Questions tagged [continuous-signals]

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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48 views

Are there any signals with brickwall autocorrelation?

Are there any signals whose autocorrelation $R(\tau)$ has the following form? Assuming $\tau_c > 0$ and $R_0 > 0$ a constant, $$R(\tau) = \begin{cases}R_0, \text{ for $|\tau| < \tau_c$} \\ 0,...
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59 views

Reason of effect of continuity and discreteness on periodicity of signal?

We know that a sine signal in continuous time is a periodic signal with a period $2\pi$ whereas the same sine signal in discrete time is aperiodic. My question is how changing just a type of signal (...
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1answer
73 views

response of LTI system to a Random Input Signal

what is LTI filter? what is the output when x(t) is input? let x(t) be the input signal to the system and y(t) denote the output signal. The output of the system may be expressed in terms of ...
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222 views

A question on Fourier Series and the frequency of the sinusoids

On studying about Fourier series, I encountered 2 doubts: How is it that a non-periodic function has a Fourier series? When expressing a periodic function as summation of sinusoids, why is the ...
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3answers
134 views

How does real-time signal processing work when the signal we deal with is assumed to be known for all times?

One thing that never sat right with me after my signal processing course is that in order to do signal processing, we must know the entire signal $x(t)$. For instance, I cannot take the Fourier or Z ...
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2answers
212 views

DC value of $x(t)=\frac{1}{t}$

Is it possible to calculate the DC value of signals with undefinable area? More specificaly, in the case of $x(t)=\frac{1}{t}$. $\int\limits_{-\infty}^\infty\frac1t \, \mathrm dt$ does not converge. ...
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1answer
163 views

Effective Nyquist frequency / signal resolution for overlapping time averaged signal samples

Say that I have a continuous signal. If I sample the signal at sampling rate f_sample, then the highest signal frequency that I can resolve without worrying about ...
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2answers
48 views

Is there such a thing as a continuous phase BPSK?

My knowledge of signals and signal processing is limited, so I apologize in advance for my naïve and possibly confusing question. In the case of BFSK, the frequencies are altered to represent the ...
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1answer
103 views

Is there an example of an infinite signal? [closed]

In the real world, Is there an example of an infinite signal?
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1answer
286 views

Fourier Series Representation of Continuous-Time Periodic Signals [closed]

As a novice in signal processing, I have been going through Signals & Systems by Oppenheim to try and understand how continuous time periodic signals are represented by Fourier series coefficients....
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1answer
300 views

How can I get the continuous-time transfer function coefficients (or poles and zeros) from the corresponding discrete-time TF and vice versa?

Let's say I have a continuous time transfer function which I know its numerator coefficients $(B^c = [b^c_m, ..., b^c_1, b^c_0])$ and denominator coefficients $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
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1answer
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Can a Fourier Transform exist even if the j$\omega$ axis is not in the Region of Convergence in it's Laplace Transform

A couple of confusions have been occurred. The Signal I'm considering is f(t) = sin(t)*u(t) Fourier Transform of it can be derived. $-i \pi (\delta (\omega -1)-\delta (\omega +1))$ According to my ...
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59 views

Simple problem regarding rectangular pulse shifting

So i have the following rectangular pulse: $$h(t)=\begin{cases} 1 & 0<t< T \\ 0 & \text{otherwise} \end{cases}$$ Now, i am supposed to create $h(T-t)$, and the ...
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1answer
74 views

Bandwidth of the Derivative of a Message [duplicate]

If I have a message signal $m(t)$ and it has a bandwidth $B$. I know that the bandwidth of $m^N(t)$ is $NB$. But what is the bandwidth of $\frac{d m(t)}{dt}$? Thanks!
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1answer
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Quite confused with Fourier Analysis results

So I'm meant to show how the DFT can find the frequencies, and respective amplitudes, associated to some data. And I have this data set from the curve $$ f(t) = 1 + 2\cos(2\pi t) + 4\cos(4\pi t) $$ ...
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1answer
93 views

Given a plot of both the magnitude $|H(\omega)|$ and its angle, How can you find the $H(\omega)$?

I'm specifically trying to use an inverse Fourier Transform to find $h(t)$, but I'm finding it difficult to get $H(\omega)$ in the first place. I'm under the impression from my textbook that $H(\...
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1answer
60 views

How to find the coefficients of the following differential equation

An arbitrary signal $v(t)$ pass through the following system, $w'(t) + 5 w(t) = v'''(t) + 320v''(t) + 40 v' (t) + 40v(t)$ How to determine the coefficients of the following differential equation, ...
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1answer
72 views

How to do convolution in Fourier Series?

Two signals are given to me : $$x(t)=\cos(4\pi t)$$ $$y(t)=\sin(4\pi t)$$ I have founded their coefficients as follows: $$a_k = a_1=a_{-1}=\frac{1}{2} $$ $$b_k = b_1=b^*_{-1}=\frac{1}{2j}...
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Intuition behind commutativity of convolution in LTI systems

Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system? If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
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2answers
129 views

How will I draw the following signal?

I want to know that if I have any signal given how will I draw it according to the following equation $$x(t-1)-1/2$$ what will be the role of $1/2$ when drawing the new signal?
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1answer
181 views

Does the Fourier series coefficient of AC components remains same if DC component is subtracted form the given signal?

Suppose a signal is defined by $ x(t)= \begin{cases} t & 0\leq t \leq 1 \\ 2-t & 1\leq t\leq 2 \\ \end{cases} $ Since $x(t)$ has even symmetry, I can calculate fourier coefficient as $$ a_n = ...
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1answer
81 views

Energy of compressed signals

I have tried a code to compress a signal using Compressed Sensing(CS). The input signal is $x$ and the compressed signal $y$ is given by : $y=Φ*x$ where $Φ$ is the sensing matrix. I have used ...
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1answer
34 views

Frequency component not filtered properly

Are frequency components other than wanted signal present in the output? If yes then why does it not disturb the original signal? I think all practical filter responses are not ideal, so all frequency ...
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109 views

Linearity of the given system

I am given the following system and I am checking the additive property: $$y(t)=x(e^t)$$ where $y(t)$ is the output and $x(t)$ is the input given to the system. Now this is what I did so far: \...
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1answer
34 views

Finding Harmonics Analytically

I've always obtained harmonics using simulation and never by hand. My question is how can someone find the harmonics for a signal (say a square wave) by hand? What equations come in handy for finding ...
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2answers
717 views

How to calculate the power of a finite length signal?

I am confused with these concepts. If the signal is expressed as r(t), I know the power of the signal is given by: But if the the length of signal T is finite and cannot approach infinity, how can I ...
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5answers
2k views

Difference Between Dirac delta and unit impulse function

The definition of Dirac delta function states that it gives a value of $\infty$ at t=0 and 0 elsewhere. But, the definition of unit impulse function states that it gives a value of 1 at t=0 and 0 ...
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1answer
30 views

identify equilibrium region after large transient

I am looking at data from a mechanical system under an unsteady load. I'm trying to find the simplest way to identify the portion of the signal once the system reaches its new equilibrium. Here's a ...
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3answers
1k views

What is the magnitude of the impulse function at t=0?

The unit impulse function, in a few textbooks that I have referred, has a value of 0 at t≠0 , and an area of unity (1). The height of the impulse function also tends to infinity at t=0. But since it's ...
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1answer
142 views

Show that any continuous-time signal $x(t)$ can be represented as $x(t)= x_e(t) + x_o(t)$

Show that any continuous-time signal $x(t)$ can be represented as $x(t)= x_e(t) + x_o(t)$ where $x_e(t) =\frac{1}{2}[x(t) + x(-t)]$ and $x_o(t) = \frac{1}{2} [x(t) − x(-t)]$ are even and odd ...
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1answer
916 views

Negative exponential signal's energy and power

Earlier I have dealt with exponential functions multiplied with unit step function. But, energy and power of exponential function alone comes out to be infinite when I put limits of the integrals to ...
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1answer
356 views

Properties of Invertible System [closed]

I have come to the understanding that if these three properties hold true then the system is a memory system: 1) Time Scaling: $$y(t)=x(2t)\,,$$ 2) Time Shifting: $$y(t)=x(t+2)\,,$$ 3) ...
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2answers
247 views

Adding/subtracting sinusoids

I'm trying to calculate resultant function from adding two sinusoids: $9\sin(\omega t + \tfrac{\pi}{3})$ and $-7\sin(\omega t - \tfrac{3\pi}{8})$ The correct answer is $14.38\sin(\omega t + 1.444)$, ...
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1answer
515 views

Bridging CTFT and DTFT for a cosine

I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT. For example if I take a basic example: $$\begin{aligned} x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
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1answer
28 views

Conversion of airflow signal into 1-D as a input for CNN [closed]

Trying to detect apnea from airflow signal. I have 100 files of the patient each file contains at least 8 hours of data and sampling rate is 32 Hz. How to prepare my dataset which is used as an input ...
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1answer
103 views

Separating two frequency component

How can we separate two frequency component when they get mixed means when signal get mixed with noise how receiver can judge which part is signal and which is noise ?
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3answers
420 views

Is $\arctan(t)$ an energy or power signal?

Is the function $\arctan(t)$ an energy or power signal? I've tried working out the integrals for energy and power but I get stuck on both.
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1answer
755 views

How can I determine the order of filter?

This is my first study about signal analysing. I'm very confused about filter order. My problem is how can I know whether its 12-th order, or 2nd order like the book says so? I already knew that slope ...
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2answers
131 views

Reconciling Continuous and Discrete Complex Domains

Having taken some courses in Systems and Stability dealing mostly with continuous time signals, I am accustomed to thinking about the Laplace and Fourier transforms dealing with complex and pure ...
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2answers
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Is there a specific preferred order of operation on signals?

Basic Signal Operations Performed on dependent variables-- The periodicity of the signal is varied by modifying the horizontal axis values, while the amplitude or the strength remains constant. These ...
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1answer
150 views

PN code generation

Can we generate PN codes (maximal length sequence) using this technique in Matlab where L is the PN length? pn=2*(rand(1,L)>0.5)-1 If yes, why?
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2answers
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Understanding the frequency domain [duplicate]

I'm trying to understand what frequency domain is. I found general explanations on the Internet, for example: frequency-domain graph shows how much of the signal lies within each given frequency band ...
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1answer
241 views

Determining sampling rate for signal reconstruction

I want to know how to determine the signal sampling rate required to reconstruct electrical signals whose frequency components are unknown, such as, for example, signals of charge/discharge voltage on ...
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0answers
30 views

Multiplicative Input-Dependent Noise [closed]

This question might not be exactly suitable to the question format of StackExchange but I couldn't find a better way to put it forward. Lately, I have been dealing with ECG Signal processing and due ...
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2answers
267 views

How to convert a sound signal function to wave file? [closed]

I am new to understanding sound signals. A sound signal, as far as I know, is a real function of time $x:[0,\infty)\to \Bbb R$. For example, $x(t)=\sin(t)$ is a sinusoidal signal. What is $x(t)$. For ...
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1answer
156 views

methods of crest factor minimization

i am studying the methodes CF minimization. and have a doubt. in each methods there are steps with DFT and IDFT or like this FFT and IFFT. Everyone provides the fact, that they use DFT and IDFT for ...
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1answer
115 views

Homodyne concept of receiver

I would like to understand a concept of homodyne architecture of I-Q demodulator and how the wave looks like at each step. It is a bandpass Signal: Step 1: multiplication with cos and sin wave. I ...
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2answers
75 views

Fourier series of $cos(\omega_0 t)$ in continuous time

Can any one please help me with understanding how we can calculate the Fourier series of Cos(w0t) using the formula: I saw that they did the following calculus, but I Don't really understand how we ...
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1answer
1k views

Converting Time Shift to Phase Shift

I have just started taking signal & systems lessons and here is my question: If we say that x0(t) = A.cos(w0t). (a cosine signal with zero phase shift, w0 ...
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0answers
25 views

How does this digital signal controlling a switch in the circuit affect the output voltage?

Suppose you have a circuit which has the input signal $x(t)=2\sin (ω_ot + \pi/6)$. The switch in the circuit is controlled with a digital signal of the form: $s(t)=\sum_{k=-\infty}^{+\infty} (u(t+ε-...

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