Virtual Labs

Which of the following functions cannot be frequency response of a discrete-time LTI system?

H(\omega)=\sin (\omega)

Explanation

H(\omega)=\sin (2 \omega)

Explanation

H(\omega)=\sin (\omega / 2)

Explanation

H(\omega)=\sin ^2(\omega)

Explanation

The signal

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

is given as input to a low pass filter with cut-off frequency of 2 which gives the output signal

y[n]

. Select the correct statement from the following:

a: Both

x[n]

and

y[n]

are periodic Explanation

Explanation

x[n]

is periodic but

y[n]

is not Explanation

Explanation

y[n]

is periodic but

x[n]

is not Explanation

Explanation

d: Neither

x[n]

y[n]

are periodic Explanation

Explanation

When the signal

x[n]=\sin (\omega_o n)

is given as input to a filter, the output is zero. Select the correct statement from the following:

a: If the system is a high pass filter, it will give zero output when the input is

x[n]=\sin (\omega_o / 2 n)

Explanation

b: If the system is a low pass filter, it will give zero output when the input is

x[n]=\sin (2 \omega_o n)

Explanation

c: If the system is a band pass filter, it will give zero output when the input is

x[n]=\sin (\omega_o / 2 n)

Explanation

d: Both (a) and (b) are correct Explanation

Explanation

If the magnitude response of an LTI system is constant and the phase response is linear, then the input and output are related by

a: output signal is a scaled and delayed version of the input signal Explanation

Explanation

b: output signal is always a scaled version of the input signal Explanation

Explanation

c: output signal is always a delayed version of the input signal Explanation

Explanation

d: cannot be determined Explanation

Explanation

If the input to an LTI system is

x[n]=e^{j n}

, the system output

a: is always of the form

y[n]=A e^{j n}

Explanation

b: is always of the form

y[n]=e^{j n}

Explanation

c: is always of the form

y[n]=A e^{j n+j \phi}

Explanation

d: cannot be determined Explanation

Explanation

LTI systems in frequency domain