What is the autocorrelation of a rectangular pulse?
Explanation: The auto-correlation function is the method of correlating the various instants of the signal with itself and that of a rectangular pulse of duration T is a triangular pulse of duration 2T.
What is the ideal bandwidth of rectangular pulse?
The optimum cutoff frequency is half this, or Bopt = 0.685/τ Hz. This is less than the frequency of the first spectral null (1/τ Hz), so the optimum bandwidth includes only about two-thirds of the signal mainlobe.
What is the maximum value of autocorrelation?
The autocorrelation function Rx(τ) has its maximum magnitude at τ = 0; that is: (1.15) To prove this property, we consider the non-negative quantity: (1.16)
What is the highest frequency that is contained in the sampled signal?
2. What is the highest frequency that is contained in the sampled signal? Explanation: We know that, after passing the signal through anti-aliasing filter, the filtered signal is sampled at a rate of Fs≥ 2B=>B≤ Fs/2. Thus the maximum frequency of the sampled signal is Fs/2.
What is Fourier transform of rectangular function?
Therefore, the Fourier transform of the rectangular function is. F[∏(tτ)]=τ⋅sinc(ωτ2) Or, it can also be represented as, ∏(tτ)FT↔τ⋅sinc(ωτ2) Magnitude and phase spectrum of Fourier transform of the rectangular function.
What is essential bandwidth?
The essential bandwidth is defined as the portion of a signal spectrum in the frequency domain which contains most of the energy of the signal.
Which modulation technique uses minimum bandwidth?
In SSB-SC modulation technique, the carrier is suppressed and only either of the sidebands is transmitted. Thus, SSB-SC has minimum channel Bandwidth.
How strong is the cyclic autocorrelation of a rectangular pulse?
However, the strength of the cyclic autocorrelation for most of those cycle frequencies is very small, so that in practical terms, the rectangular-pulse signal possesses ten or so significant features. That’s actually quite a lot compared to practical real-world signals like BPSK with square-root raised-cosine (SRRC) pulses.
What is the power of the autocorrelation function for BPSK?
Figure 1. Estimated cyclic autocorrelation function for a rectangular-pulse BPSK signal in noise. The power of the noise is 0.1 and the power of the signal is 1.0. The non-conjugate CAF for is the conventional autocorrelation function.
How does an intensity autocorrelator work?
In an intensity autocorrelator as shown in Figure 1, a beam splitter splits an incoming pulse into two pulses, which are then focused and sent into a crystal with a χ(2) nonlinearity. The arm length difference and thus the relative timing of the pulses can be mechanically adjusted via the variable optical delay line .
How to measure the pulse shape with an autocorrelation trace alone?
From a measured autocorrelation trace, one can well retrieve the pulse duration if the pulse shape is known, and also check whether the autocorrelation trace is consistent with a given pulse shape. However, one can not uniquely measure the pulse shape with an autocorrelation trace alone.