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- Q3 in a digital telephony network, the signal of human voice needs to be sampled and digitized before transmission. it is found that limiting the bandwidth of human voice to 3000 hz would be enough to ensure good-quality phone calls. a. Human voice contains frequency components above 3000 Hz. How canwe ensure that the voice signal will only occupy a bandwidth of 3000Hz? b. The sampling rate is determined to be 50% higher than the Nyquistsampling rate. Determine the sampling rate c. A pulse-code modulation (PCM) scheme is used to represent thedigitized voice signal, where 10 bits are used for each sample.Determine the data rate of a single voice call. d. Time-division multiplexing (TDM) is used to aggregate a maximum of 40voice calls in a telephone line. Determine the maximum data rate thatyou can observe over a telephone line. e. Determine the minimum required bandwidth of the telephone line thatcan support a maximum of 40 phone calls.- d. Explain what…PleaseThe input-output relationship of a discrete-time LTI system is given as follows?[n] = 2x[n − 4] − 3x[n − 6].a) Determine the impulse response of the system, h[n].b) Using h[n], show that the system is causal.c) Using h[n], show that whether the system is BIBO stable or not.d) Determine the transfer function H(z). Plot pole-zero diagram. Indicate ROC.e) Using H(z), show that whether the system is stable or not.f) Determine the frequency response of the system, if exists. Why?g) Determine the impulse response of the inverse system calculated in f).During a vibration measurement experiment in the Mechanical Engineering Department at Hacettepe University, a piezoelectric accelerometer output is given by this mathemtaical equation: a (t) = 1 + 4 sin(43.98t) + 7sin(100.53t) in gravity acceleration (g) value. a) Determine the frequencies (in Hz) contained in the signal. Round your results to nearest integer value. b) What is the minimum sampling rate to avoid aliasing? c) Sketch clearly the frequency spectrum if the signal is sampled at 15 Hz. d) Now, the signal is filtered with a low-pass Butterworth filter to remove the maximum frequency component. It is desired to attenuate the amplitude of this component to at least 5 % of its value. If the sampling rate is now 20 Hz, what will be the order of the filter? e) If the blue one is our signal, then what is red and green ones? Write down the mathematical relation between the three signals? (Use labels as blue, red and green signal.)
- b) G(?)=K [(S−1)(S−2) / (S+2)(S+3)] ; Construct nyquist curves for K=1, 5/3, 9 values. Write down the Nyquist stability criterion and explain whether the system is stable or not. c) Define the gain and phase margin, this time on the nyquist curve.please answer with solution. An analog signal with a bandwidth of 36MHz is sampled at a frequency (fs) of 72,000,000 samples per second during the ADC (analog-to-digital conversion) process. What is the outcome of the received signal after the DAC (digital-to-analog conversion) process? a. the signal will have experienced aliasing b. the signal will not experience aliasing c. the signal will not experience quantization errors d. none of the above describes the outcomeAn analog signal, with an absolute bandwidth of 10 KHz, is to be converted to a digital signal usingan A/D converter and stored in a PC. If the quantization error must be within ±0.05% of the peak-to-peakvalue of the analog signal, determine the storage requirement. Please assume that we are going to record 8seconds of data, sampled at 1.5 times the Nyquist rate.
- Ex. 1780. A closed-loop system has sustained oscillations (i.e. constant amplitude) with a period of 85 seconds when the gains are: proportional=96, integral=0, and derivative=0. Determine the ideal- PID gains Kp, Ki (minutes^-1), Kd (minutes) using the Ziegler-Nichols method. Also determine the standard-PID values which are commonly used in industry, such as LabVIEW: Kc, Ti (min), Td (min). ans:61. Given an analog signal. m(t) =5cos(2π .2000t)+2cos(2π .4000t), for t>0, sampled at a rate of 7,000 Hz, a. sketch the spectrum of the original signal; b. Sketch the spectrum of the sampled signal up to 20 kHz; c. sketch the recovered analog signal spectrum if an ideal low pass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal.1. Since this is a first order system, provide expression for the time constant. 2. Provide a state space representation of the system. 3. Obtain the transfer function of the system using the state space model. 4. Determine the control gain Kp that results in steady-state error of 0.1
- 1. Consider the state space system with the given picture. Is this a valid state-space system? 2. (sperate problame0 Write down a transfer function of a stable system for which pure proportional feedback could drive the system unstable.For the system defined by the first-order differential equation: Draw the log magnitude (dB)-log frequency graph of H(jw). (The phase graph is not required. The frequency axis is expected to be logarithmic when drawing the log magnitude graph.) The input is assumed to be suppressed when the magnitude of H(jw) is -40dB. It is given that the x(t)=coswat signal is suppressed by this system. What is the smallest value of wa in this case?1. Given an analog signal x(t)=10 cos(2π.5500t)+5 cos(2π.7500t) is sampled at a rate of 8,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal low pass filter with a cutoff Frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal; c. determine the frequency/frequencies of aliasing noise.