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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24 views

Finding Filtered Output using Convolution property of Continuous Fourier Transform

why the derivative of u[t] is delta[t] ? also I don't understand why the sin term disappeared once the derivative is taken.
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1answer
97 views

Effect on signal bandwidth due to multiplication?

Recently I came across an statement which says, If signal m(t) has bandwidth B then pow(m(t),n) will have bandwith nB. To prove it mathematically I startted with, Let n=2, y(t)= m(t)xm(t) ...
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2answers
112 views

Checking whether the system is linear or non linear

Consider this system equation y(t)=x(t)*cos(3t). where,x(t)=input. Using the superposition theorem, we can prove that the system is linear. For input x1(t), the output is y1(t)=x1(t)*cos(3t). For ...
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2answers
53 views

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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1answer
35 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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189 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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1answer
409 views

How does this Matlab code work?

I came across this uncommented Matlab code except for the header: ...
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2answers
56 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
700 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
68 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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2answers
227 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
87 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
129 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
84 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
2k 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
287 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
6k 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
371 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 ...