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Determine the equivalent response when two LTI systems with impulse responses ha (t) and hb (t) are cascaded.Group of answer choicesh(t) = ha(t) * hb(t)h(t) = ha(t) โ€“ hb(t)h(t) = ha(t) hb(t)h(t) = ha(t) + hb(t)

Question

Determine the equivalent response when two LTI systems with impulse responses ha (t) and hb (t) are cascaded.Group of answer choicesh(t) = ha(t) * hb(t)h(t) = ha(t) โ€“ hb(t)h(t) = ha(t) hb(t)h(t) = ha(t) + hb(t)

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Solution

The equivalent response when two Linear Time-Invariant (LTI) systems with impulse responses ha(t) and hb(t) are cascaded is given by the convolution of the two impulse responses. Therefore, the correct answer is:

h(t) = ha(t) * hb(t)

This is because in LTI systems, the output for the cascaded systems is the convolution of the individual systems' impulse responses.

Similar Questions

Determine the output ofย  two LTI systems with impulse response h1 (t) and h2 (t)ย  are connected in parallel.Group of answer choicesy(t) = x(t) * (h1(t) h2(t))y(t) = x(t) *(h1(t) + h2(t))y(t) = (x(t) * h1(t)) + h2(t)y(t) = x(t) + (h1(t) + h2(t))

The impulse responses of two LTI systems are given below. These two LTI systems are connected in series to form anoverall LTI system โ„Ž๐‘œ๐‘œ(๐‘ก๐‘ก).โ„Ž1(๐‘ก๐‘ก) = 4 ๐‘’๐‘’ โˆ’ 4๐‘ก๐‘ก ๐‘ข๐‘ข(๐‘ก๐‘ก) โ„Ž 2(๐‘ก๐‘ก) = ๐›ฟ๐›ฟ ๏ฟฝ๐‘ก๐‘ก โˆ’ ๐œ‹๐œ‹8 ๏ฟฝe) (2) Find the system functions ๐ป๐ป1(๐‘ ๐‘ ) and ๐ป๐ป2(๐‘ ๐‘ ) by integration.f) (2) Find the frequency response of the overall system ๐ป๐ป๐‘œ๐‘œ(๐‘—๐‘—๐‘—๐‘—)

The impulse response of a continuous-time system is denoted by โ„Ž(๐‘ก)h(t), while for a discrete-time system, it is denoted by โ„Ž[๐‘›]h[n]. Compare the properties of โ„Ž(๐‘ก)h(t) and โ„Ž[๐‘›]h[n] and explain how they differ.

Choose the correct interpretation of unit impulse response from the following.Group of answer choicesThe output of an LTI system due to unit Impulse signalThe response of an invariant systemThe output of a linear systemNone

The impulse response of a continuous-time system is denoted by โ„Ž(๐‘ก)h(t), while for a discrete-time system, it is denoted by โ„Ž[๐‘›]h[n]. Compare the properties of โ„Ž(๐‘ก)h(t) and โ„Ž[๐‘›]h[n] and explain how they differ.a)โ„Ž(๐‘ก)h(t) is discrete, while โ„Ž[๐‘›]h[n] is continuous and time-limitedb)Both โ„Ž(๐‘ก)h(t) and โ„Ž[๐‘›]h[n] are time-limited and causalc)โ„Ž(๐‘ก)h(t) is continuous, while โ„Ž[๐‘›]h[n] is discrete and time-limitedd)Both โ„Ž(๐‘ก)h(t) and โ„Ž[๐‘›]h[n] are continuous and time-limited

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