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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

LTI systems in time domain

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Beginner

Intermediate

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A system with input

x(t)

, gives the output signal

y(t)=x^2(t)+x\left(t^2\right)

. Which of the following properties does this system have?

a: Only linearity Explanation

Explanation

b: Only time-invariance Explanation

Explanation

c: Both linearity and time-invariance Explanation

Explanation

d: None of these Explanation

Explanation

Find the magnitude of a 5-point moving average filter

H(\omega)

where the output of the system is given by

y[n]=1 / 5[x[n+2]+x[n+1]+x[n]+x[n-1]+x[n-2]]

\frac{1}{5}(1+2(\cos (\omega)+\cos (2 \omega)))

Explanation

\cos (\omega)+\cos (2 \omega)

Explanation

1+e^{j \omega}+e^{2 j \omega}

Explanation

\frac{1}{5}\left(1+e^{-j \omega}+e^{2 j \omega}\right)

Explanation

An impulse input signal generates two impulses at the output for an LTI system. If sum of two distinct impulses is given as input to this system, the output will contain

a: exactly 4 impulses Explanation

Explanation

b: 3 or 4 impulses Explanation

Explanation

c: exactly 2 impulses Explanation

Explanation

d: cannot be predicted Explanation

Explanation

When a moving average system of length

M

is used for noise suppression,

a: For large M, there is more suppression of noise Explanation

Explanation

b: For small M, there is more suppression of noise Explanation

Explanation

c: the system does not change the signal at all Explanation

Explanation

d: None of these Explanation

Explanation

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