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s (t) is a rectangular pulse given by, s(t) 0, elsewhere. A matched filter which is...
+00 k-00 The signal z(t) received by a binary communication system can be expressed as z(t)...
+00 k-00 The signal z(t) received by a binary communication system can be expressed as z(t) = axpe(t – kT)+w(t) where ax = £1, an equally likely and independent binary sequence, and w(t) is white Gaussian noise with spectral density S(f)= N, /2. The pulse shape pe(t) is as shown below. a) Write down and sketch the noncausal matched filter impulse response. b) Without making any calculation, make a sketch of the expected filter output wave shape when the input...
Consider a matched filter receiver for a binary communication system where a binary '1' is represented by a pulse s() as shown below and a binary 0' is represented by st Consider the...
Consider a matched filter receiver for a binary communication system where a binary '1' is represented by a pulse s() as shown below and a binary 0' is represented by st Consider the case when there is no noise, i.e, n(t)0 1. Determine and sketch the output s,() of the matched filter due to the input s(1) and - s(t), respectively 2. What is the sample value of so( atT where T is the pulse duration? 3. Why is it...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T,...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T, x) T T1 Find the Fourier transform of the signal and sketch it
45(f) s(t0) Determine the impulse response of the filter matched to the pulse shape shown in...
45(f) s(t0) Determine the impulse response of the filter matched to the pulse shape shown in the accompanying figure. Assume that the filter is designed to maximize the output SNR at time3to Sketch the output of the matched filter designed in part (a) when the signal s(t) is at the input. (a) to 3to 0 (b)
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t)...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t)...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2)....
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2). a(n) Apr(t - nT) exp (j2 fet)}, where the t-T./2 Let the constellation be a(n)e {2,-2,2j,-2j,0. 1. What is the appropriate matched filter to apply for this signal. Draw the optimum receiver 2. What is the average energy of the constellation, i.., E,? 3. Assume the the received signal is r(t)= s(t) +n(t), where n(t) is AWGN with variance 1. Find the error probability...
3. A white Gaussian noise signal W (t) with autocorrelation function it passes through a linear filter invariant in time h (t). Calculate the average power of the W(T) J-oo h2 (t) dt = 1 exit process...
3. A white Gaussian noise signal W (t) with autocorrelation function it passes through a linear filter invariant in time h (t). Calculate the average power of the W(T) J-oo h2 (t) dt = 1 exit process Y (t) knowing that
3. A white Gaussian noise signal W (t) with autocorrelation function it passes through a linear filter invariant in time h (t). Calculate the average power of the W(T) J-oo h2 (t) dt = 1 exit process Y (t)...
The input r(t) to a DSBSC receiver is a DSB signal s(t) = A m(t)cos (21fet)...
The input r(t) to a DSBSC receiver is a DSB signal s(t) = A m(t)cos (21fet) corrupted by additive white Gaussian noise with two-sided power spectral density N,/2, where No = 10-12 W/Hz, m(t) is a message signal bandlimited to 10 kHz. Average power of m(t) is Pm = 4 W and Ac = 2 mV. The block diagram of the receiver is shown below. Note that the receiver has filters which have slightly larger bandwidths than a typical DSB...
+00 k-00 The signal z(t) received by a binary communication system can be expressed as z(t) = axpe(t – kT)+w(t) where ax = £1, an equally likely and independent binary sequence, and w(t) is white Gaussian noise with spectral density S(f)= N, /2. The pulse shape pe(t) is as shown below. a) Write down and sketch the noncausal matched filter impulse response. b) Without making any calculation, make a sketch of the expected filter output wave shape when the input...
Consider a matched filter receiver for a binary communication system where a binary '1' is represented by a pulse s() as shown below and a binary 0' is represented by st Consider the case when there is no noise, i.e, n(t)0 1. Determine and sketch the output s,() of the matched filter due to the input s(1) and - s(t), respectively 2. What is the sample value of so( atT where T is the pulse duration? 3. Why is it...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T, x) T T1 Find the Fourier transform of the signal and sketch it
45(f) s(t0) Determine the impulse response of the filter matched to the pulse shape shown in the accompanying figure. Assume that the filter is designed to maximize the output SNR at time3to Sketch the output of the matched filter designed in part (a) when the signal s(t) is at the input. (a) to 3to 0 (b)
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2). a(n) Apr(t - nT) exp (j2 fet)}, where the t-T./2 Let the constellation be a(n)e {2,-2,2j,-2j,0. 1. What is the appropriate matched filter to apply for this signal. Draw the optimum receiver 2. What is the average energy of the constellation, i.., E,? 3. Assume the the received signal is r(t)= s(t) +n(t), where n(t) is AWGN with variance 1. Find the error probability...
3. A white Gaussian noise signal W (t) with autocorrelation function it passes through a linear filter invariant in time h (t). Calculate the average power of the W(T) J-oo h2 (t) dt = 1 exit process Y (t) knowing that
3. A white Gaussian noise signal W (t) with autocorrelation function it passes through a linear filter invariant in time h (t). Calculate the average power of the W(T) J-oo h2 (t) dt = 1 exit process Y (t)...
The input r(t) to a DSBSC receiver is a DSB signal s(t) = A m(t)cos (21fet) corrupted by additive white Gaussian noise with two-sided power spectral density N,/2, where No = 10-12 W/Hz, m(t) is a message signal bandlimited to 10 kHz. Average power of m(t) is Pm = 4 W and Ac = 2 mV. The block diagram of the receiver is shown below. Note that the receiver has filters which have slightly larger bandwidths than a typical DSB...
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