Signals and Systems - Convolution

In summary, the conversation discusses the process of solving a convolution problem involving a signal x(n) and an unknown signal h(n). The solution involves determining the length of h(n) and using placeholder values to complete the convolution. It is important to remember to flip the final result.
  • #1
l46kok
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Homework Statement


http://img166.imageshack.us/img166/1162/untitledte2.jpg [Broken]


Homework Equations


Convolution

y[n] = x[n] * h[n]


The Attempt at a Solution



I've never done convolutions going backwards..

right off the bat, I know I'll noly have 2 terms in the convolution sum, because of x term, but I don't have a clue how to determine the h[n]. It is not possible to write a response y as a convolution between x and h because h is unknown.

Any ideas?
 
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  • #2
You know what signal x(n) is right? -- hint: what is the value of the digital delta function
You know how long h(n) is right? -- hint: Length of Conv = Length of x + length h -1

Put in place holders for the values of h and grind it out just like you were doing the convolution. It is the same idea as 2+x = 3 except that you have to add several values. Use two strips of paper if that helps. Don't forget to flip the final result.
 
  • #3


Hello, thank you for sharing your question about convolutions. Convolution is a mathematical operation that is commonly used in signal processing and systems analysis. It is used to describe the output of a linear system when the input is given by a specific function.

In this case, the given function is x[n] and the output is y[n]. The convolution is represented by the * symbol and is defined as y[n] = x[n] * h[n], where h[n] is the impulse response of the system.

In order to determine the impulse response h[n], you can use the convolution theorem which states that the Fourier transform of the output is equal to the product of the Fourier transforms of the input and the impulse response. In other words, H(ω) = X(ω) * Y(ω), where H(ω) is the Fourier transform of h[n] and X(ω) and Y(ω) are the Fourier transforms of x[n] and y[n], respectively.

You can also use the inverse Fourier transform to find h[n] as h[n] = F^-1{H(ω)}, where F^-1{} represents the inverse Fourier transform.

In summary, to determine the impulse response h[n], you can use the convolution theorem or the inverse Fourier transform. I hope this helps you in solving your homework problem. Good luck!
 

1. What is convolution in signals and systems?

Convolution is a mathematical operation that is used to describe the output of a linear system when the input is a signal. It involves multiplying two signals together and integrating the result over time. The resulting output signal represents the effect of the input signal on the system.

2. How is convolution used in real-world applications?

Convolution is used in a variety of real-world applications, such as digital signal processing, image processing, and communication systems. It is used to filter and manipulate signals, remove noise, and extract information from the input signal.

3. What is the difference between continuous-time and discrete-time convolution?

The main difference between continuous-time and discrete-time convolution is the type of signals that are being multiplied and integrated. Continuous-time convolution is used for signals that vary continuously over time, while discrete-time convolution is used for signals that are sampled at specific time intervals.

4. Can convolution be performed on non-linear systems?

No, convolution can only be performed on linear systems. Non-linear systems do not follow the principle of superposition, which is necessary for convolution to be valid. However, non-linear systems can be approximated by linear systems, allowing convolution to be used in their analysis.

5. What is the relationship between convolution and the impulse response of a system?

The impulse response of a system is the output of the system when the input is an impulse function. Convolution can be used to find the output of a system for any input signal by convolving the input signal with the impulse response. This relationship is known as the convolution integral.

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