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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

LTI systems in frequency domain

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Beginner

Intermediate

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The signal

x[n]=1+\cos (n)+\cos (\pi n)

is given as input to a high pass filter with a cut-off frequency of 2. Select the correct statement from the following:

a: Both

x[n]

and

y[n]

are periodic Explanation

Explanation

b:

x[n]

is periodic but

y[n]

is not Explanation

Explanation

c:

y[n]

is periodic but

x[n]

is not Explanation

Explanation

d: Neither

x[n]

or

y[n]

are periodic Explanation

Explanation

An LTI system with input output relation given by

y[n]=x[n]-x[n-1]

acts as an

a: low pass filter Explanation

Explanation

b: high pass filter Explanation

Explanation

c: band pass filter Explanation

Explanation

d: all pass filter Explanation

Explanation

An LTI system with input output relation given by

h[n]=x[n]+x[n-1]

acts as an

a: low pass filter Explanation

Explanation

b: high pass filter Explanation

Explanation

c: band pass filter Explanation

Explanation

d: all pass filter Explanation

Explanation

If the input to an LTI system is

x[n]=e^{j \omega_1 n} + e^{j \omega_2 n}

, which of the following output is not possible?

a:

e^{j \omega_1 n} + e^{j \omega_2 n}

Explanation

Explanation

b:

e^{j (\omega_1 + \omega_2) n}

Explanation

Explanation

c:

e^{j \omega_1 n}

Explanation

Explanation

d:

e^{j \omega_2 n}

Explanation

Explanation

If the input to a band pass filter is

x[n]=e^{j \omega_1 n} + e^{j \omega_2 n}

, which of the following output is not possible?

a:

e^{j \omega_1 n} + e^{j \omega_2 n}

Explanation

Explanation

b:

e^{j \omega_1 n}

Explanation

Explanation

c:

e^{j \omega_2 n}

Explanation

Explanation

d: all the above are possible Explanation

Explanation

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