You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

1st Law of Thermodynamics

A zero mean w...

Question

$A zero mean white Gaussian process X (t), with two-sided power spectral density of \frac{N_{0}}{2}, is applied to a real LTI system whose impulse response is h (t) . The auto-correlation function of the corresponding output process R_{Y} (τ) can be expressed as$

\frac{N_{0}}{2} h^{2} (τ)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{N_{0}}{2} h (τ)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{N_{0}}{2} h (τ) * h (τ)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{N_{0}}{2} h (τ) * h (- τ)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{N_{0}}{2} h (τ) * h (- τ)$
$S_{X} (f) = \frac{N_{0}}{2}$

$R_{X} (τ) = \frac{N_{0}}{2} δ (τ)$

$R_{Y} (τ) = R_{X} (τ) * h (τ) * h (- τ)$

$= \frac{N_{0}}{2} δ (τ) * h (τ) * h (- τ)$

$= \frac{N_{0}}{2} h (τ) * h (- τ)$

Suggest Corrections

Similar questions

A zero mean white Gaussian process X(t), with a two-sided power spectral density of 20 μ W/Hz is passed through the system shown in the figure below.

The bandpass filter (BPF) has ideal characteristics with a passband bandwidth of 2B centered around f_{0} and the low-pass filter (LPF) has ideal characteristics with a passband bandwidth of B. If f_{0} = 1 MHz and B=5 kHz. then the average power present in the output process Y(t) will be _____W.

Q. You look down at a coin that
lies at the bottom of a pool of liquid
of depth

d

and index of refraction n. Because you view with
two eyes, which intercept different
rays of light from the coin, you perceive the coin to be where
extensions of the intercepted rays
cross, at depth

d_{a}

instead of

d

.
Assuming that the intercepted rays
in Figure are close to a vertical axis through the coin, show that

d_{a} = d / n

. (Hint: Use the small-angle
approximation

sin θ \approx tan θ \approx θ

Using the given pattern, find the missing numbers.
$1^{2} + 2^{2} + 2^{2} = 3^{2}$
$2^{2} + 3^{2} + 6^{2} = 7^{2}$
$3^{2} + 4^{2} + 12^{2} = 13^{2}$
$4^{2} + 5^{2} + . . .^{2} = 21^{2}$
$5^{2} + . . .^{2} + 30^{2} = 31^{2}$
$6^{2} + 7^{2} + . . . .^{2} = . . . .^{2}$ .

Q. What is the stability order of the following species?

O_{2}^{2 +}

O_{2}^{+}

O_{2}

O_{2}^{-}

O_{2}^{2 -}

Using the given pattern, find the missing numbers.

1² + 2² + 2² = 3²

2² + 3² + 6² = 7²

3² + 4² + 12² = 13²

4² + 5² + _ ² = 21²

5² + _ ² + 30² = 31²

6² + 7² + _ ² = __²

Join BYJU'S Learning Program

A zero mean white Gaussian process X(t), with two-sided power spectral density of N02,is applied to a real LTI system whose impulse response is h(t).The auto-correlation function of the corresponding output process RY(τ) can be expressed as

The correct option is D N02h(τ)∗h(−τ)SX(f)=N02 RX(τ)=N02δ(τ) RY(τ)=RX(τ)∗h(τ)∗h(−τ) =N02δ(τ)∗h(τ)∗h(−τ) =N02h(τ)∗h(−τ)

$A zero mean white Gaussian process X (t), with two-sided power spectral density of \frac{N_{0}}{2}, is applied to a real LTI system whose impulse response is h (t) . The auto-correlation function of the corresponding output process R_{Y} (τ) can be expressed as$

The correct option is D $\frac{N_{0}}{2} h (τ) * h (- τ)$
$S_{X} (f) = \frac{N_{0}}{2}$

$R_{X} (τ) = \frac{N_{0}}{2} δ (τ)$

$R_{Y} (τ) = R_{X} (τ) * h (τ) * h (- τ)$

$= \frac{N_{0}}{2} δ (τ) * h (τ) * h (- τ)$

$= \frac{N_{0}}{2} h (τ) * h (- τ)$