Anything related to convolution, its properties and applications. Convolution is the mathematical operation which is used to model the time-domain I/O relationship of linear time-invariant initially-at-rest systems.

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Convolution with sinusoids using convolution theorem

y(t)= h(t)*x(t) where h(t) is a decaying exponential and x(t)= sin(5t) u(t). Find y(t) using convolution theorem. I'm confused about the sine wave. If i write sinusoid in exponential form then I get ...
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32 views

Unit input response - LTI sysem

Let S1 and S2 be 2 LTI systems with responses to the unit impulse given by \$g_1(t)\$ and \$g_2(t)\$.Consider that we associate S1 and S2 .Knowing that \$g_1(t)=e^{-t}u(t)\$ (u is the heavside ...
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82 views

Proof: A strictly bandlimited signal must also be a signal of infinite time duration [duplicate]

How can I show that a bandlimited signal is also of infinite time duration? I know it has to do with Fourier transforms and convolution but I'm not sure how to actually prove it. I also know that the ...
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33 views

Channel simulation using convolution

I have to simulate channel noise (cable in my case), I have voltage characteristics of cable with me and I'm using convolution with incoming data to get the amplitude response. I also have forward ...
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0answers
103 views

Convolution in Matlab of transfer function

My problem is find the output to U(t+1)-U(t-1) with Matlab given the transfer function H(s). I know that I should be able to find the output to any input of an LTI system when given H(s), so I tried ...
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1answer
248 views

How does this Matlab code work?

I came across this uncommented Matlab code except for the header: ...
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54 views

wrong answer for convolution with \$ e^{-t}\delta (t) \$

I am trying to do convolution of a function \$ x(t)\$ with \$e^{-t}\delta(t)\$ Here are the steps I followed: \$ x(t)e^{-t}\delta(t) = \int x(\tau)e^{t+\tau}\delta(t-\tau)d\tau =e^t\int ...
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2answers
246 views

How to find the steady-state response from the impulse response

If we have an impulse response of a circuit which is u(t) and if one has the input and wants to find the output, we use convolution of the input and the impulse response to find the output, that is to ...
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1answer
56 views

finding out the bandwidth of m(t)*m(t) if the bandwidth of m(t) is a known quantity

m(t)*m(t) in time domain is equivalent to the convolution of m(w) and m(w) in frequency domain.Thus if the bandwidth of m(t) is a known quantity then how is the bandwidth of m(t)*m(t) is determined?
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132 views

What is the bandwidth of an imaginary convolution?

I am trying to figure out the bandwidth of \$f_1f_2\$, where \$f_1 = sinc^2(3t)\$ and \$f_2 = sin(100t)\$. So when I take the Fourier Transform, I can rewrite the equation as such: \$F(\omega) ...
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1answer
77 views

How to apply fourier transform to \$0.5^n u(n)\$

I'm working in a signals class for continuous signals, and we have this problem shown above. I have tried using this function \$f_1*f_2 = F_1 * F_2\$, where I'm assuming this means multiplication of ...
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4answers
124 views

Convolution Equation Help

I'm currently working through some convolution examples and I'm unsure of something. The question is given as: Consider the input \$\ x(n) = u(n) \$ and the impulse response \$\ h(n) = (0.5)^n ...
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1answer
78 views

Finding Impulse Response for System?

I have an LTI system with input and output related as per below: $$ y(t) = \int_{-\infty}^t \! x(T-2)e^{-(t-T)} \, \mathrm{d}T $$ and I need to find \$h(t)\$. I am familiar with two methods of ...
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3answers
1k views

Convolution perfomed by an analog circuit

As a Electronic Engineering student I have a fair knowledge about convolution and DSP. But, I was wondering if it is possible to perform a convolution only using analog circuit (without memory)? And ...
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2answers
225 views

Termination of a convolutional encoder vs. state register reset

Usually, when designing a convolutional encoder for a transmitter, some sort of termination mechanism is applied to drive the encoder back to its zero-state after a message was transmitted. This is ...
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5answers
4k views

How to implement a self tuning PID-like Controller

I am trying to write a micro-controller program for controlling temperature in a system with the following characteristics: output can only be On or Off, with fixed cycle frequencies (~2-10 per ...
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1answer
344 views

Using impulse response to control the system

This post by Olin Lathrop is rather inspiring. The system response is the convolution of the control input with this impulse response, computed every control sample, which is every 500 ms in ...