[amp_mcq option1=”Product of h1(t) and h2(t)” option2=”Sum of h1(t) and h2(t)” option3=”Convolution of h1(t) and h2(t)” option4=”Subtraction of h2(t) from h1(t)” correct=”option3″]<\/p>\n
The correct answer is C. Convolution of h1(t) and h2(t).<\/p>\n
The impulse response of a linear time-invariant (LTI) system is the output of the system when the input is a unit impulse. The convolution of two functions is a mathematical operation on two functions $f$ and $g$, which produces a third function that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.<\/p>\n
In the context of LTI systems, the convolution of the impulse responses of two systems is the impulse response of the cascade of those systems. This is because the output of a cascade of two systems is the convolution of the outputs of the individual systems.<\/p>\n
For example, if the impulse responses of two systems are $h_1(t)$ and $h_2(t)$, then the impulse response of the cascade of those systems is given by:<\/p>\n
$$h_{12}(t) = h_1(t) * h_2(t) = \\int_{-\\infty}^{\\infty} h_1(u) h_2(t-u) du$$<\/p>\n
This can be seen by considering the output of the cascade of the two systems when the input is a unit impulse. The output of the first system is $h_1(t)$, and the output of the second system is $h_2(t)$. The output of the cascade is therefore the convolution of $h_1(t)$ and $h_2(t)$.<\/p>\n
The other options are incorrect. Option A is incorrect because the product of two impulse responses is not an impulse response. Option B is incorrect because the sum of two impulse responses is not necessarily an impulse response. Option D is incorrect because the subtraction of two impulse responses is not necessarily an impulse response.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”Product of h1(t) and h2(t)” option2=”Sum of h1(t) and h2(t)” option3=”Convolution of h1(t) and h2(t)” option4=”Subtraction of h2(t) from h1(t)” correct=”option3″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"class_list":["post-59210","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n