Beamforming: Signal Processing

Lab 5: Beamforming

• Beamforming applies signal processing to sensor arrays for directional signal transmission/reception.
• By weighting and summing sensor signals, beamforming achieves constructive interference for signals from a specific direction and destructive interference for others.
• Beamforming enhances the signal-to-noise ratio (SNR) and extracts signals from the desired direction.

Basic Principle

• Consider a linear array of N sensors with inter-element spacing d.
• A narrowband signal with wavelength λ arrives at an angle θ relative to the array normal.
• Time delay between adjacent sensors is τ = (d sin(θ))/c, where c is the speed of sound.
• The beamformed output can be analyzed by plotting the beam pattern and analyzing the main lobe width and side lobe levels.

Time-Domain Beamforming

• The signal received by each sensor is delayed and summed.
• Output signal y(t) = ∑(N n=1) w**n x**n(t - τn), where x**n(t) is the signal received, w**n is the weight, and τn is the time delay for the n-th sensor.

Frequency-Domain Beamforming

• Signals are transformed into the frequency domain using Discrete Fourier Transform (DFT).
• Output signal in the frequency domain Y(f) = ∑(N n=1) w**n X**n(f) e^(-j2πfτn), where X**n(f) is the DFT.

Beamforming Types

• Delay-and-Sum Beamforming: Simplest form, with equal weights (w**n = 1 for all n).
• Minimum Variance Distortionless Response (MVDR) Beamforming: Minimizes output signal variance while maintaining distortionless response in the direction of interest.
• Adaptive Beamforming: Advanced techniques adapt weights based on received signals, such as Least Mean Squares (LMS) and Recursive Least Squares (RLS).

Lab 3: Population Genetics

• Population genetics are studied using the Hardy-Weinberg model.
• Beads represent alleles, simulate random mating to observe changes in allele and genotype frequencies over generations

Objectives

• Understand the principles of population genetics.
• Learn how to apply the Hardy-Weinberg equation.
• Simulate random mating in a population.
• Observe changes in allele and genotype frequencies across generations.

Materials

• Use beads of two colors
• Containers represent populations
• A worksheet will be used for recording data

Setting Up Population

• Begin with 50 red and 50 white beads to represent the population
• Number of each bead color is recorded in the "Initial Population" section of the worksheet.
• Initial allele frequencies (p and q) are calculated where p + q = 1.
• Expected genotype frequencies are calculated using the Hardy-Weinberg equation: p^2 + 2pq + q^2 = 1.

Simulating Random Mating

• Two beads are randomly selected (mating of two individuals).
• Genotype is recorded based on bead combination (RR, RW, WW)
• Selected beads are returned to the container to maintain population size
• These steps are repeated over a number of generations
• The number of each genotype is recorded in the "Generation 1" section of the worksheet.
• Allele and genotype frequencies are calculated for Generation 1.
• Repeat the simulation for multiple generations using previous generation's allele frequencies.

Data analysis

• Compare allele and genotype frequencies across generations.
• Discuss if the population is in Hardy-Weinberg equilibrium.
• Changes in allele and genotype frequencies are analyzed.

Guía fácil de administración de insulina Lantus®

What Is Lantus® Insulin?

• Lantus® is insulin glargine, a long-acting insulin that works to improve blood sugar control in diabetic adults and children.
• It releases insulin slowly and uniformly over 24 hours.

Key Information

• Lantus® should be taken once a day, at the same time each day and never mixed with other insulins
• Lantus® should be clear and colorless, injected subcutaneously, and the injection site should be rotated.
• It should be used to treat diabetic ketoacidosis
• Patients should monitor blood sugar, inform doctor of any medical changes/conditions, and never share Lantus® pens or syringes.

Preparing a Lantus® Injection

Forms of Lantus®:

• 10 ml vial - used with a syringe.
• 3 ml Lantus® SoloStar® Pen.

Injection Prep (Vial & Syringe)

• Wash hands, clean vial with alcohol wipe.
• Inject air into the vial. Take syringe and extract air equal the dosage of insulin.
• Draw correct dose; remove syringe from vial. Check for and remove any air bubbles.

Injection Prep (Lantus® SoloStar® Pen)

• Wash hands, and remove pen cap. Check that the insulin should be clear and colorless.
• Attach new needle, perform safety test (dial two units, tap cartridge to move air bubbles, press injection button to see if insulin emerges).
• Dial correct dose (adjust if needed avoiding accidental injection).

Injecting Lantus®

• Choose injection site (abdomen, thigh, upper arm), clean with alcohol wipe, and pinch skin.
• Insert needle straight, push syringe plunger to the end, hold needle for 10 seconds.
• Remove needle; don't rub injection spot. Dispose of safely.
• Lantus® needs to be refrigerated before use, and it can be stored at room temperature for up to 28 days after opening.

Lantus® Side Effects includes:

• Hypoglycemia
• Injection site reactions
• Lipodystrophy
• Weight gain

Servere Side Effects Includes includes:

• Allergic reactions
• Low potassium
• Heart failure

Low blood sugar (hypoglycemia) side affects includes:

• Sweating
• Shakiness or Dizziness
• Blurred vision
• Confusion
• Rapid heartbeat
• Anxiety/Irritability

For Hypoglycemic Actions

• The patient needs to eat or drink something with fast-acting sugar
• The patient needs to recheck their blood sugar in 15 minutes

Physics: Vectors

Vector Summation

• The sum of vectors $\vec{A}$ and $\vec{B}$ (resultant vector $\vec{R}$) involves placing the origin of $\vec{B}$ at the end of $\vec{A}$ and connecting the $\vec{A}$ origin to the $\vec{B}$ end.
• Equation: $\vec{R} = \vec{A} + \vec{B}$

Vector Components

• Vector $\vec{A}$ can be decomposed into component vectors along the x-axis ($\vec{A_x}$) and y-axis ($\vec{A_y}$).
  • Equation: $\vec{A} = \vec{A_x} + \vec{A_y}$, where $\vec{A_x} = A_x \hat{i}$ and $\vec{A_y} = A_y \hat{j}$.
  • Scalar components $A_x$ and $A_y$ are obtained by projecting $\vec{A}$ onto the axes:
    • $A_x = A \cos \theta$.
    • $A_y = A \sin \theta$.
    • $A$: Magnitude.
    • $\theta$: Angle with the x-axis.

Analytical Vector Addition

• For two vectors $\vec{A} = A_x \hat{i} + A_y \hat{j}$ and $\vec{B} = B_x \hat{i} + B_y \hat{j}$, their resultant $\vec{R} = \vec{A} + \vec{B}$ is calculated by:
• $\vec{R} = (A_x + B_x) \hat{i} + (A_y + B_y) \hat{j}$.
• The scalar components of $\vec{R}$ are then:
  • $R_x = A_x + B_x$.
  • $R_y = A_y + B_y$.
• The magnitude of $\vec{R}$ is:
  • $R = \sqrt{R_x^2 + R_y^2}$.
• The angle $\theta$ that $\vec{R}$ forms with the x-axis is:
  • $\theta = \arctan \left( \frac{R_y}{R_x} \right)$.