A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum.
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1answer
49 views
How can I determine fundamental period of an exponential signal [closed]
For instance I have signals like these,
$$x(t)=e^{\cos(t)}$$
$$x(t)=t\cdot e^{\cos(t)}$$
How should I approach these kinds of signals to determine their fundamental periods?
**The fundamental ...
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3answers
48 views
Is the system represented by the equation $y(t) = x(2t)$ time invariant?
I came across this problem in the text book Signals and Systems - Oppenheim (Example-1.16).
To solve this, I followed the following algorithm (described in the book earlier for a separate problem):
$...
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1answer
63 views
Combining 2 sinusoids of equal amplitude with different frequencies into 1 new “wave”
This question is about combining 2 sinusoids with frequencies $\omega_1$ and $\omega_2$ into 1 "wave shape", where the frequency linearly changes from $\omega_1$ to $\omega_2$, and where the wave ...
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1answer
50 views
Confused about the period of a discretised time-series
I have managed to confuse myself about the periods of discretised time series. It is all rather embarrassing.
This is one period extracted from my continuous signal (radians on y, time on x):
To ...
0
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1answer
30 views
Recommended signal processing books? [duplicate]
I am learning about signals in school but I found it very hard. Can someone help me by giving some references about any books?
We are studying Fourier transform, signal power, filters, digital and ...
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2answers
69 views
why human voice is band limited while it's time limited?
According to Wikipedia, time-limited signals can not be band-limited and vice versa. Also we know that human voice is band-limited and has frequencies from $50\textrm{ Hz}$ to $4\textrm{ kHz}$.
So ...
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0answers
66 views
How to calculate radar distance from Signal to Noise Ratio which calculated with probability?
Lets say we have a radar signal x(t)=cos(wpit) which hits to target and returns. Returning signal is in form of y(t)=A.x(t-G)+n(t) where n(t) is white gaussian noise with mean of 0. And G is the time ...
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0answers
18 views
Fourier transformation and energy question
Given are following signals x(t) and y(t):
Now consider signal z(t) which is defined as:
Question:
Find angular frequency omega at which the interval [-omega,omega] contains 70% of the total energy ...
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1answer
52 views
Combining Bandpass filters on 1D signal to obtain better SNR?
I have a signal which I'm trying to extract information from (specifically, features to recognize using DTW). Parts of it have very clear and unique features which are unfortunately only sometimes ...
0
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1answer
38 views
Find the center of positive plateaus of rectangular function
If I have a rectangular function with irregular positive parts, is there a clever way of finding the center of each positive "plateau"?
The application is, that I threshold a continuous function and ...
1
vote
2answers
88 views
Signal and system convolution
In the convolution equation $y(n)=x(n)\circledast h(n)$ if two things are given like $y(n)$ and $x(n)$ then how can find the $h(n)$?
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3answers
130 views
Why DTFT coefficients are periodic and why continuous Fourier transform coefficients are not periodic?
As I understand, when the input signal is discrete in time and we want to find the coefficients of Fourier transform, DTFT is used and the coefficients in frequency domain are periodic, but I can't ...
1
vote
1answer
120 views
What is the Fourier transform of a multiplied cosine signal with rect?
I tried to find the Fourier transform for this signal, but I have some doubt about the result:
$$g(t) = \cos\left(\pi\Delta{f}t\right) \text{rect}\left(\frac{t-\frac T2}{T}\right)$$
My calculation ...
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0answers
11 views
How to teach NN to extract features of time-series where Cor > 15%?
I want to teach a Neural Network to extract features of many time-series which have 15-20% Correlation together.
My experience is low in such tasks.
Recordings are minimally 25 minutes and maximally ...
4
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1answer
54 views
What is the total impulse response in a system with feedback interconnection?
Let's assume that we have a system with a typical feedback interconnection where the output is given by the following equation:
$$y(t) = \left(x(t) - z(t)\right) \star h_{1}(t) \tag{1} $$
where:
$$z(...
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0answers
15 views
How can I combine signals with unknown lead-lag relationships
Suppose I have a series of data inputs, each of which carries information about a slightly similar signal, but with some unknown lag.
The signals are slightly different, but highly correlated. These ...
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1answer
33 views
Continuous-time frequency response question
Suppose the CTFT of continuous-time input $x_c(t)$ to an LTI system is $X_c(j\Omega)$ and that of its continuous-time output $y_c(t)$ is $Y_c(j\Omega)$. We have,
$$X_c(j\Omega) = 0,\phantom{1}\text{...
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1answer
52 views
How to change a continuous signal to form a discrete signal? [closed]
I have a continuous signal $$ x(t)= 2\cos(200\pi t)+8\cos(250\pi t)$$ and it is sampled at 400Hz.
How is this changed into the discrete time domain in order to determine the two discrete frequency ...
5
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2answers
132 views
Example of an LTI system with complex impulse response
In general, I know that the impulse response $h(t)$ of an LTI system can be complex. However, all of physically realizable, useful systems I've come across have purely real impulse responses. I did a ...
1
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2answers
204 views
Convolution of two exponential signals
I'm a little new to signal processing and I'm trying to wrap my head around convolutions.
I know the definition of convolution for a continuous signal is
$$y(t) = x(t) * h(t) = \int_{-\infty}^{\...
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3answers
97 views
LTI systems inverse of each other
So my question looks like this:
Suppose that we have two LTI systems with impulse responses
$$h_1(t) = \frac 12\delta(t-1)\quad\text{and}\quad h_2(t)=2\delta(t+1).$$
Determine whether these ...
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1answer
71 views
Convolution: generating a continuous-time signal from a discrete-time sequence
Given a discrete-time (DT) sequence $g[n]$, I want to represent it as a continuous-time (CT) signal. I can do this by representing this sequence as a weighted sum of Dirac delta impulses. Would it ...
1
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0answers
50 views
Received signal envelope PDF to power PDF [Wireless Communications]
I am deriving the probability density function (pdf) of the received wireless signal envelope in multi-path fading channels. I wish to transform this envelop PDF to the power PDF of that signal.
I ...
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2answers
221 views
How to derive $r(t) = c(t) \circledast \frac{1}{2} h_b(t, \tau)$?
Consider a linear time-variant channel. The transmitted signal is $x(t)$, the channel impulse response is $h(t, \tau)$, and the received signal is $y(t)$. Then
$$ y(t) = \int_{-\infty}^\infty x(\tau) ...
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0answers
20 views
What is the signal processing's interpretation of $H_2$ space?
It is well known throughout signal processing community that $L_2$ space over some domain on the real line consists the set of finite energy signals $\|f(t)\|_2<\infty$
Is there a similar ...
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0answers
35 views
Autocorrelation function of two signals
I have that according data:
Two Wide sense stationary random function $X(t)$ and $Y(t)$ with $E[x]=E[y]=0$,
$Rx(t)=Ry(t)=R(t)$, $Z(t)=aX(t)+bY(t)$, $a,b$ real numbers
and I have to find the $R_z(t)$. ...
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votes
1answer
1k views
What is the difference between continuous, discrete, analog and digital signal?
It's my first time studying DSP and I've faced a problem finding a convenient definition.
Are the following definitions correct? And if so why there are some resources defining it in other terms such ...
3
votes
4answers
175 views
Relation between curve fitting and filtering
Before I ask the question: I am from mechanical background and would appreciate a detailed answer.
Generally, for automobiles, I am trying to understand the following:
Given, say $1\;\mathrm{sec}$ ...
0
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0answers
22 views
ZOH and FOH for discretization [duplicate]
Pretty new to this topic, But i was reading on various discretization methods, read somewhere about ZOH and FOH. but when i tried to read about more about them FOH. It's actually a reconstruction ...
0
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0answers
21 views
Windowing for Accelerometer Data in MATLAB
I'm working with some accelerometer data and it has been suggested that I do some windowing for isolating different events in the signal. Unlike most things, windowing is poorly documented in MATLAB ...
1
vote
1answer
80 views
Convolving a discrete time sequence with a continuous-time filter?
I am a newbie to DSP, and have what seems to me a fundamental question.
I have a discrete-time sequence $g[n]$ of length $N$. I am supposed to pass this signal through a root-raised cosine filter $...
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1answer
61 views
Normalized autocorrelation of a sum of two signals
I obtained the autocorrelation function of a sum of two signals:
as
but I want to know what is the normalized autocorrelation of above equation?
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3answers
146 views
Identifying steps in walking accelerometer
I have some recorded walking data from an android phone and want to determine when someones foot hits the ground using the acceleration data. I'm making an assumption here that the person will "bob" ...
0
votes
1answer
74 views
Energy of $\text{sinc}^2(kt)$ function multiplied by variable
I know how to determine the energy of $\text{sinc}^2(kt)$, but how does this change when I need to find the energy of $(kt)\cdot \text{sinc}^2(kt)$.
If the $(kt)$ in front is squared (in energy ...
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votes
1answer
62 views
PSD of a sum of two stationary real signals
I have 4 signals ($w_1(t),w_2(t),u_1(t),u_2(t)$ of which I know the power spectral densities (PSDs) $S_{w_1,w_1}(\omega),S_{w_2,w_2}(\omega),S_{u_1,u_1}(\omega),S_{u_2,u_2}(\omega)$ and the cross PSD $...
0
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1answer
36 views
What is the link between equation of a continuous signal versus equation of its sampled form?
I have just started DSP self-learning. I am a little confused by this 'end of the chapter' exercise question from Chapter 2 of "Understanding Digital signal processing" 3rd edition by Richard G. Lyons....
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1answer
46 views
Is calculus background a must for learn DSP? [closed]
I'm beginner in DSP and in the literature some Authors suggest Analog (Continuous) Signal Processing a prerequisite for learn DSP. But it demands calculus background, that I do not have. Is calculus ...
0
votes
1answer
165 views
Sampling signal after root raised cosine
I am generating series of 1 and 0. then pulse shaped them with root raised cosine and after than deciding to do match filtering and recovering the bits however it turns out that I am not getting the ...
0
votes
1answer
17 views
Relating phase shift to the ROL/ROR operations
Is phase-shifting in continuous-time analogous to the rotate-left (ROL) and rotate-right (ROR) operations in discrete-time?
1
vote
1answer
34 views
Graph of $[u(\tau)-u(\tau-4)]\cdot[u(t-\tau)-u(t-\tau-4)]$
I'm trying to visualize what would the following signal be like
$$[u(\tau)-u(\tau-4)]\cdot[u(t-\tau)-u(t-\tau-4)]$$
Consider that $\tau$ is the independent variable here, $t$ is the shift variable.
...
1
vote
1answer
37 views
Help in sketching a CT signal with discontinuities
This is the Original signal:
And I'm supposed to sketch
$[x(t) + x(-t)] .u(t)$
I know that unit step signal will make the signal starts from 0 to $+\infty$
My problem is at key point (0) and key ...
0
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0answers
71 views
How do we find the Power Spectrum Density (PSD) and which data type is valid for that?
I want a simple explanation on how to find PSD and which type of data (in which units, I mean) can be used for doing so.
If found similar interesting questions 1 & 2 and some on Mathworks, like ...
3
votes
1answer
78 views
How to do continuous signal processing (i.e without windowing)?
I'm working in speech recognition research, and I wonder if there is a way to analyse sound just like how ears do (i.e. without windowing), so for example to take some feature continuously with an ...
1
vote
1answer
35 views
Transmit power of non-orthogonal FDM
It is known that the total power of an OFDM signal equals to the sum of the powers on each individual subcarriers. I am a bit puzzled by the total transmit power of a generalized FDM system if ...
3
votes
1answer
50 views
Envelop detection with low sample rate?
I have a signal up to $3\textrm{ MHz}$. The ADC that sample it has a rate of $1.5\mu s$. So a full $T$ of the signal is $0.3\mu s$, and I can only sample each $1.5\mu s$. It sounds not enough, but I ...
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votes
1answer
235 views
When does the convolution of $2$ signals equals zero?
For example, how can I determine if the convolution of $x(t)$ with $y(t)$ is equal to $0$?
0
votes
1answer
27 views
Behaviour of the poles in transfer function $H(s)$, given system properties
If a linear system is causal and its impulse response is an energy signal. What's the behaviour of the poles of $s$-domain transfer function $H(s)$?
4
votes
2answers
245 views
Special case: Band-limited in time domain and band-limited in frequency domain
I know except for some special cases, aliasing is unavoidable. Assume we time-limit a function, $f(t)$, so that it is zero outside an interval say $[0,T]$ to form $y(t)$. Then, in the frequency domain,...
0
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0answers
57 views
3D wiggle plot for an analytic signal: Heyser corkscrew/spiral
Just reading The Analytic Impulse, A. Duncan, 1988, I met the name "Heyser corkscrew" for the first time in my DSP life, for a cisoid.
This representation is quite common for analytic signals, but ...
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2answers
50 views
How do we actually obtain samples to form discrete time samples? [closed]
I'm in my second week of an online DSP class and I'm still kinda lost on some of the concepts of what we are actually doing. I'm hoping you guys can help clear up my understanding. Please forgive me ...
