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George Mason University
A comprehensive guide to frequency domain techniques in biomedical engineering. This download includes solutions for separating respiratory artifacts from ECG signals, comparing Hanning vs. Hamming windows for spectral analysis, analyzing EMG agonist/antagonist covariance, and modeling system dynamics using Bode plots.
Part 1 (40 pts) Conceptual Questions When recording the ECG using chest leads, the movement due to respiration results in an artifact in the ECG signal. Idealized spectra of the ECG, X1(ω), and the respiration signal, X2(ω), are shown in Fig. 4. Draw the spectrum of the actual measured signal which is a combination of the two. Can they be separated using a filter? Explain what kind of filter can be used to extract the ECG and whether the entire ECG will be extracted. Describe how you could obtain an impulse response estimate of muscle activation from EMG to force data. What assumptions are required for the system to be modeled as LTI (linear time invariant)? If you were to convolve an input spike train (motor neuron firing) with this impulse response, what output would you expect to see? A noisy ECG was filtered three separate times with different filters as shown in figure B. Identify each filter as either a low pass, high pass, band stop, or band pass filter, and match each filter to the correct output. You are analyzing EMG signals using FFT. Compare the Hamming vs Hanning windows: how do they affect spectral leakage and frequency resolution? If you have 2 minutes of EMG sampled at 1000 Hz, what trade-offs arise if you choose 1-s vs 10-s window lengths? Build Hanning and Hamming windows using a half raised cosine function (do not use the built-in hann() and hamming() commands). Run a simple test: compute the FFT of a sinusoid plus noise with both window types and discuss the differences. Use 1000 Hz as the sampling frequency and N = 4000. Select your own frequency and amplitudes for the signal and the noise. Hann (Hanning) window: w_"hann" [n]=0.5(1-cos(2πn/(N-1))) Hamming window: w_"hamming" [n]=0.54-0.46cos(2πn/(N-1)) Part 2 (30 pts) aBP with Embedded Respiration Signal Using the included dataset: abp_with_resp.csv Plot the aBP data. (Must include code and plot here) Research a physiologically typical adult respiration rate (Hz and bpm). Method A (Cross-correlation): Generate a sinusoid at the estimated breathing rate and compute the cross-correlation with the ABP signal. Report the frequency/lag of peak correlation. Method B (FFT): Compute the FFT or Welch spectrum and show that a peak exists at or near the estimated breathing frequency. How close was your estimate to the observed peak? Part 3 (30 pts) Agonist and Antagonist EMG Paired Dataset Use dataset: emg_agonist_antagonist_walking.csv Band-pass filter the raw EMG between 20–450 Hz. This will remove low-frequency _________________ and high-frequency _________________. Calculate the sampling frequency of the given dataset using the diff() command. Compute the power spectral density (PSD) of the filtered EMG using Welch’s method. (Read MATLAB documentation on pwelch). From the PSD, determine the dominant bandwidth (range of frequencies with most EMG power). Based on the Nyquist theorem, select a minimum sampling rate that preserves the identified EMG bandwidth. Compare your chosen rate to the dataset’s given rate. Provide a short paragraph justification of your chosen sampling rate. Select a 10-second segment of agonist and antagonist EMG signals. Calculate the covariance between the two signals: "cov"(x,y)=1/(N-1)∑(x_i-x ˉ)(y_i-y ˉ) Interpret the result (short paragraph, plus covariance value) in terms of whether the two muscles are positively correlated, negatively correlated, or independent. The following is a transfer function with a time delay, which can represent any number of physiological processes. Construct Bode Plots for the following and identify all poles and zeros of the transfer function. G(s)= 100/(s+30) e^(-0.01t)
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A comprehensive resource for biomedical signal analysis and image enhancement in MATLAB. This download includes theoretical analysis of noise in biosystems (ECG, EEG, MRI), practical code for implementing digital filters (Low-pass, High-pass, Bandpass) to improve ECG Signal-to-Noise Ratio (SNR), and an unsharp masking algorithm for sharpening X-ray images.
Question 1 (15 pts) Describe three biological or biomedical systems/signals that often require filtering (e.g., ECG, EEG, MRI). Identify sources of unwanted components (noise, artifacts, or irrelevant frequencies) in each case, and explain why filtering is necessary Question 2 (15 pts) Find a dataset of a 1D biosignal. Find a dataset of a 2D biosignal. Describe each with regards to what it is depicting, what noise is present, and what kind of filtering each would require. Load datasets into MATLAB and show plots. Question 4 (20 pts) Develop a moving average filter for the ECG signal included with the project and the 1D dataset found in Question 2. Describe the pseudocode below, then implement in MATLAB and show the “before” and “after” graphs. Question 5 (10 pts) Introduce random noise to both of your biosignals (using MATLAB). Show the “before” and “after”. Question 6 (20 pts) Now run a low pass, high pass, and bandpass filter on the signals. Describe your findings regarding the random noise and the “before” and “after” of each signal. What do the filters tell you about the introduced noise? Question 7 (20 pts) Implement the code below with the image provided. Describe what the code is doing and how it impacts the image provided. Show all output.
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A detailed solution for processing raw ultrasound RF data into clear B-mode images using MATLAB. This download covers envelope detection (Hilbert transform), log compression, and the implementation of Delay-and-Sum beamforming to resolve point scatterers and remove image blurring.
1. Signal processing for B-mode image A linear ultrasound array with 128 active elements was used to acquire image data (US_prebeamformed.mat) from a tissue-mimicking medium with several nylon strings acting as point scatterers. The image is 38.4 mm long and 57.75 mm long. a. We discussed that envelop detection and log compression improves visualization of image. A pseudo-code for this as is follows: i. Compute the magnitude of the Hilbert transform (this gives envelope) to obtain the envelope. ii. Divide the envelope image with its maximum value – referred to as normalization. iii. Compute the log-base-10 of the normalized envelope and multiply by 20. Use the imagesc function, “figure, imagesc([0 38.4],[0 57.75],image_variable)”, to display the raw ultrasound data, envelope image, and log compressed image. Note that the dynamic range of the log-compressed image may have to be adjusted as follows: “figure, imagesc([0 38.4],[0 57.75],image_variable,[-40 0])”. Describe the differences in each image. Use the colorbar function to see the range of image-intensity values. What are the maximum and minimum values of the log-compressed image? Do you see the point scatterers? If not, explain why not? b. Use the included beamformDAQ function, “bmRF = beamformDAQ(RF, 32);”, to apply delay-and-sum beamforming to the raw ultrasound data with a moving aperture of 32 elements. Compute the envelope and log-compressed images of the beamformed data. Compare the log-compressed-envelope image of the beamformed data to that from the raw (not beamformed) data and describe the difference. Why are the point targets visible?
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A complete technical guide for designing a Linear Phased Array Beamforming system. This download includes a solution report detailing the calculation of geometric time delays and sampling frequencies for a 16-element ultrasound array, paired with a MATLAB walkthrough for simulating beam focusing at multiple depths.
Linear Array Transmit Beamforming and Sampling RequirementsContext:You are designing the transmit beamformer for a linear ultrasound array. The system needs to focus energy at specific depths along the central axis of the array. You are tasked with calculating the required time delays for the elements and determining the necessary sampling parameters for the system.System Parameters:Array Type: Linear ArrayNumber of Elements ($N$): 16Element Pitch ($d$): $300 \mu m$Speed of Sound ($c$): $1540$ m/sCenter Frequency ($f_c$): 5 MHzFractional Bandwidth: 80%Tasks:Delay Calculation (10 cm Focus):Calculate the transmit time delays required to focus the beam at a depth of 10 cm on the array's central axis ($x = 0$).Assume the delays are calculated relative to the array center.Ensure all delays are positive values (the element closest to the focal point should have the maximum delay, or conversely, the reference time is set such that the first firing element has $t=0$).Plot the Time Delay (ns) vs. Element Number.Effect of Focal Depth:Repeat the delay calculation for focal depths of 8 cm (shallower) and 12 cm (deeper).Generate a single comparative plot showing the delay profiles for all three depths (8 cm, 10 cm, and 12 cm) on the same axes.Observe how the curvature of the delay profile changes as the focal depth increases.Sampling Frequency Requirements:To accurately synthesize these delays digitally, the system requires a sufficient sampling clock.Calculate the upper cutoff frequency ($f_{max}$) of the transducer based on the center frequency and bandwidth.Determine the minimum sampling frequency ($F_s$) required to satisfy the Nyquist criterion for the signal band.
George Mason University
A complete solution guide for biomedical modeling tasks. This download includes the mathematical derivation and Python simulation for steady-state drug delivery via transdermal patches (Fick's Law), along with a MATLAB script for animating the expansion of a coronary stent.
Question 1 (50 pts). A transdermal patch is placed on the arm of a patient to deliver a specific dose of medication through the skin. The equation governing the concentration c of the drug is ∂c/∂t=D (∂^2 c)/(∂x^2 )- k_up c where x is the depth through the skin, D is the diffusion coefficient and kup is the rate of uptake of the drug into the bloodstream. Find the steady-state concentration as a function of x given the boundary conditions c = C0 at x = 0 (skin surface) and c = 0 at x = dc (critical depth). D, kup, C0 and dc are fixed parameters. Fentanyl patches are typically designed to deliver a steady dose over an extended period, and the drug concentration can vary based on skin depth. Taking the diffusion coefficient D as 1×10−9 cm2/s, and starting concentration at the surface as 5 mg/cm3, model the drug concentration over skin depth in Python. Take 0.2 cm as critical depth, and select appropriate skin depth intervals. Produce a concentration profile and mark skin depth on the plot where drug concentration is half the initial concentration. For drug A with a critical depth of 0.3 cm, (where the drug reaches a concentration of zero), and a diffusion coefficient of 0.8 x 10−9 cm2/s, determine C0 using the solution to part a. Assume the transdermal patch is designed to deliver 5 mg of the drug over 24 hours through an area of 10 cm². Suggest dimensions for the transdermal patch if the patch is made of a gel with an absorbency of 2 mg/cm3 Question 2 (50 pts). Create an animation in MATLAB of a coronary stent expanding from an initial radius of 1 cm to 3 cm. Model the stent as a cylinder with initial length of 10 cm. Submit both the code and a screen recording of your animation with your homework.
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A complete SystemVerilog project for a Traffic Light Controller using a Moore Finite State Machine (FSM). This download includes the source code for cycling through Green, Yellow, and Red states , a 7-segment decoder for visual output , and a ModelSim testbench to verify state transitions and timing .
The objective of this project is to design and verify a digital control system for an automated traffic light. Real-world traffic management relies on precise timing and clear visual feedback to maintain safety. The specific technical challenge is to implement a Finite State Machine (FSM) using SystemVerilog that automatically cycles through a fixed sequence of states: Green (G), Yellow (Y), and Red (R). The system must meet the following requirements: State Control: The controller must transition states (G → Y → R → G) on every clock cycle when the reset is low ("0") and immediately return to the default Green state when the reset is high ("1"). Visual Output: The design must include a 7-segment decoder that translates the internal 2-bit binary state codes (00, 01, 10) into the corresponding 7-bit binary patterns required to display the characters 'G', 'Y', and 'R' on a common 7-segment display. Verification: The functionality of both the FSM and the decoder must be verified through waveform analysis in ModelSim to ensure glitch-free transitions and accurate character representation.
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A complete design guide for a 4-Bit BCD Counter with 7-Segment Display output. This download includes a technical report and walkthrough covering the SystemVerilog implementation of sequential counting logic (Modulo-10), combinational decoding, and testbench verification with waveform analysis.
The objective of this project is to design and simulate a synchronous digital system using SystemVerilog that functions as a 4-Bit BCD (Binary Coded Decimal) Counter. The core technical challenge involves implementing specific Modulo-10 logic to restrict the standard 4-bit binary counting range (0–15) to a decade sequence (0–9), ensuring the system correctly resets to zero upon reaching nine. Additionally, the system requires a combinational decoder module to translate the 4-bit binary output into active-high 7-bit control signals suitable for driving a 7-segment display. The final design must be verified through a ModelSim testbench to confirm correct timing, rollover logic, and display mapping.
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A complete solution guide for electronics problems covering semiconductor properties and diode applications. This PDF includes detailed calculations for drift current density and resistivity in n-type silicon, along with circuit analysis for half-wave rectifiers, bridge rectifiers, and diode logic gates.
Q 1:Consider an intrinsic silicon bar of cross-section $4\text{cm}^2$ and length $0.35 \text{ cm}$ at room temperature $300^\circ \text{K}$. An average field of $20\text{V/cm}$ is applied across the ends of the silicon barCalculate:Electrons and hole components of current densityTotal current in the barResistivity of the barGiven: Electron mobility ($\mu_n$) is $1400 \text{ cm}^2/\text{V-s}$Hole mobility ($\mu_p$) is $450 \text{ cm}^2/\text{V-s}$Intrinsic carrier concentration ($n_i$) of Si at room temperature ($300^\circ \text{K}$) = $1.5 \times 10^{10}/\text{cm}^3$If now donor impurity to the extent of 1 part in $10^8$ atoms of Si is added. Find the density of minority carriers and the resistivity, given that the Number of Si atoms/$\text{m}^3 = 4.99 \times 10^{28}$Q 2:Calculate the drift current density for a given semiconductor. Consider silicon at T = 300 K doped with arsenic atoms at a concentration of $N_d = 8 \times 10^{15}/\text{cm}^3$. Assume mobility values of $\mu_n = 1500 \text{ cm}^2/\text{V-s}$ and $\mu_p = 400 \text{ cm}^2/\text{V-s}$. Assume the applied electric field is $100 \text{ V/cm}$.Q 3:Plot $i_D(t)$, $v_D(t)$ and $v_O(t)$ for the following circuit shown below assuming $V_\phi=0.6\text{V}$ for diode.[Circuit diagram showing a voltage source $v_I$, a diode $D$, and a resistor $R$]The wave form of input $v_I = 15 \sin(200t - 25)$Q4:Assuming $V_\phi=0.6\text{V}$ for each diode, find the values of $I$ and $V$ in the following circuits:(a) [Circuit with +5V source, 2.5 k$\Omega$ resistor, diode to ground](b) [Circuit with +5V source, 2.5 k$\Omega$ resistor, reversed diode to ground](c) [Circuit with diode from ground, 2.5 k$\Omega$ resistor to -5V](d) [Circuit with reversed diode from ground, 2.5 k$\Omega$ resistor to -5V](e) [Circuit with +2V and +1V inputs, two diodes meeting at a node with a 1 k$\Omega$ resistor to ground]Q5:Assuming $V_\phi=0.6\text{V}$ for each diode, find the values of $I$, $I_D$, and $V$ in the following circuits:(a) [Circuit with +10V source, 10 k$\Omega$ resistor, two diodes ($D_1$, $D_2$), and a 5 k$\Omega$ resistor to -10V](b) [Circuit with +10V source, 5 k$\Omega$ resistor, two diodes ($D_1$, $D_2$), and a 10 k$\Omega$ resistor to -10V]Q6:*2.17 Sketch $v_o$ versus time for the circuit in Figure P2.17 with the input shown. Assume $V_\gamma = 0$.[Figure P2.17: Bridge rectifier circuit with resistors $R_1=2.2\text{ k}\Omega$, $R_2=2.2\text{ k}\Omega$, and Load $R_L=2.2\text{ k}\Omega$]Input graph shown: Sine wave with peak +40 and -40.Q7:*2.18 (a) Sketch $v_o$ versus time for the circuit in Figure P2.18. The input is a sine wave given by $v_i = 10 \sin \omega t \text{ V}$. Assume $V_\gamma = 0$. (b) Determine the rms value of the output voltage.[Figure P2.18: Bridge rectifier circuit layout with resistors $R_1=2.2\text{ k}\Omega$, $R_2=2.2\text{ k}\Omega$, and Load $R_L=6.8\text{ k}\Omega$]
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A comprehensive resource for the Vehicle Interface and Car Class implementation project. This download contains a technical report explaining key OOP concepts like encapsulation and polymorphism , along with a visual walkthrough for configuring the project in IntelliJ IDEA.
Problem Statement: Vehicle and Car Interface: Vehicle Using IntelliJ, write a Java interface (not a class) called Vehicle that includes: startEngine(): A method that returns void and simulates starting the vehicle's engine. stopEngine(): A method that returns void and simulates stopping the vehicle's engine. drive(int distance): A method that returns void and accepts an integer parameter representing the distance to be driven. refuel(int amount): A method that returns void and accepts an integer parameter representing the amount of fuel to be added. Class: Car Create a Java class called Car that implements the Vehicle interface that has: Attributes: fuelLevel (int): Represents the current fuel level of the car. isEngineOn (boolean): Represents whether the car's engine is on or off. Add at least one attribute to simulate additional functionality. Implement all methods from the Vehicle interface: In the startEngine() method, set isEngineOn to true and print a message indicating the engine has started. In the stopEngine() method, set isEngineOn to false and print a message indicating the engine has stopped. In the drive(int distance) method, reduce the fuelLevel by the distance driven (1 unit of fuel per unit distance) and print the distance driven. In the refuel(int amount) method, increase the fuelLevel by the specified amount and print the new fuel level. Add at least one method to simulate additional functionality. Main Method In the main method, instantiate the Car class, and demonstrate the functionality of all the methods in the Car class by performing the following operations: Start the car's engine. Drive the car for a specified distance. Stop the car's engine. Refuel the car with a specified amount. Project Structure Your project should contain 3 files: Interface Vehicle. Class Car. Class containing the main method. Sample Run Output Plaintext Starting the car's engine... Engine started. Driving for 50 units of distance... Driven 50 units. Remaining fuel: 50 Stopping the car's engine... Engine stopped. Refueling the car with 30 units of fuel... Refueled. Current fuel level: 80 Final car status: Is engine on? false Current fuel level: 80 (Note: The sample run text is reconstructed based on the visual output described in the file ). Coding Guidelines Add Javadoc for each class and each method within every class. Use descriptive identifiers. Use letter-case standards for naming variables, classes, and methods. Use white space effectively (indenting blocks of code and blank lines between major sections). Add inline or block comments for non-trivial parts of your code.
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