## Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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## Consider an electrical circuit shown in the drawing. Determine the current though the resistor. A. 1A B. 2A C. 3A + D. 4A E. 5A

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## 2. Problem 7.2 The flyback converter of Figure 7.2a has an input of 48V, and output of 30V, a duty ratio of 0.45, and a switching frequency of 25kHz. the load resistor is 15Ω. a. Determine the transformer turns ratio b. Determine the transformer magnetizing inductance Lm such that the minimum inductor current is 25% of the average.

## Consider an ideal transformer with 100 turns of wire in the primary and 500 turns of wire in the secondary. If the primary coil is fed with 110 V, rms, what is the power consumed by the device connected to the secondary that behaves as a resistor.

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## ELEC153 Circuit Theory II M2A3 Lab: AC Series Circuits Introduction Previously you worked with two simple AC series circuits, R-C and R-L circuits. We continue that work in this experiment. Procedure 1. Setup the following circuit in MultiSim.The voltage source is 10 volts peak at 1000 Hz. Figure 1: Circuit for analysis using MultiSim 2. Change R1 to 1 k and C1 to 0.1 uF. Connect the oscilloscope to measure both the source voltage and the voltage across the resistor.You should have the following arrangement. Figure 2: Circuit of figure 1 connected to oscilloscope To color the wires, right click the desired wire and select “Color Segment…” and follow the instructions. Start the simulation and open the oscilloscope. You should get the following plot: Figure 3: Source voltage (red) and the voltage (blue) across the resistor The red signal is the voltage of the source and the blue is the voltage across the resistor. The colors correspond to the colors of the wires from the oscilloscope. 3. From the resulting analysis plotdetermine the peak current. To determine the peak current measure the peak voltage across the resistor and divide by the value of the resistor (1000 Ohms). Record it here. Measured Peak Current 4. Determine the peak current by calculation. Record it here. Does it match the measured peak current? Explain. Calculated Peak Current 5 Determine the phase shift between the current in the circuit and the source voltage. We look at the time between zero crossings to determine the phase shift between two waveforms. In our plot, the blue waveform (representing the circuit current or the voltage across the resistor) crosses zero before the red waveform (the circuit voltage). So, current is leading voltage in this circuit. This is exactly what should happen when we have a capacitive circuit. 6. To determine the phase shift, we first have to measure the time between zero crossings on the red and blue waveforms. This is done by moving the oscillator probes to the two zero crossing as is shown in the following figure Figure 4: Determining the phase shift between the two voltage waveforms We can see from the figure that the zero crossing difference (T2 – T1) is approximately 134 us. The ratio of the zero-crossing time difference to the period of the waveform determines the phase shift, as follows: Using our time values, we have: How do we know if this phase shift is correct? In step 4 when you did your manual calculations to find the peak current, you had to find the total impedance of the circuit, which was: Now, the current will be: Here, the positive angle on the current indicates it is leading the circuit voltage. 7. Change the frequency of the voltage source to 5000 Hz. Estimulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 8. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift Writeup and Submission In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up should contain a one page, single spaced discussion of the lab experiment, what went right for you, what you had difficulty with, what you learned from the experiment, how it applies to our coursework, and any other comment you can think of. In addition, you should include screen shots from the MultiSim software and any other figure, table, or diagram as necessary.

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## Problems Marking scheme 1. Let A be a nonzero square matrix. Is it possible that a positive integer k exists such that ?? = 0 ? For example, find ?3 for the matrix [ 0 1 2 0 0 1 0 0 0 ] A square matrix A is nilpotent of index k when ? ≠ 0 , ?2 ≠ 0 , … . . , ??−1 ≠ 0, ??? ?? = 0. In this task you will explore nilpotent matrices. 1. The matrix in the example given above is nilpotent. What is its index? ( 2 marks ) 2. Use a software program to determine which of the following matrices are nilpotent and find their indices ( 12 marks ) A. [ 0 1 0 0 ] B. [ 0 1 1 0 ] C. [ 0 0 1 0 ] D. [ 1 0 1 0 ] E. [ 0 0 1 0 0 0 0 0 0 ] F. [ 0 0 0 1 0 0 1 1 0 ] 3. Find 3×3 nilpotent matrices of indices 2 and 3 ( 2 marks ) 4. Find 4×4 nilpotent matrices of indices 2, 3, and 4 ( 2 marks ) 5. Find nilpotent matrix of index 5 ( 2 marks ) 6. Are nilpotent matrices invertible? prove your answer ( 3 marks ) 7. When A is nilpotent, what can you say about ?? ? prove your answer ( 3 marks ) 8. Show that if ? is nilpotent , then ? − ? is invertible ( 4 marks ) 30% 2. A radio transmitter circuit contains a resisitance of 2.0 Ω, a variable inductor of 100 − ? ℎ?????? and a voltage source of 4.0 ? . find the current ? in the circuit as a function of the time t for 0 ≤ ? ≤ 100? if the intial curent is zero. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 3. An object falling under the influence of gravity has a variable accelertaion given by 32 − ? , where ? represents the velocity. If the object starts from rest, find an expression for the velocity in terms of the time. Also, find the limiting value of the velocity. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 4. When the angular displacement ? of a pendulum is small ( less than 60), the pendulum moves with simple harmonic motion closely approximated by ?′′ + ? ? ? = 0 . Here , ?′ = ?? ?? and ? is the accelertaion due to gravity , and ? is the length of the pendulum. Find ? as a function of time ( in s ) if ? = 9.8 ?/?2, ? = 1.0 ? ? = 0.1 and ?? ?? = 0 when ? = 0 . sketch the cuve using any graphical tool. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 5. Find the equation relating the charge and the time in a electric circuit with the following elements: ? = 0.200 ? , ? = 8.00 Ω , ? = 1.00 ?? , ? = 0. In this circuit , ? = 0 and ? = 0.500 ? when ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 6. A spring is stretched 1 m by ? 20 − ? Weight. The spring is stretched 0.5 m below the equilibrium position with the weight attached and the then released. If it is a medium that resists the motion with a force equal to 12?, where v is the velocity, sketch and find the displacement y of the weight as a function of the time. Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 7. A 20?? inductor, a 40.0 Ω resistor, a 50.0 ?? capacitor, and voltage source of 100 ?−100?are connected in series in an electric circuit. Find the charge on the capacitor as a function of time t , if ? = 0 and ? = 0 ?ℎ?? ? = 0 Correct solution 5% Graph the general solution 2.5% Graph the function and particular solution 2.5% 10% quality and neatness and using Math equations in MS word. –

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## EE214 Fall 2015 Problem Set1 I am submitting my own work in this exercise, and I am aware of the penalties for cheating that will be assessed if I submit work for credit that is not my own. Print Name Sign Name Date Contains material © Digilent, Inc. 7 pages 1. (15 points) Below are some circuit elements from a simple digital system. 3.3V 20mA VB 1Kohm VA 1.3V RB 1K RC RD SW1 SW2 RA VC When the pushbutton SW1 is not pressed, what is the voltage at VA? (1pt) When the SW1 is pressed, what is the voltage at VA? (1pt) When the SW1 is pressed, what current flows in the 1K resistor RA? (1pt) When SW1 is pressed, what power is dissipated in RA? (2pt) In the LED circuit, 1.3V is required at VB to forward-bias the LED and cause current to flow. Given there is a 1.3V drop across the LED, what resistance RB is required for 20mA to flow through the LED? (2pt) What power is dissipated in the LED? (1pt) In the circuit on the far right, if RC dissipates 25mW, what is VC? (2pt) Using the VC voltage you calculated, if RC is changed to 100Ohms, how much power would it dissipate? (2pt) Using the VC voltage you calculated and a 1K RC, if pressing SW2 causes the total circuit power to increase to 75mW, what value must RD be? (3pt) EE214 Problem Set 1 2. (20 points) Complete the truth tables below. Provide SOP equations for the bottom three tables. F <= Σ ( ) F <= Σ ( ) F <= Σ ( ) 3. (12 points) Write the number of transistors required for each logic gate below inside the gate symbol, and then write the logic gate name below the symbol. 4. (12 points) Complete truth tables for the circuits shown below A B F AND A B F OR A B F XOR A F INV A B C F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 ? = ? ̅ ∙ ? + ? A B C F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 ? = ? ∙ ? ∙? ̅ + ? ∙ ? A B C F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 ? = ? ∙? ̅+? ̅ ∙ ? A B C F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A F B C A B C Y EE214 Problem Set 1 5. (18 points) Show the total transistor count and gate/input number for the circuits below. Then sketch equivalent circuits using NAND gates that use fewer transistors (do not minimize the circuits). 6. (12 points) Sketch circuits for the following logic equations F = A̅ ∙ B ∙ C + A ∙B̅ ∙C̅ +A̅ ∙ C F = A̅ ∙ B ∙C̅ ̅̅̅̅̅̅̅̅̅̅ + ̅A̅̅+̅̅̅B̅ F = (? +? ̅ ) ∙ ̅̅?̅̅̅̅̅+̅̅̅̅̅̅̅?̅̅̅∙̅̅?̅̅ G AB C D AB C D H G F F AB C EE214 Problem Set 1 7. (22 points) Sketch a circuit similar to the figure below that asserts logic 1 only when both switches are closed. Label the switches 1 and 2, and complete the truth table below. Then circle the correct term (high or low, and open or closed) to complete the following sentences describing the AND and OR relationships: AND Relationship: The output F is [high / low] when SW1 is [open / closed], and SW2 is [open / closed]. OR Relationship: The output F is [high / low] when SW1 is [open / closed], or SW2 is [open / closed]. Sketch a circuit similar to the figure below that asserts logic 0 whenever one or both switches are closed. Label the switches 1 and 2, and complete the truth table below. Circle the correct term (high or low, and open or closed) to complete the following sentences describing the AND and OR relationships: AND Relationship: The output F is [high / low] when SW1 is [open / closed], and SW2 is [open / closed]. OR Relationship: The output F is [high / low] when SW1 is [open / closed], or SW2 is [open / closed]. 8. (4 points) Complete the following. A pFET turns [ ON / OFF ] with LLV and conducts [ LHV / LLV ] well (circle one in each bracket). An nFET turns [ ON / OFF ] with LLV and conducts [ LHV / LLV ] well (circle one in each bracket). Vdd GND F SW1 SW2 Vdd GND F SW1 SW2 SW1 SW2 F SW1 SW2 F EE214 Problem Set 1 9. (8 points) Sketch circuits and write Verilog assignment statements for the following equations. F = m(1, 2, 6) F = M(0, 7) 10. (21 points) Complete the truth tables below (enter “on” or “off” under each transistor entry, and “1” or “0” for output F), and enter the gate name and schematic shapes in the tables. You get 1/2 point for each correct column, and 1/2 point each for correct names and shapes. Q1 Q2 Q3 Q4 A B F Vdd Q2 Q1 Q3 Q4 A B F Vdd A B Q1 Q2 Q3 Q4 F 0 0 0 1 1 0 1 1 Gate Name AND shape OR shape A B Q1 Q2 Q3 Q4 F 0 0 0 1 1 0 1 1 Gate Name AND shape OR shape EE214 Problem Set 1 Q2 Q1 Q3 Q4 A B F Q5 Q6 Vdd Q1 Q2 Q3 Q4 A B F Q5 Q6 Vdd (2 points) Enter the logic equation for the 3-input circuit above: A B Q1 Q2 Q3 Q4 F 0 0 0 1 1 0 1 1 Gate Name AND shape OR shape A B Q1 Q2 Q3 Q4 F 0 0 0 1 1 0 1 1 Gate Name AND shape OR shape A B C Q1 Q2 Q3 Q4 Q5 Q6 F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 F = Q1 Q2 Q4 Q5 A B F Q6 Vdd C Q3 EE214 Problem Set 1 11. (20 points) In a logic function with n inputs, there are 2? unique combinations of inputs and 22? possible logic functions. The table below has four rows that show the four possible combinations of two inputs (22 = 4), and 16 output columns that show all possible two-input logic function (222 = 16). Six of these output columns are associated with common logic functions of two variables. Circle the six columns, and label them with the appropriate logic gate name. Draw the circuit symbols for the functions represented. INPUTS ALL POSSIBLE FUNCTIONS A B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 A table like the one above for 3 inputs would need _________ rows and _________ columns. A table like the one above for 4 inputs would need _________ rows and _________ columns. A table like the one above for 5 inputs would need _________ rows and _________ columns. 12. (15 points) Find global minimum circuits for the following three logic signal outputs that are all functions of the same three inputs. Show all work. F1 = m (0, 3, 4) F2 = m (1, 6, 7) F3 = m (0, 1, 3, 4)

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## What is the electrical energy dissipated in the resistor in 39 s?

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