# signals and systems homework help

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• Q1:5) Find the system response to the input x(t), given the impulse response given by h(t), and as described in the figures below (hint: Graphical Convolution), where: x(t) = t & h(t) = tSee Answer
• Q2: An actie filter has been designed as shown. Determine the (а)Order of the low pass filter; what are the Butterworth Coefficients? (b) (3 dB) cutoff frequency (c) Approximate Stopband frequency and stopband attenuation by calculation. You can confirm your results using MultiSim See Answer
• Q3: (a) Use Table 10.4 Conversion of BJT high-frequency modeling parameters into find Cu and C1 (10 points)your textbook (b) Find the low frequency poles. What is the dominant pole frequency, and which capacitor dominates the low frequency pole location?(20 points) (c) Draw the high frequency amplifier model with Cụ and Cr . Find the high frequency cutoff using Cu and Cz . You may choose to use the small signal hybrid-n model of the amp to find the cut-off frequency. Or you can apply Miller's theorem and calculate the cutoff frequency. Or, use a virtual BJT, insert your value of Br for the transistors, and draw inMultiSim Cu connected between base and collector, and Cn connected between base and emitter. Then simulate the amp to find its high cutoff frequency. (30 points) The amplifier BJTS in the circuit below, have the following specifications shown has the following specifications:BF = 220, VA = 350 V, rb = 0.13 Q. CJE=27 pF, VJE = yF 0.75,MJE = m = 0.33, TF = 0.325 ns, fr = 490 MHz, CJC =9.12 pF, CJS =0 pF.See Answer
• Q4: Consider a hydraulic press that lifts a weight of 100 kg by applying a 10 kg force. What is the ratio of area of the load' piston to the area of the 'force'piston? А. V10В. 10C. V0.1D. 0.1See Answer
• Q5: (а)Determine the DC conditions of the amplifier (b) Draw the AC model of the amplifier (c)Determine the midband voltage gain A, (you can use Sim) (d) Determine the low frequency poles of the amplifier (You can calculate the low frequency poles, or find the pole due to Cl by making Cs and C2 equal to 1F, etc for each pole and each capacitor). If you simulate to find the low frequency poles, please include the resulting frequency responses. 3. The enhancement NMOSFET used in the amplifier shown has the following specifications: K=0.16 mA/V² , V7=2 V, and V,= 300 V. You can show Simulations results for each part – just make sure you highlight the results as a text in your simulations.See Answer
• Q6: Question 4: Using the designed DAC in the previous question, find the output analog voltage if the digital input is 1001.See Answer
• Q7: Question 2: A 4-bit SAR-type ADC can convert analog samples of up to6V to digital form. Explain the working process behind the conversion of a 4V analog sample into its digital form using the ginSAR-type ADC configuration.See Answer
• Q8: Question 5: (a) Design a single-supply amplifier with a gain of -15 that can amplify signals with frequencies between 10kHz to 25 kHz and a supply voltage of 7V. The input impedance of the amplifier must be at least 2 M2. (b) Further then, draw the output waveform of the output signal if the input signal is 0.25 Sin 70000t.See Answer
• Q9: Question 3: Design a 4-bit DAC with a maximum output of 4V. Use a reference voltage of 12V.See Answer
• Q10: Question 1: Using two 74192 ICs decade counters, two 7447 ICs 7-segment decoders, two 7- segment displays and negative-edge triggered D-flipflop. Design a box counting system that works with a conveyor belt. The system should stop the conveyor belt when the count of boxes reaches 23 boxes. A manual push button should reset the count and restart the working process of the conveyor belt.See Answer
• Q11: 1. The following questions concern plotting of signals. (a) Find the equation:Note: The signal continues following the same pattern to the left back toward t → -∞. (b) Find the equation:Note: The signal takes on a sinusoidal shape in the range t E [1,3]. Otherwise the lines are straight.See Answer
• Q12:Consider the following signal, x(t): Draw y(t)=-2x(-1/3t+1). Label both axes on your plot completely.See Answer
• Q13:Problem 3 [12 points] The feedback system configuration shown in Figure (1) is called the compensator feedbackSee Answer
• Q14:Problem 3 [28 points, 4 points each] Consider the continuous-time linear time-invariant system with transfer-function: Answer the following questions: a. What is the differential equation associated with the above transfer-function? b. Calculate the poles and zeros of G(s). c. Is G(s) asymptotically stable? d. Use the bilinear transformation (aka Tustin transformation) S = 2 z 1 Tsz + 1 to calculate the corresponding discretized transfer-function Ga(z). e. Calculate the poles and zeros of Ga(z). f. Is Ga(z) asymptotically stable? (A discrete-time system is asympotically stable if the poles satisfy |pi|< 1.) g. Use a computer program or calculator to sketch the magnitude and the phase of the frequency response G(jw). Now sketch the magnitude and phase of Gd(es) as a function of w when Ts = {0.01, 0.1, 1}s. Compare all the obtained responses. What is the role of Ts?See Answer
• Q15:Problem 2 [15 points] For the given signals 1. r(t) = 4 sin(20πt) 2. r₂(t) 4 sin(80nt) 3. T3(t) = -4 sin(40πt) Answer the following questions a. [6 points] Using the MATLAB command stem to plot the signals formed by sampling the above three functions over the interval 0 < t <1 with sampling rate of 30 Hz. b. [6 points] Determine the Nyquist sampling rate for each signal. c. [3 points] What do you observe?See Answer
• Q16:Problem 3 [15 points] A commonly used method for converting discrete-time signals to continuous- time signals is zero-order hold, in which z(t) is held constant between its known samples at t = nTg. Zero-order hold interpolation of samples is illustrated in the following figure a. [10 points] Zero-order hold is a low pass filter. Compute its frequency response H(w). Hint: The sampled signal is z, (t) = a[n]d(t-nT) and the zero-order hold signal is equivalent to convolving the sample signal r(t) with a rectangular pulse of with T. b. [5 points] Zero-order hold is used to reconstruct cos(0.1t/T.) from its samples at t = nT,. The first copy of the spectrum induced by sampling lies inSee Answer
• Q17:Problem 4 [20 points] Use MATLAB command tf and bode, generate magnitude (in decibel) and phase plots (in degree) for the following voltage transfer functions.See Answer
• Q18:Problem 5 [10 points] A signal z(t), bandlimited to 10 Hz, is sampled at 12 samples/s. what portion of its spectrum can still be recovered from its samples? Please draw a sketch (with an arbitrary signal shape of bandwidth 10Hz) that illustrates your findings.See Answer
• Q19:Problem 6 [25 points] What does aliasing sound like? Load the file P673.mat from the Canvas. This is a speech signal (a single sentence) sampled at 24000 samples/s. a. [5 points] Listen to the signal using Describe what you hear. b. [5 points] Plot the one-sided magnitude spectrum from 0 to 8 kHz using N-length (X)/3; F=linspace (0,8000,N); FX=abs(fft (X)); plot (F,FX(1:N)) c. [5 points] Repeat (a) and (b) after reducing the sampling rate to 6000 samples/s. Do this by keeping only every fourth sample and discarding the other three samples. Use Y=X(1:4:end); soundsc (Y,6000) Describe what you hear. It should sound different. d. [5 points] Plot the one-sided magnitude spectrum of the signal in (c) from 0 to 3 kHz using Nl-length (Y)/2; Fl=linspace (0,3000, N1); FY=4*abs (fft (Y)); plot (F1,FY(1:N1)) e. [5 points] Compare (note differences) answers to (a) and (c), and to (b) and (d).See Answer
• Q20:Question 3 The system of the figure below is to be used to filter continuous time music signals using a sampling rate of 6 kHz. The lead singer of the group sings at the frequencies A=1.3 kHz~ B=2 kHz.See Answer

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