# 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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### Impulse response of ideal filters

I am aware that an ideal low-pass filter in both continuous time and discrete time has a $\mathrm{sinc}$ impulse response. What would the impulse response of an ideal high-pass or band-pass filter ...
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### BIBO Stability and the convergence of the frequency response of a system

It is my understanding that an LTI system is BIBO stable if and only if its impulse response $h(t)$ is absolutely integrable. This also happens to be one of the Dirichlet conditions for the ...
581 views

### Fourier transform of even/odd parts of a complex signal

Why does Oppenheim state the following properties: \begin{align} \mathcal F\big\{x_e (t) \big\} &= \Re\big\{ X(j\omega) \big\}\\ \mathcal F\big\{x_o (t) \big\} &= j \Im\big\{ X(j\omega) \big\...
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### Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals

If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away? Suppose we are given the ...
614 views

### Periodicity of the discrete-time Fourier Transform

The DTFT of a sequence $x[n]$ can be written as $$X(e^{j\omega}) = \sum_{n = -\infty}^{\infty} x[n] e^{-j\omega n}.$$ Is the smallest (fundamental) period in frequency of the DTFT always $2\pi$? Or ...
51 views

### Echo effect on sinusoidal input: Intuition

I am currently reading about adding echo effects on signals. I was wondering if my understanding is correct. In the attached figure, the blue line represents the original signal and the red line is ...
143 views

### Causality as applied to capacitors

This question stems from a point of confusion that I still have about the causality, linearity, and time-invariance in LCCDEs. I wanted to use the capacitor as an example. Consider a capacitor with ...
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### why total energy of a finite duration continuous signal becomes infinite after sampling

If I have a continuous-time energy signal and multiply it with an impulse train, the frequency domain representation has infinite replicas. The total energy if we sum them up becomes infinite. What ...
706 views

### Minimum possible sampling frequency for continuous time signal

A continuous-time signal $x(t)$ has the magnitude spectrum $\lvert X(F)\rvert$ shown in Figure 6. The signal is sampled to obtain $x(n)$ using the sampling frequency $F_s$. Determine the minimum ...
899 views

### What is the product of Dirac Delta function and $t$? [closed]

$t\cdot \delta (t)$ Does it equal to zero? If so, how can we prove it?
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### Problem identifying the analytic expression of such determined signal

I came across this problem I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal. The teacher suggests that I should consider ...
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### How to convolve an arbitrary signal with a causal decaying exponential?

I need to simplify the following convolution $$x(t)\star [e^{-2t} u(t)]$$ where $u(t)$ is the unit step function. I'm very confused with this. Using the definition of convolution of continuous-time ...
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### Reconstruction of a signal using an ideal DAC

I think I was able to do part (a) correctly, but now am stuck on part (b). I don't know how to approach this part or what is the theory behind it. My MATLAB code is shown below. Please let me know if ...
252 views

### Impulse response rest conditions of LTI systems

Why the impulse response (initial) rest conditions are taken like $h(t)=0$ and $h'(t) =1$, if the order of differential equation is $2$.
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### How to generate colored Gaussian noise and adding it to a ODE system - Do I need Euler-Maruyama method?

In the tutorial, when white noise process is added to ordinary differential equations (ODE), the ODE becomes a stochastic process. Then the stochastic process needs to be solved using Euler Maruyama ...
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### Derivative of delta function

I've come across the below. Can you please help me understand the proof for this? $$\int_{-\infty}^{\infty}x(t)\delta'(t-2.5)dt=-\frac{dx(t)}{dt}{\Big |}_{t=2.5}$$
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### How to Generate White Gaussian Noise with Known PSD in MATLAB

I want to generate white Gaussian noise with known PSD. Using wgn I can generate noise with specific power (dBW) but I want to generate a white noise with constant or know PSD. Can anyone give me ...
550 views

### Question on convolution

I am stuck at question number 2.8 This is how I have gone about solving it: I have calculated $y(t)$ by convolving $x(t)$ with $h(t)$ using the fact that $x(t)$ convolved with an impulse at $t=t_0$ ...
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### Time invariance of a System

I have this small question about the time invariance of a system. Which is: If the current output is multiplied by the current input (see both are variables) will the system be time variant or time ...
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### whether the system is linear or not for the given problem

Given the system: $$y(t)=x(t+1)+x(t−1)$$ is the system linear? For a system to be a linear first it should satisfy zero input and zero output. How can we calculate output at 0 input if the system ...
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### Smoothing a Signal which contain White Noise

I'm trying to smooth a signal in order to reduce white noise as a result of changes in amplitude across sequential frames of an audio signal. I've been investigating using a moving average or ...
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While I was learning signal theory, I have come across different definitions for the unit step signal. For example. $u(t)=\begin{cases} 1 & t\geq0\\ 0 & t<0\\ \end{cases}$ $u(t)=\begin{... 1answer 140 views ### Overshoot computations not matching Take the following transfer function of a 3rd order system: $$H(s)=\dfrac{2.302~s+0.3548}{s^3+0.739~s^2+3.223~s+0.3548}$$ with poles: ... 1answer 274 views ### Frame overlapping I 'm reading the following article from NVIDIA which involves some audio processing a the beginning : link just here (part 3.2) I don't understand the following part : In practice, we use 520ms ... 1answer 68 views ### Trouble understanding an article about MFCC I'm willing to apply the same audio preparation that this article page 3. However, I don't understand the final part : ... 1answer 566 views ### Differential Equation and Transfer Function of Multiple Summer Integrator Block Diagram I've been working on this more than 5 hour, I know how to solve feedback, summer, but was not able to solve this one, I've tried to simplify it by choose A(i) to be the first output of first summer ... 0answers 217 views ### Software based synchronizing of multiple data streams/sensors with slightly differing sampling rates Situation: I try to synchronize the data streams of multiple sensors (ADXL372) of the same type but with different data output rates. The data sheet states all sensors should have the same sampling ... 1answer 568 views ### Measure the amount of drift in video and audio frames I setup a stereo system using 2 GoPro Hero Session Cameras, since I need a larger baseline than the one of the Dual Hero System. This unfortunately means the two cameras are not ... 1answer 92 views ### What is special about the frequency$\omega_0=\pi\$ that suddenly causes rate of oscillation decrease?

In Alan Oppenheim's book Signals and Systems a comparison is made between the properties of discrete-time and continuous-time complex exponential signals in section 1.3 pg. 26. Specifically it says: ...
Yesterday, during my exam, I had the following exercise: Given $$H(s) = \frac{1}{s^2+2s+4}$$ check if it's stable. which was supposed to be the hardest (since it was the last one). From my ...