Questions tagged [convolution]

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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48 views

Change of variable from t to \$\tau\$ during convolution

I am not able to understand that in the standard convolution formula how we can change the variable from t to \$\tau\$. $$\int{x(\tau)\cdot h(t-\tau)d\tau }$$ Isn't this incorrect mathematically?
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25 views

What is the time axis array after we convolve two functions in Matlab after sampling it with frequency \$f_s\$?

Suppose we have a continuous time function \$f(t)\$ , we sample it at frequency \$f_s, (t = -5:1/f_s:5)\$, and store it in an array \$a\$ in Matlab. Now we convolve it with itself using \$b = conv(a,a)...
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37 views

Contradiction while using the convolution sum for a non-LTI system

In a recent quiz, we were given the following problem: The cascaded LTI systems \$\mathcal{T}_1\$ and \$\mathcal{T}_2\$ respectively have impulse responses \$h_1 \lbrack n \rbrack = \delta\lbrack n ...
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1answer
43 views

Determine the impulse response of the following discrete system

I'm not sure how they got the answer (provided below) for the following discrete system y[n] = x[n]- 2x[n-2]+ x[n-3]- 3x[n-4] the answer is given as .... h[n] = [1 0 -2 1 -3] why is this? any help ...
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153 views

Brute-force convolution reverb in FPGA

I'm completely new to the world of FPGAs, and would like to get a sense of what is possible to achieve, and since I happen to have an interest in convolution reverb algorithms, I will use that example....
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1answer
30 views

How to construct a LTI system with a specific impulse response function, say \$h(t) = \delta '(t)\$?

I want to ask the question on a generic basis, but using \$h(t) = \delta '(t)\$ as my example. I have Mathematical knowledge on the LTI system, but no hands on experience. In real life, how can we ...
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55 views

Define LTI system from a single input output pair

I am currently studying signals and systems, and am learning about LTI systems right now. I know any LTI system whose impulse response is known can be completely defined through the use of the ...
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1answer
37 views

What is the transfer function of an ideal buffer in time domain?

Convolution is is defined as the integral of the product of the two functions after one is reversed and shifted. And in a system where its transfer function is g and the input is f, the output is the ...
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1answer
692 views

2D convolution on 32x32 grayscale image on FPGA using verilog for inference of CNN

Hi I am new to the world of convolutional neural networks and would like to implement a 2D convolution operation using the sliding window approach on a xilinx FPGA. The input to the image is a 32x32 ...
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1answer
574 views

Square wave autocorrelation integral

Given the following square wave signal g(t) : I'm trying to find the \$R(\tau)\$ of this signal, but I'm confused about how to solve the integral. In the signal above, the red square wave is the ...
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1answer
79 views

convolution of \$ e^{-t} \$ and 1-t

I cannot solve the convolution based on \$h= e^{-t}\$ for \$ t\ge0 \$ and \$u(t) = 1-t \$ when \$ 0 \le t \le1 \$. Every time I try I keep getting a factor with \$ te^{-t} \$ whilst the answer shows: ...
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83 views

Convolution with two unbounded signals

So I have a convolution problem. I have two signals: I need to find the output, y(t), through graphical convolution. So I set the convolution integral up like this: $$ \int h(\tau)*x(t-\tau)d\tau $$...
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1answer
88 views

Fourier Transform - convolution theorem

I have been studying the Fourier Transform and the convolution theorem is not clear to me. Sometimes, I see this: But other times I see this: Which one is correct? Where is this constant factor ...
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1answer
389 views

Multiplication and convolution

We know that squaring a signal doubles its bandwidth. Can you please justify this case in time domain for non sinusoid signals,say Rect(t/T)? On squaring the signal i don't see any changes in tine ...
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119 views

Convolution integral for LTI system

We know that any continuous time signal can be expressed as follows: $$x(t)=\int_{-\infty}^\infty x(τ)δ(t-τ)dτ$$ I came across a certain relation regarding linear time invariant systems . Using $$x(t)...
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616 views

Graphical CT Convolution

The question asks to compute the convolution of x(t) and h(t). While I know how to do this mathematically, using a combination of derivatives and integrals, I don't know how to convolve the two using ...
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1answer
416 views

How to find the Nyquist rate

I have the following signals and their Fourier transforms: \$x(t)\$ and \$r(t)\$. The signals are limited such that \$X(e^{j\omega}) = 0\$ for \$|\omega| > \Omega\$ and \$R(e^{j\omega}) = 0\$ for \$...
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105 views

Problem about the properties of convolution

I have a difficulty to understand the convolution integral itself. Can anyone please explain what are the differences between the following 3 convolutions? x(t)*h(t), x(-t)*h(t), x(-t)*h(-t). Thanks....
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388 views

Derivation of convolution integral from the discrete convolution sum?

I was wondering if anyone can provide a derivation of the continuous-time convolution integral $$y(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)d\tau$$ from the discrete-time convolution sum $$y[n]=\sum_{...
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2answers
29 views

Invertiblity of LTI System

Can any one please explain me how the convolution of the following leads to delta(t). To convolve these to function i considered delta(t+T) as x(t) and delta(t-T) as the response. Then these ...
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2answers
200 views

Analog circuit for multiplying in the frequency domain [duplicate]

I have an idea I want to experiment with - doing boolean logic with analog (OFDM) signals. Each frequency component represents a different 'bit'. A key factor is performing the AND operation. I would ...
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3answers
944 views

Concept of convolution

I am having trouble understanding the concept of convolution. I get the mathematical idea behind it. I am able to evaluate that the convolution of the following problem is $$f*g(t) = {0,\ \ t <= -...
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1answer
405 views

How to derive the solutions of the Differential Equations when using convolution?

I am currently learning convolution (which is not the easiest topic for sure). Just as by many fields in electronics also here are differential equations involved. With this (what I have seen until ...
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1answer
44 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
2k 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) y(t)=...
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4answers
26k 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
99 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
45 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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1answer
1k 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
539 views

How does this Matlab code work?

I came across this uncommented Matlab code except for the header: ...
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2answers
65 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 x(\tau)e^{\...
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2answers
2k 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
133 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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444 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
273 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
156 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 u(n)...
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1answer
93 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
4k 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
625 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
13k 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 hour) ...
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1answer
458 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 ...