In this case we are convolving their spectra which is why ring modulation results in the sum and difference frequencies of each component being present in the output, though an understanding of this result depends on the mathematics of the complex domain.
In other words, the basic theorem about the time domain and the frequency domain is that multiplication in one domain is equivalent to convolution in the other domain. Finally, there is a technical difference between "direct convolution", which is a very slow process given that every sample in each signal must be multipled by every sample in the other signal, and the faster version used by programs like SoundHack which analyzes each signal using an FFT Fast Fourier Transform then multiplying those results and performing the Inverse FFT to return the result to the time domain.
Besides increasing the speed of the calculation thereby bringing it into a reasonable working process , other variables involved in the analysis phase are brought into play, such as the window shape used in the analysis. However, in practice, this variable only affects the result quite subtly. However, other curved forms of windows result in a difference between the two versions, mainly the overall amplitude shape of the result. Convolving a signal with two impulses farther apart and closer together.
Additional discussion in this paper and practical strategies including auto-convolution i. Q: As in continous time impulse response has the amplitude equals to infinity, if we want to plot the convolution of this continous time impulse response with any of input signal x , in plot Please illustrate your answer Even in matlab you can do it, but this would require you to sit in front of the plot, or require increasingly powerful computer, forever!
Now regarding convolution. I am sure that you have a polynomial expression which defines your impulse response. Also it will definitely have uncanceled poles. The infinite impulse response system that you have can be of 3 types, converging, diverging and oscilatory. A diverging system is unstable and no realizable system should be like that. That leaves you with 2 scenarios; converging and oscilatory.
An oscilatory system would keep on giving out the same output periodically so you will get the idea of how the outputis going to be. Lastly a convergent system, which is probably what you have, will give an output forever but the output signal after some time will be so small that you can neglect it for all practical purposes. So decide a certain time duration for your output and stop the convolution after that point.
This should give you a rough but sufficiently accurate response of your system to the input x. I hope this helps. Dmitrij Advanced Member level 4. All the distinguishing differences are underlined in the previous replies.
Time domain convolution has great significance in DSP at least because this way we can apply a FIR-filter to a signal. The convolution operation can be imagined as swiping a credit card ,each instance of both the signals are multiplied with each other. In which case a bar code scanner is more like multiplication ,only two instances of each signals are multiplied. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Asked 7 years, 7 months ago. Imagine the world 5, years ago. How would a farmer count the number of plants in his land? For example, if he has 22 rows of plants, and 33 plants in each row, how does he count the total number of plants? I just had that realization myself.
Said in other words, convolution is equivalent to multiplying the coefficients of polynomials. How about 12 x 34, which we know is ? How do we get from that? Did I do something wrong with my convolution?
You probably forgot to reverse one of the signals.
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