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4. Signal X(t) has a bandwidth of 10 kHz, and its amplitude at any time is a random variable whose PDF is showing in Figure 1. We want to transmit this signal using a uniform PCM system (a) Show that a (b) Determine the power in X(t) (c) What is the SQNR is decibels if a PCM system with 128 level is employed. (d) What is the minimum required transmission bandwidth in (c) (e) If we need to increase the SQNR by a least 15 dB, by how much should the transmission bandwidth increase?
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Figure 1: PDF of X(t) 4. Signal X(t) has a bandwidth of 10 kHz, and its amplitude at any time i...
Question 1 A given message signal, x (t), with bandwidth of 5 kHz, power of Watts,...
Question 1 A given message signal, x (t), with bandwidth of 5 kHz, power of Watts, and Tmaz 1 V, will be transmitted using a PCM system. If sampling is done at the Nyquist rate and a uniform quantizer with 32 levels is employed (a) What is the resulting SQNR? (b) What is the resulting bit rate?
(5) A PCM system encodes samples using an 8-bit ADC. In the case of peak signal...
(5) A PCM system encodes samples using an 8-bit ADC. In the case of peak signal amplitude, estimate the signal to quantization noise ratio in dB (6) The output SQNR of a 10-bit PCM was found to be insufficient at 30 dB. To achieve the desired SQNR of 42 dB, an increase to the number of quantization levels was needed. Determine the fractional increase in the transmission bandwidth required. (7) A signal x(t) band-limited to 3kHz is sampled at a...
Exercise 6: Consider an audio signal with an amplitude that ranges over the interval [-10,10] and...
Communication systems theory:
Exercise 6: Consider an audio signal with an amplitude that ranges over the interval [-10,10] and with spectral components limited to the frequency band of 300 Hz to 3300 Hz. The signal is sampled at a rate of 8000 samples/second and used to generate a PCM signal. The signal-to-quantization- noise ratio (SQNR) is required to be maintained at 43.9 dB a) What is the minimum number of uniform quantization levels needed, and what is the minimum number...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) |...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) | and phase θ(f) response given below H(f) 90 70 50 30 10 10 θ(f) 25 -50 70 05 35 -3-252 -15105 0 05 115 2 25 3 35 -35-3-25-2-15-1-05 0 0.5 15 2 25 35 frequency (kHz) frequency (kHz) a) For x,(t)-2cos(22500t) find output signal ya(t) b) For x,(t) 4cos(27750t) find output signal yb(t) c) For x,(t)=2cos(2π500t) +4cos(2π750t) find output signal ye(t) d) For...
KS31603 SULIT/CONFIDENTIAL QUESTION 4 (20 marks) (a) A message signal has a peak voltage of 1V...
KS31603 SULIT/CONFIDENTIAL QUESTION 4 (20 marks) (a) A message signal has a peak voltage of 1V and its average power is 125 mW. Design a PCM system (find minimum value of R of the R bit A/D) with uniform quantization to achieve at least a signal to quantization noise ratio of 36 dB. What is the signal to quantization noise ratio obtained in your design? [6 marks] (b) If the signal is sampled at 9kHz in 4(a), what is the...
8 8.6-4 For a DSB-SC system with a channel noise PSD of Sn() 10-12 and a baseband signal of bandw...
8 8.6-4 For a DSB-SC system with a channel noise PSD of Sn() 10-12 and a baseband signal of bandwidth 5 kHz, the receiver output SNR is required to be at least 47 dB. The receiver is as shown in Fig. 8.30. (a) What must be the signal power Si received at the receiver input? (b) What is the receiver output noise power No? (c) What is the minimum transmitted power Sr if the channel transfer function is He)10-3 over...
b) The figure below shows an FM demodulator. s'(t)Envelope detector Demodulated signal s(t) Differentiator Figure 4: Question 2(b) In the system above, the differentiator performs the time-differ...
b) The figure below shows an FM demodulator. s'(t)Envelope detector Demodulated signal s(t) Differentiator Figure 4: Question 2(b) In the system above, the differentiator performs the time-differentiation operation s'(t) = as(t). Also, the envelope detector is assumed to be ideal, capable of extracting the envelope of the incoming signal perfectly. Describe, by equations, how the above FM demodulator may exactly recover the message signal from the FM signal. (6%) (c) Is the FM demodulator in Question 2(b) a coherent detector,...
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10...
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10 cos[20xt+10 sin(t/4)) (b) x(t) = 262719) () X(t)=10[cos(2nt) cos(atº/4) + sin(24t) sin( nt/ 4)] Suppose that the information signal is as shown in the following figure. When each modulating this signal using 100KHz as the carrier frequency, find the frequency shift and phase shift when FM is modulated with 5,=10. What is the maximum frequency shift and maximum phase shift? 0.5+ -0.5 ost Suppose...
Please do Part 4 and Show all work! 1. 145 points) <FM/FSK Modulation/Demodulations A periodic wave m(t) in Figure 1 below The resulting FM signal is demodulated as shown in the following figure b...
Please do Part 4 and Show all work!
1. 145 points) <FM/FSK Modulation/Demodulations A periodic wave m(t) in Figure 1 below The resulting FM signal is demodulated as shown in the following figure by using frequency discriminator. Assume no attenuation of the signal due to propagation loss (in other words assume amplifiers properly restored the amplitude of the transmitted signal at the receiver) [10 points] Find the Fourier Series (trigonometric Fourier Series) of the message signal m (t) where To...
Points) Consider the signal s(t) with Fourier Transform 10 1+ω. S(a) figure below, we impulse sam...
points) Consider the signal s(t) with Fourier Transform 10 1+ω. S(a) figure below, we impulse sample s) at a frequency o, rads/second, e signal sa(t). Can you find a finite sampling frequency o such that ly recover s(t) from so()? If so, find it. If not, explain why not. a) (5 pts) In ting in the can perfectly you s (t) sa(t) →| Impulse sample at- rate o b) (5 pts) Now suppose we filter the signal s() with an...
Question 1 A given message signal, x (t), with bandwidth of 5 kHz, power of Watts, and Tmaz 1 V, will be transmitted using a PCM system. If sampling is done at the Nyquist rate and a uniform quantizer with 32 levels is employed (a) What is the resulting SQNR? (b) What is the resulting bit rate?
(5) A PCM system encodes samples using an 8-bit ADC. In the case of peak signal amplitude, estimate the signal to quantization noise ratio in dB (6) The output SQNR of a 10-bit PCM was found to be insufficient at 30 dB. To achieve the desired SQNR of 42 dB, an increase to the number of quantization levels was needed. Determine the fractional increase in the transmission bandwidth required. (7) A signal x(t) band-limited to 3kHz is sampled at a...
Communication systems theory:
Exercise 6: Consider an audio signal with an amplitude that ranges over the interval [-10,10] and with spectral components limited to the frequency band of 300 Hz to 3300 Hz. The signal is sampled at a rate of 8000 samples/second and used to generate a PCM signal. The signal-to-quantization- noise ratio (SQNR) is required to be maintained at 43.9 dB a) What is the minimum number of uniform quantization levels needed, and what is the minimum number...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) | and phase θ(f) response given below H(f) 90 70 50 30 10 10 θ(f) 25 -50 70 05 35 -3-252 -15105 0 05 115 2 25 3 35 -35-3-25-2-15-1-05 0 0.5 15 2 25 35 frequency (kHz) frequency (kHz) a) For x,(t)-2cos(22500t) find output signal ya(t) b) For x,(t) 4cos(27750t) find output signal yb(t) c) For x,(t)=2cos(2π500t) +4cos(2π750t) find output signal ye(t) d) For...
KS31603 SULIT/CONFIDENTIAL QUESTION 4 (20 marks) (a) A message signal has a peak voltage of 1V and its average power is 125 mW. Design a PCM system (find minimum value of R of the R bit A/D) with uniform quantization to achieve at least a signal to quantization noise ratio of 36 dB. What is the signal to quantization noise ratio obtained in your design? [6 marks] (b) If the signal is sampled at 9kHz in 4(a), what is the...
8 8.6-4 For a DSB-SC system with a channel noise PSD of Sn() 10-12 and a baseband signal of bandwidth 5 kHz, the receiver output SNR is required to be at least 47 dB. The receiver is as shown in Fig. 8.30. (a) What must be the signal power Si received at the receiver input? (b) What is the receiver output noise power No? (c) What is the minimum transmitted power Sr if the channel transfer function is He)10-3 over...
b) The figure below shows an FM demodulator. s'(t)Envelope detector Demodulated signal s(t) Differentiator Figure 4: Question 2(b) In the system above, the differentiator performs the time-differentiation operation s'(t) = as(t). Also, the envelope detector is assumed to be ideal, capable of extracting the envelope of the incoming signal perfectly. Describe, by equations, how the above FM demodulator may exactly recover the message signal from the FM signal. (6%) (c) Is the FM demodulator in Question 2(b) a coherent detector,...
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10 cos[20xt+10 sin(t/4)) (b) x(t) = 262719) () X(t)=10[cos(2nt) cos(atº/4) + sin(24t) sin( nt/ 4)] Suppose that the information signal is as shown in the following figure. When each modulating this signal using 100KHz as the carrier frequency, find the frequency shift and phase shift when FM is modulated with 5,=10. What is the maximum frequency shift and maximum phase shift? 0.5+ -0.5 ost Suppose...
Please do Part 4 and Show all work!
1. 145 points) <FM/FSK Modulation/Demodulations A periodic wave m(t) in Figure 1 below The resulting FM signal is demodulated as shown in the following figure by using frequency discriminator. Assume no attenuation of the signal due to propagation loss (in other words assume amplifiers properly restored the amplitude of the transmitted signal at the receiver) [10 points] Find the Fourier Series (trigonometric Fourier Series) of the message signal m (t) where To...
points) Consider the signal s(t) with Fourier Transform 10 1+ω. S(a) figure below, we impulse sample s) at a frequency o, rads/second, e signal sa(t). Can you find a finite sampling frequency o such that ly recover s(t) from so()? If so, find it. If not, explain why not. a) (5 pts) In ting in the can perfectly you s (t) sa(t) →| Impulse sample at- rate o b) (5 pts) Now suppose we filter the signal s() with an...
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