Questions tagged [discrete-signals]
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.
0
votes
1answer
25 views
Conversion from continuous to sampled signal?
I am bit confused regarding sampling as i read different types of statements in different texts
Forexample i have a continous time signal $x=sin(t)$ defined for $t=0:10$
and i want to sample it with ...
3
votes
1answer
24 views
How to match two signals that have similar shape but are scaled and expanded?
I have two signals A and B in time domain as follows:
Visually both signals look very similar; however the X and Y axis range are different for both the signals. Signal B is basically a "stretched" ...
0
votes
0answers
21 views
Is it correct to say the maximum possible angular velocity of a discrete-periodic signal is pi? [on hold]
For a discrete signal, is it correct to say the maximum possible angular velocity is $$ \pi
$$
I did not completely understand this except for the fact that the signal can alternate between positive ...
0
votes
0answers
25 views
Angular velocity of discrete time exponentials, increasing and then decreasing over 0 to 2 pi [duplicate]
So, the differences between:
$$
x(t) = e^{j(\omega_{0} t) } \,\,\,\,\, \textbf{Vs.} \,\,\,\,\, x[n] = e^{j(\omega_{0}n)}
$$
Are:
For $x(t)$ the $\omega_{0} \to \infty $ means the oscillation rate ...
2
votes
1answer
75 views
When Two Sampled Sinusoidal Are Orthogonal?
If two analog sinusoidal are orthogonal with duration T, their minimum frequency difference should be 1/2T in case of no phase offset between them.
And if there is phase offset, the difference is 1/...
0
votes
0answers
21 views
How is time shifting of signals important in LTI Systems.What is it concept in Convolution? [closed]
Convolution is quite simply the output y of a system h when x is given as input. Why would you need that? The same reason as why you would wish to know what would the result of adding 2 with 3 will be....
0
votes
0answers
15 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 ...
0
votes
0answers
61 views
Division of sines as sinc
$\DeclareMathOperator\sinc{sinc}$I've come across a text that states that $\frac{\sin(\frac{3\pi}{10}n)}{\sin(\frac{\pi}{10}n)}, n=0\ldots9$ is a 'weighted' $\sinc$ function. Thus, its Fourier ...
0
votes
2answers
28 views
Frequency Domain Correction of Frequency Offset or Doppler Frequency in LTE
We are working on LTE Uplink CFO Correction for 3 MHz band. The time domain CFO correction is easy, which depends on the processing of 3840 samples step by step multiply by $\exp(-j 2\pi f_\text{...
1
vote
1answer
32 views
Usefulness of Matched $z$ transform Method
I'm aware that the matched $z$ transform method maps between the continuous $s$ plane and the discrete/digital $z$ plane but my question is - when would this be necessary? Why would we need to convert ...
0
votes
0answers
15 views
Discrete Wavelet Transform (DWT) Filter Bank
I have some stumbling block in my thesis writing.
Do we use the same filter pair while implementing DWT filter bank with downsampling of the filter output, or filters do change also from level to ...
0
votes
0answers
25 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. ...
0
votes
1answer
16 views
Mathematical operations with given discrete frequency response function
Let's say I have a given discrete frequency response function H(w) and corresponding n frequencies as MATLAB arrays, ranging from 0 to 512 Hz.
If I do an n-point FFT on a discrete time domain signal ...
1
vote
1answer
55 views
Why does this not work: Alt. way to compute the period of a discrete periodic signal that is a sum of 2 complex exponentials
I want to compute the fundamental period of the following discrete time signal:
$ x[n]= \exp^{(j\frac{2\pi}{3})n} + \exp^{(j\frac{3\pi}{4})n}$
I know I can do this by taking the fundamental periods ...
1
vote
1answer
47 views
What is a sliding window?
I tried to find the answer by my own but unfortunately I couldn't.
Let's say I have the discret values of a signal which is 10s long.
What is the FFT which is performed on a sliding window with ...
0
votes
1answer
31 views
explanation of Hybrid systems?
I want to study Detailed explanation of hybrid systems?Which incorporate both continuous and discrete time signals & systems?
for example
In which a continuous-time input signal is transformed ...
0
votes
1answer
45 views
Ideal Discrete Time Hilbert Transformer with constant group delay
Let's assume we have an ideal discrete time Hilbert Trasnformation system (90-degree phase shifter) with a frequency response over one period:
$$H(e^{jw}) =
\left\{
\begin{array}{ll}
-j & \...
0
votes
1answer
34 views
Inverse FFT of complex exponential with time delay - window leakage?
I am working in MATLAB with a frequency domain signal that is a sum of complex exponentials, e.g.
$X(\omega) = \sum_i e^{-j\omega t_i} $ where $t_i > 0$ $ \forall $ $ i $
I expect the output to ...
0
votes
0answers
18 views
What is k and n in this Discrete Hilbert Transform formula and how to use it with a time series?
I have a time series and I need to find the Discrete Hilbert Transform of that.
This paper says that about the Hilbert Transform.
Suppose I have a time series f(t)...
2
votes
0answers
30 views
How do 2D DCT basis functions interact to produce 8x8 JPEG tiles?
This section is a bit of an intro. If you want to skip directly to where the problem is explicitly outlined, skip to the bottom of this post. Please note that I'm not hip with mathematical lingo, so ...
0
votes
1answer
38 views
Fourier transform of dirac comb with function: The scaling factor
Multiplication in the time domain corresponds to convolution in the frequency domain:
$$
f(t) \cdot x(t) \iff F(j \omega) * X( j \omega) \tag*{No scaling factor}
$$
I know the fourier transform of ...
0
votes
1answer
50 views
What is the algorithm to do a Discrete Hilbert Transform?
I have a time series data. I have applied Empirical Mode Decomposition and obtained several IMFs.
Now I need to apply a Hilbert Transform to the IMFs to get the instantaneous frequencies.
I have ...
2
votes
1answer
60 views
Using Matlab's filter() function for solving difference equation with initial conditions
I am trying to solve a difference equation with initial conditions using Matlab's filter function:
$$y[n]=\frac12y[n-1]+x[n],\qquad y[-1]=1\tag{1}$$
For $x[n]=6u[...
0
votes
1answer
25 views
Deriving difference equation
I have this block-diagram of Karplus-Strong basic algorithm.
Where $$H_{d}(z) = \frac{1+z^{-1}}{2}$$
The problem occurs when I try to get the difference equation. As I can see from the diagram, that ...
2
votes
1answer
111 views
Differential Pulse Code Modulation (DPCM)
In the following figure we see an encoder and a decoder of a Delta Modulation System, which is a simple DPCM System with a 1-bit quantizer:
We assume that signal $x(n)$ is known, that $\hat{x}(-1)=0$ ...
1
vote
2answers
200 views
Time series of Poisson Process
I want to run a numerical simulation of a system (eg first order low pass filter) that is stimulated with a photocurrent-like signal. My preferred language is Python.
I'm failing to understand how to ...
1
vote
1answer
123 views
Cepstrum Calculation of Rational Function H(z)
I am trying to solve my first problems at cepstrum calculation. I want to calculate the complex cepstrum $\hat{h}[n]$ of a signal $h[n]$ with Z-Transform:
$$H(z)=\frac{(1-0.5z^{-1})(1+4z^{-2})}{(1-0....
1
vote
1answer
74 views
What is discrete angular frequency?
I am currently reading a paper about speech enhancement. The paper uses Spectral Subtraction Method. On that section, The paper stated that ω is the "discrete angular frequency index of the frames"
...
2
votes
0answers
18 views
Is it possible to create a causal filter with a positively-sloped phase response?
I am currently prototyping a set of noise-cancelling headphones that utilize active EQ to modify the noise-cancelling signal, allowing the user to modify the frequencies that they hear or don't hear. ...
2
votes
1answer
19 views
Plane Settings of the Matched $z$-transform Method
I've come across that the matched $z$-transform maps poles of the $s$-plane design to locations in the $z$-plane. My question is, what is the $s$-plane and what does this mean? I'm aware that the ...
0
votes
1answer
44 views
ADC and Matched Filtering
A basic theorem in communications is the matched filter maximizes the SNR at sampling. I'm a little confused on how this relates to discrete time systems and sampling rate.
Normally if you sample at ...
0
votes
1answer
24 views
Time Setting of $z$ and Laplace Transforms
I'm aware that the z-transform and the Laplace Transform have an analogous relationship but I want to be doubly-sure that the z-transform only works in discrete-time and that the Laplace transform ...
0
votes
1answer
21 views
Differences in moving window rms due to sampling rate
I have a 10 second recorded signal band pass filtered from 100-500 Hz. The original sampling rate is 10 kS. Now I run a moving window RMS with a window length: 10 ms on the signal (10/1000 * sampling ...
0
votes
0answers
29 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 ...
0
votes
0answers
8 views
How to match resolution of two or more signals
I have received the following 4 time-series signals and wanted to do some data analytics using these. Although the sampling is the same for all of these signals, 2 samples per second, problem is that ...
0
votes
0answers
19 views
IFFT, negative frequencies and noncausal impulse
When using the IFFT to compute an approximation to the IDTFT, frequency range is 0 to 2$\pi$ versus $-\pi$ to $\pi$. This produces a different impulse sequence(causal I think).
How do you calculate ...
0
votes
2answers
27 views
Does a phase rotation introduce a delay?
Suppose I have 2 complex time series, $x_1$ and $x_2$.
If I measure the delay between $x_1$ and $x_2$, I get $t$.
If I make $x_2 = x_2 e^{-j 2 \pi 10}$, and measure the delay between $x_1$ and $x_2$...
0
votes
1answer
20 views
Equivalence of difference equation with system of difference equations
I have this system and tried to write down its difference equation as follows
$$ y[n] = b_0v[n] + b_1v[n-1]\\
v[n] = x[n] - a_1v[n-1] $$
I was asked to prove that the system can be ...
1
vote
2answers
30 views
Confused in difference between sequence versus signal?
I am learning basics of signals and systems with MATLAB
If i create a vector in matlab such that
x=[ 2 5 10 20], will it be considered a sequence or a signal?
As ...
2
votes
0answers
37 views
Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?
Let
$$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$
Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure
what will the frequency domain for $Y(\nu)$ look like for a ...
1
vote
1answer
48 views
what is the output of MFCCs?
I had calculated 13 MFCCs coefficients of a speech signal and i got output in the form numerical vectors please see below figure.
My confusion whether it is in time domain or frequency domain.
suppose ...
1
vote
1answer
30 views
Downsampling by block averaging
Many spectroscopic detectors used to study light absorbance as a function of time. These detectors cab sample data at 160 to 250 Hz. There is an option of choosing lower sampling rates such 80, 40, 20,...
2
votes
2answers
43 views
Contradiction while using the convolution sum for a non-LTI system
In a recent quiz, we were given the following problem:
The cascaded LTI systems $\mathcal{T}_1$ and $\mathcal{T}_2$ respectively have impulse responses $h_1[n]=\delta[n+3]$ and $h_2[n]=\delta[5−n]$....
0
votes
1answer
40 views
Matlab FFT not producing symmetric spectrum
I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset.
...
0
votes
0answers
13 views
Punctured Turbo Code Decoding: Convergence Issue
I have been trying to create a basic BCJR decoder for a rate (1/2) punctured turbo code. The puncturing is simple, the encoder alternatively selects between the parity bits generated by the two ...
-1
votes
2answers
59 views
Convolution of Two Impulse Signals
I have encountered convolution of two different impulse signals.
...
0
votes
0answers
31 views
how can I know this system is Time invarient?
y(t) = 0 (t<0);
x(t) + x(t-2) (t>=0);
y(t) = 0 (x(t) < 0);
x(t) - x(t-2) (x(t) >= 0);
y[n] = x[n] (n>=1)...
1
vote
0answers
11 views
Frequency warping while creating filter coefficients
If I have an audio signal at 16kHz with frequencies band-limited to 8kHz. I want to low-pass filter this signal such that fc=4000Hz. Meaning when I reconstruct the signal I do not want any content ...
0
votes
1answer
32 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 ...
6
votes
3answers
567 views
Compress a signal by storing signal diff instead of actual samples - is there such a thing?
I am working with EMG signals sampled at 2kHz and 16 bits, and noticed that they "look smooth", that is, the signals are differentiable, and if I apply a "diff" function (...
