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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Minimum number of points to specify a sine wave with a given accuracy

I am generating a sine wave from a DAC at a constant frequency. If each full cycle is specified by N data points what is the relationship between the accuracy of the rendered sine wave and N? N=1 ...
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Parseval's theorem

A question asks for the energy and power of the following signal; $$x[n]=\text{sinc}\left(\frac{n}{5}\right)$$ given that $$\Omega_c=\pi/5$$ Energy is $$E=\sum_{n=-\infty}^{\infty}{\left |\text{sinc}\...
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Mathematical equation for 'Relative and absolute power' of a signal

Can somebody provide me with the mathematical equation to calculate relative and absolute power of a signal (continuous) from FFT.
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Fourier Transform & Convolution to get response - confused

in the past couple of years I've always been using Laplace transform for system responses, but today tried to do it with Fourier transform and failed. What am I doing wrong? If we have a signal $x(t) ...
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1answer
532 views

2-PAM or 4-PAM if I want to send data as fast as possible?

I would like to ask if I should use 2-PAM modulation or 4-PAM modulationif I want to send data as fast as possible given that in each case I have the same frequency spectrum available.
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981 views

understanding time constant meaning in signal processing

from my DSP book,i am reading that exponential signal $x(t)=e^{-a*t}$ has some time constant value $c$ let say if $e^{-a*t}=e^{-t/c}$ which means that $a=1/c$,but i want to understand what is ...
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680 views

Autocorrelation of a stochastic process which is a sum

Let's say that a stochastic process is defined as $$X(t) = \sum_{n = -\infty}^{+\infty} X_n * f(t- nT)$$ where $X_n$ is the $n$-th symbol among independent random symbols. I have proved that $\...
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Deriving the Fourier transform of cosine and sine

In this answer, Jim Clay writes: ... use the fact that $\mathcal F\{\cos(x)\} = \frac{\delta(w - 1) + \delta(w + 1)}{2}$ ... The expression above is not too different from $\mathcal F\{{\cos(2\pi ...
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Find another cosine y(t), whose frequency is as close as possible to that of x(t),

I am going to be straight forward and say this is one of the problem sheets and I am stuck on one of the questions. I already know the answer as I have been given them but I am trying to work ...
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For an LTI system, why does the Fourier transform of the impulse response give the frequency response?

I know that for a given system, the Fourier transform of its impulse response gives its frequency response. I want to find where this property comes from, but haven't been able to find if it's a ...
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1answer
192 views

Detect signals degree of imbalance

I have got this question: let's suppose that I have three signals, representative of the same variable, but taken on three different component of a same device; in my case, three load signals, ...
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Sum of Sine and Cosine with Random Phase as LTI System

I have the following system: Where $ {H}_{1} \left( f \right) = {H}_{2} \left( f \right) $ and $ \theta \sim U[0, 2\pi]$ independent of any other factor in the system. Given the input is identical, ...
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What is the opposite of sampling called?

We call the conversion from a continuous time signal $f(t)$ to a discrete time signal $f_s[k]$ "sampling". Is there a name for the reverse operation, i.e. creating a continuous time signal from a ...
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1answer
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Confusion with regards to STFT and MFCCs

I'm wondering if someone can clear the following up for me as I'm having a difficult time understanding the concept. I'm looking to implement and learn about the processes and uses using short-time ...
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2answers
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Why does pulse-width modulation work?

When we apply pulse-width modulation (PWM) on controlling the brightness of a LED or the speed of a DC motor, is it the lag in our eyes that is responsible for the feeling of a continuous powering or ...
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How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
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What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: ...
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1answer
804 views

Signal approximation using linear combination of functions

How I can approximate the signal $x(t)=0.001\,t^3 \exp(-0.1t)$ in the interval $[0,100]$ using a linear combination of the following functions: $f_1(t)=A_1$ $f_2(t)=A_2\cos(0.05t)$ $f_3(t)=A_3\cos(...
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Mathematically Inclined Signal and Systems / Signal Processing Book Recommendations

I'm an electronics engineering student with high inclination to analysis and pure mathematics. I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal ...
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1answer
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How to derive stability of analogue and digital systems

I'm trying to find out why digital systems are stable iff poles oh their transfer function are inside the unit circle (or are there any others conditions?). I understand analogous systems are stable ...
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2answers
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Main differences to take into account between continuous and discrete time signals

I started studying DSP and the first things that came out were the differences between continuous and discrete time signals. So, I was wondering if I understood well these concepts before I keep going ...
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1answer
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Discretizing a continuous time signal

This may be a very straightforward question but I've been trying to understand this for a long time and can't wrap my head around it. How would one go about discretizing the following continuous time ...
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Simulink continuous to discrete question

I'm new to Matlab/Simulink and would like to convert the continuous system below to discrete for eventual conversion to C code. Matlab has a c2d function, but I don't know how to apply it to a ...
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1answer
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Sampled signal reconstruction using matlab

I have a wav file recorded from my smartphone's mic, and I want to reconstruct the sampled signal and plot the reconstructed signal. After some research and search, I was able to get the following ...
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939 views

One Source Signal Separation

I have a wav file which is gained by playing 2 different wav files with 2 speakers and recorded with mic. If I want to get one of the original signals using the resulting wav file and the other ...
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1answer
437 views

In a periodic square wave, how to change in a particular condition?

The periodic square wave, $$x(t) = 1, |t| < T_1 \\ x(t) = 0, T_1 < |t| < T/2$$ What I wonder is .. (1) If $T_1$ is constant and $T \to \infty$, is x(t) a constant function? (2) If $T_1$ is ...
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A simpler method or more descriptive answer to the Fourier Transform

I'm trying to do a CT Fourier Transform of these two signals $$x_1(t)=e^{−a(t−1)} \cdot u(t−1)$$ and $$x_2(t)=e^{−a(t−1)} \cdot u(t)$$ Where $a$ is any real number, and $u(t)$ is the unit step ...
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394 views

How to model/estimate channel in discrete time with different sampling time?

I want to estimate a channel based on LTE 3GPP EVA with given power delay profile (set of average power and delay of channel taps). ...
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1answer
52 views

Estimate input from measuring only RC filtered input

I am interested in knowing the step amplitude on a signal which can only be measured through a hardware RC filter. The measured signal follows this formula: $$ V(t) = V_0 \left(1 - e^{-\frac{t}{RC}}\...
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2answers
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Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ...
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1answer
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How do I use the step and ramp functions to create a specific signal?

I am trying to figure out how to use the step $u(t)$ and ramp $r(t)$ functions to create the function $f(t)$ below: $f(x) = \begin{cases}0 & \text{for } t < 0 \\ t & \text{for }-1 \lt t \...
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3answers
856 views

creating a seamless signal / loop using interpolation

I'm trying to create a seamless loop using a "non-periodic" signal using interpolation to smooth out the beginning and the end but I'm still getting a click at the beginning when it loops and I listen ...
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1answer
816 views

Correct method for drawing waveforms

I need to draw waveforms for biometric data like ECG and EEG signals. When I have more samples than pixels at the X-axis, I need to draw a vertical line between the MIN and MAX sample-value for that ...
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1answer
306 views

Signal Processing using Fourier Transform

So I'm trying to understand how MRI machines work. I understand all the concepts of it, the parts, what they do, how the machine works, etc. The part I'm having trouble with is the fourier transform ...
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1answer
75 views

Need an Identity for CTFT Polynomial Raised to an Exponent

I need to the find the inverse continuous time Fourier transform for unitary angular frequency of the following signal: $e^{a\omega^2 - b\omega + c}$ where $a$ and $b$ and $c$ are real numbers and I ...
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1answer
160 views

Role of Kalman filter in nonlinear dynamics

I am quite interested to know the significance of using kalman filter,unscented kalman filter and extended kalman filter in chaos synchronization when infact the very basics of chaos synchronization(...
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12answers
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Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original ...
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Why do linear systems show sinusoidal fidelity?

I am looking for a proof for sinusoidal fidelity. In DSP we study a lot about linear systems. Linear systems are homogenous and additive. One more condition it satisifies is that if a signal is a sine ...
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880 views

determine two signals with a scale factor

Suppose I have 2 signals from function $f_1(x)$ and $f_2(x)$, respectively, and assume the sampling rate is above Nyquist frequency, so we can restore the underlying functions $f_1(x)$ and $f_2(x)$. ...
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1answer
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Why would I want to define a modulation index for each tone (DSB-FC)?

So the exercise is basically a signal $f(t)$ that is going to modulate the carrier $A\cos(\omega_ct)$ using a modulation index of $m=1$. I have to find $A$ and the power of the modulated signal: $$ f(...
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2answers
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What should the amplitude be when plotting 1-sided Amplitude Spectrum?

I have a continuous signal x(t) such that $x(t)=12cos(6\pi t)+6cos(24\pi t)+3cos(30 \pi t)$ and is asked to sketch a 1-sided Amplitude Spectrum of the signal x(t) if sampled above the minimum ...
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Alias frequency Formula

I'm taking a multimedia systems class in my MSc Computer Science, and I'm having some trouble understanding the formula for the alias frequency - this could stem from my misunderstanding of the alias ...
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2answers
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A signal containing no pure sinusoidal components

I'm trying to decipher what exactly this statement means. So if I have a signal which has no pure sinusoidal components, does that mean I can't decompose my signal completely into sine-waves which ...
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2answers
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What does it mean to combine signals coherently?

What does the expression 'combine signals coherently' imply?
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Does the inverse-CTFT exist for a dirac delta?

Does the inverse continuous time Fourier transform exist for a Dirac delta (A single causal/non-causal spike)?
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1answer
849 views

How to 'interpret' the Fourier Transform (specifically, of a convolution kernel)

As part of a homework assignment, I had to take the Fourier transform of the kernel I was using to convolve a signal. The kernel was a constant rectangular function, that was 1 within the square $(-1,...
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1answer
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When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?

Heads up, this is for homework. I never took a signals and systems course, so I'm behind on this stuff. I want to compute the convolution of two rectangular regions. I know the standard equation ...
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2answers
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How does shift and scaling inside of a function affect its Fourier Transform?

The properties aren't entirely clear to me, sorry for the basic question. I know the Fourier Transform of one function. Say, $\text{rect}(x,y) \Leftrightarrow \frac{\sin \pi u}{\pi u} \frac{\sin \...
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1answer
234 views

Is it possible to simplify the convolution integral if the functions are non-zero in disjoint areas? [duplicate]

Possible Duplicate: When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start? I have a function $f(x,y)$ and $h(x,y)$. $f(x,y)$ has a ...
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1answer
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Filter coefficients for colored noise Voss Algorithm

If I use a generic filter for generating colored noise like pink,brown,white then how do I modify this statement and how do I know what are the coefficients to be used in AR model for different noise....

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