A linear, time-invariant system has the following impulse response:


(a) Describe in words the effect of this system.

(b) What is the corresponding polynomial

Short Answer

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Step by step solution

01

Step – 1:

a) consequence of the method:

From the urge response,

ẟ(t) =1t0,tt00,t>t0- .....1.

02

 Step – 2:

The response of the system stays constant with both the value of 1t0until it approaches zero t = t0after extending the (t0) duration.

As a result, the effect of the system's original signal is defined.

b)

The following is a general representation of a polynomial equation:

Based on the impulsive reaction,

B(x) = b0 + b1x + ....... +btxt ......2.

Extend Equation (1)'s auto - correlation functional as follows::

Whent=0, b0 = 1t0 .......3.

When t=1, b1 = 1t0 ……4.

When t=2, b2 = 1t0 ......5.

When t= t0, bt0 = 1t0 .......6.

When t= t0+ 1, bt0 = 1t0+1 …… (7)

To find the polynomial, change formula (3), argument (4), equation (5), equation (6), then equation (7) in equation (2).

Bx=1t0+1t0x+1t0x2+.....+1t0xt0=1t01+x+x2+....+xt0(8)

Therefore, the corresponding polynomial is:

B(x) =1t0 (1 + x + x2 + ......+xt0)

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