has P.S.D. S_{xx} f then y has P.S.D
Consider Y= ax+b, a>0. If the density and distribution functions of x are F. (x) and f_{x} (x), then F_{y} (y) is equal to
Consider a random process x(t). Which of the following can represent R_{x}. (r)?
It is required to transmit at 100 Kbit/s and a bandwidth of 2 MHz is used. The
minimum S/N ratio is ___________________
⇒
SNR when the system is uncoded is 4 dB, when it is coded is 2 dB then the coding gain is ________________ (dB)
Coding gain = SNR _{encoded } SNR. _{coded }= 4.dB2dB = 2dB
In the set up shown below, determine the number of bits required to encode each sample of x (t) such that bandwidth of signal y(t) is greater than 5 MHz.
Nyquist sampler is a sampler that samples a given signal at a rate twice the highest frequencies
f_{s} = 2 f_{m}, f_{5} = 2 x 350 kHz = 0.7MHz
Band width of output of PCM =
A sinusoidal signal whose peakpeak amplitude is 6 V is modulated using deltamodulator. At what rate should be sinusoidal signal sampled such that slope over load distortion is prevented with step size of 0.942 V?
2A = 6V ⇒ A = 3V
In order to overcome slope over load distortion in delta modulator
The probability of the five possible outcomes of an experiment are given as
Determine the informationrate, if there are 8 outcomes per second.
= 1.875 bits / sec; r=8 outcomes/sec
Information rate R=r.
=15bits / sec
Probability of picking 3 symbols are P_{0}, P_{1} and P_{2} respectively. The maximum entropy is achieved, when P_{0}, P_{1}, P_{2} are
P_{O} =P_{1} =P_{2} =P; P_{O} + P_{1} + P_{2} ^{= 1;}^{ }3P=1^{ ⇒} P= 1/3
Hartley's law can be defined as r = 2 Blog_{2} M . When compared to Shannon Hartley theorem, C, M are
Comparing C=B log ; r = C;
The probability of a bit decoded correctly at receiver is `p'. If n bits are sent, what is the probability that one bit is decoded correctly?
correct : p; error: 1p
out of n bits, only one bit is decoded correctly=
A stationary random process x(t) has the following correlation function is constant) . Find the psd of random signal x(t).
PSD of input is expressed as
If random variable 'x' has Gaussian pdf with mean M, then y=2x has PDF andmean respectively
so y has pdf N(2m,40^{2}) which is Gaussian
If x has P.S.D S_{xx} (f), then y has P.S.D of ( Assume H(f) is the Fourier Transform
A Gaussian random variable 'x' has mean 1 and variance√2. If y = x^{2}, then the mean of y is
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