it would affect my signal. So considering my channel is LTI, I can model it as an FIR filter. I've been reading Telecommunication Breakdown and ...
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0answers
52 views
Rigorous proof of the convolution- Sum Representation of LTI Systems
We've started learning LTI systems and I have confusion regarding the convolution sum representation of a system.
My problem stems from insufficient mathematical formalism in signals and systems ...
1
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1answer
23 views
Show That a 2D Linear Transform $ T \left( \cdot \right) $ Is Homogeneous
By my understanding, a transform T is homogeneous if T[0] = 0.
Then to prove that a linear transformation is homogeneous we say that:
T[ax(n1, n2) + bx(n1, n2)] = aT[x(n1, n2)] + bT[x(n1, n2)]
What ...
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2answers
26 views
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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1answer
53 views
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0answers
11 views
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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1answer
20 views
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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1answer
33 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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1answer
31 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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0answers
24 views
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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0answers
20 views
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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0answers
19 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
31 views
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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9 views
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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2answers
36 views
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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1answer
73 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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2answers
60 views
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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0answers
57 views
How to filter out noise in high frequency signal?
I am trying to filter this signal (download-zip):
...
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1answer
122 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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0answers
21 views
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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0answers
19 views
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 ...
1
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1answer
48 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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0answers
26 views
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
24 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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1answer
38 views
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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0answers
13 views
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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2answers
86 views
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
58 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
31 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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2answers
64 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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1answer
44 views
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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3answers
62 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 $2$.
