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The power spectral density of deterministic signal is given by [sin(f)/f]2. where 'f' is frequency. The auto-correlation function of the signal in the time domain is -
- a)a sine pulse
- b)a delta function
- c)a triangular pulse
- d)a rectangular pulse
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The power spectral density of deterministic signal is given by [sin(f)...
The Auto - correlation function is a measure of similarity between a signal and itself delayed by τ.
The function is given by,
F[x (t)] ↔ x(w)
F[x (t - τ)] ↔ e-jwτ ×(w).
F[x × (t - τ)] ↔ e-jwτ x × (w).
By using parseval's identity for transform,
Inverse Fourier transform of square of sine function is always a triangular signal in time domain.
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Community Answer
The power spectral density of deterministic signal is given by [sin(f)...
Explanation:
Power Spectral Density (PSD) given by [sin(f)/f]^2:
- The power spectral density of a deterministic signal is given by [sin(f)/f]^2.
- This means that the frequency content of the signal is proportional to the square of the sine function divided by the frequency.
Auto-correlation function in the time domain:
- The auto-correlation function of the signal in the time domain is the convolution of the signal with itself.
- For the given PSD [sin(f)/f]^2, the corresponding auto-correlation function in the time domain is a triangular pulse.
Explanation for Triangular Pulse:
- The auto-correlation function of a signal with a PSD of [sin(f)/f]^2 results in a triangular pulse in the time domain.
- This triangular pulse shape arises due to the properties of the sine function and its relationship with the frequency.
Conclusion:
- Therefore, the correct answer is option 'C', which is a triangular pulse for the auto-correlation function of the given deterministic signal with a PSD of [sin(f)/f]^2.
Power Spectral Density (PSD) given by [sin(f)/f]^2:
- The power spectral density of a deterministic signal is given by [sin(f)/f]^2.
- This means that the frequency content of the signal is proportional to the square of the sine function divided by the frequency.
Auto-correlation function in the time domain:
- The auto-correlation function of the signal in the time domain is the convolution of the signal with itself.
- For the given PSD [sin(f)/f]^2, the corresponding auto-correlation function in the time domain is a triangular pulse.
Explanation for Triangular Pulse:
- The auto-correlation function of a signal with a PSD of [sin(f)/f]^2 results in a triangular pulse in the time domain.
- This triangular pulse shape arises due to the properties of the sine function and its relationship with the frequency.
Conclusion:
- Therefore, the correct answer is option 'C', which is a triangular pulse for the auto-correlation function of the given deterministic signal with a PSD of [sin(f)/f]^2.
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The power spectral density of deterministic signal is given by [sin(f)/f]2. where f is frequency. The auto-correlation function of the signal in the time domain is -a)a sine pulseb)a delta functionc)a triangular pulsed)a rectangular pulseCorrect answer is option 'C'. Can you explain this answer?
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