Lesson 4: Signal and Noise
What Students Learn
- Signal is the meaningful information you are trying to receive or observe.
- Noise is unwanted random data without meaning that can corrupt or interfere with a signal.
- Scientists must evaluate signal & noise to interpret observations.
- Voltage can be used as a proxy variable.
- An Operational Amplifier can be used to amplify a voltage signal.
- Transducers transform one type of energy input to a differing type of energy output.
- Electronic devices have noise originating from thermal effect, EM interference, and quantum mechanical interactions.
What Students Do
- Generate operational definitions for signal and noise from common everyday experiences.
- Quantify Signal, Noise, and Signal to Noise ratio for a graphed radio transmission example.
- Use semiphore (hand signals) to send and receive a message where noise generally becomes an issue in the reception (see ‘extensions’ below).
- Analyze the trade-offs in amplifying a signal for measurements.
NOTE: for advanced (physics) students, the following activities offer an alternative to the semiphore activity.
- Build an Operational Amplifier circuit on a bread board to amplify the signal from an iPod to a speaker.
- Collect & Analyze Signal & Noise data for the built speaker circuit using voltage probes and real time graphing software such as LoggerPro from Vernier
In this set of activities, students will attempt to communicate using hand signals or assemble an operational amplifier to play their iPods through a small speaker. The focus of activities will be the concepts of signal and noise and the trade-offs involved in amplifying the signal. Students are not expected to have a background in electronics. Student groups will need access to computers or another data collection device with voltage probes for the final investigation.
1. INTRODUCTION (Class Discussion and Semaphore activity)
Open with a discussion of students’ list of instruments that utilize other types of proxy variables from the final question on the AFM student worksheet. This should serve as the introduction to the idea of an electrical signal being used as a proxy variable. Instrumentation that has been used in the course to date relying on electrical signals can be discussed (for example, the majority of Vernier probes). A second connection to the AFM lesson is that very small changes in data may not be noticeable. Examples of more common transducer devices that use an electric signal—such as an electric guitar—could lead students to suggest that the signal is amplified in some way.
2. Use ‘Semaphore’ to Teach Signal to Noise
The students first meet for about 3 minutes to decide their technique for accurate delivery/receipt of the signal. During the activity, the students must be absolutely silent. Feel free to add any “noise” to the activity as you walk between groups, etc. Set students up in teams of 3 students each. One student should be the “receiver” on one end of the classroom and another the “transmitter” on the other end of your classroom. Have the 3rd student record what the receiver interprets the signal to be. The transmitters should use semaphore to send the signal, which is a randomly generated haiku (keeps the students from guessing what the message is). Have students meet again to discuss the accuracy of the message. Students generally want to trade jobs and try again. Alternatively, students could try Morse code to send and receive messages. See “Extensions” below.
Resources needed: Semaphore signs (Word Doc | Google Doc), Haiku for Semaphore (Word Doc | Google Slide) Student Guide for Evaluating Signal to Noise using Semaphore (Word Doc | Google Doc), Random Haiku Generator site
3. Signal and Noise
(PowerPoint | Google Doc )
- What is signal? What is noise?
After students have completed the semaphore activity, ask them how successful the sending and receiving of the message was. If they tested the OpAmp with various inputs, ask them to describe the sound quality emanating from the speaker. How does it compare to their car stereos? IPod headphones? Why is it different? The conversation should transition to an introduction of signal and noise using the PowerPoint Intro to Signal & Noise. To clarify the potential confusion over these common terms, students are asked to build and then refine an operational definition from examples.
Slide 2 Classroom Signal: teacher’s voice Noise: sound from all of the other students talking
Slide 3 Commodities traders Signal: buy or sell order Noise: Audible & Visual background confusion from other traders
Slide 4 Urban Astronomer Signal: Light from star Noise: light pollution
For slide 5, students should work in groups to formally write a definition of signal and noise that is shared & discussed. From the provided examples, ‘signal’ should be loosely understood as: the information of interest one is trying to observe. At this point, students’ definition of noise will probably revolve around something interfering or coming between the signal and the receiver to make observation difficult.
Slide 6 introduces a different type of noise with a low-res webcam and a poor analog tv signal. For both devices, the noise similarly makes the signal (the visual image) difficult to observe. What is different, however, is that both of these devices are interpreting a signal and presenting it to us for observation. Rather than a third entity coming between the signal and the observer, the noise is inherent to the device itself through the grain of the low- res webcam or the poor reception of the analog tv.
Slide 7 pushes the examples to include “noise” where no signal is being transmitted such as a static filled tv or a radio tuned between stations. Students should discuss how to alter their definition of “noise” to include devices displaying random, meaningless data or corrupting the signal with this data.
Slide 8 asks students to identify the signal and noise for motion data collected by a sonic ranger (motion detector). The signal is the position and time data with the associated calculations for velocity and acceleration, while the “noise” is the spike on the graph. This spike represents random, meaningless data interpreted by the motion detector as a position value. If students are familiar with motion detectors, they should be able to brainstorm possible causes for the noise in the data—such as another object (a hand or book) being read by the motion detector, classroom sound interfering with the detector, etc.
Slide 9 shows a zoom in of same data collection during the initial motionless period. Students should be asked to identify the signal and noise for this section as well. The signal again is the position and time data interpreted by the motion detector. Questions to ask the students: How does this noise compare to the spike in the last example? (happens continuously, very small fluctuations in signal) How can we account for this noise? (most likely part of the device itself, not an outside interference) How does this noise impact our measurements? (limits the precision of our data, can only be confident of position data with a certain range of uncertainty) How do calculations affect this noise? (Students should be able to notice that small fluctuations in the data are exaggerated and amplified as calculations are performed for velocity and acceleration graphs).
The final slide (10) introduces the main source of noise within electronics—random electron movements related to thermal energy.
- How can we measure signal & noise?
The student worksheet provides a simplified approach to estimate signal to noise ratio. Students numeric answers for the worksheets may vary slightly depending on how closely they adhere to the time tick marks to pull values. The student worksheet provides ranges of expected answers. It is important to clarify confusion with the process at this point, as the next activity is more open ended in terms of how students will estimate signal and noise. Teacher Background: Examples of the differing means used to calculate signal to noise ratios for different disciplines beyond the scope of this lesson’s goals can be found here.
You completed Instructional Activities. Please move to Career Connection
Based on how much time you have available, choose a career-connected activity below. In each case, recap what your students just learned in the lesson to the activity.
outside of class
|B 5-10 minutes in class||C half of class period (~25 minutes)||D entire class period (~50 minutes)|
|Give handout for students to watch Monish’s video and answer questions at home as homework.||A + Brainstorm on interview questions for Monish using a whiteboard or projector.||A + Have students think about the role of data in science. Students interview each other about math, coding, computers (some of the things Monish talked about), and positive experiences they had that enhanced skills in these areas.||C + Have students report to the class on their interview results.Then have students write a short letter to a younger sibling or friend about how to succeed and enjoy a tech, science, or math track in school.|
Example questions for Monish:
What are some similarities you found between the skills needed for a pharmacy career path and a computer science career path?
What advice do you have for someone to learn computer science if they do not have a computer science background?
Assessment[panel style="panel-default"][panel-header]How will I know they know[/panel-header][panel-content]
- Review students’ operational definition for signal and noise.
- Review student’ summary of using semiphore as signal and influence of noise.
- Review students’ Quantifying Signal and Noise for a Radio Example.
- PowerPoint: Intro to Signal & Noise (PowerPoint | Google Doc), Random Haiku Generator site
- Student Handouts: Semaphore (signs), sample Haikus for Semaphore (Word Doc | Google Slide), Student Guide for Evaluating Signal to Noise using Semaphore (Word Doc | Google Doc), Quantifying Signal and Noise for a Radio Example (Word Doc | Google Doc)
- Teacher: Answer Key: Quantifying Signal and Noise for a Radio Example (Word Doc | Google Doc)
Students may be challenged to send messages via Morse code after experimenting with Semaphore.
Building The Op Amp – advanced (PowerPoint, Student Activity)
Materials Not Included (op-amp) (for ~25 students, ~8 groups of ~3):
9V Batteries (2 per group)
Alligator Leads (4 per group)
Audio Device (IPod, Computer with audio jack, or similar)
Voltage Probes with Real Time Data Collection capabilities (Vernier or Pasco) (2 sets per group)
Mini Breadboard (1 per group)
Jump Wires (approx 9 smaller wires per groups)
741 IC Chip (1 per group)
22 μF capacitor (1 per group)
1kΩ variable resistor (1 per group)
1kΩ resistor (1 per group)
47kΩ resistor (1 per group)
Battery caps with leads (2 per group)
Speaker (1 per group)
Audio Plug (1 per group)
Students in small groups will build an OpAmp using a 741 IC chip and a breadboard. The PowerPoint OpAmp Circuit Assembly introduces the breadboard and the common wiring located underneath (slides 1-3). The schematic for the circuit they will assemble is shown on slide 4. The final slide illustrates the assembly step by step in the same sequence as the printed student instructions Signal and Noise in the Op Amp prompt a set of actions to explore the voltage input & output signal and noise related to different elements in the op amp circuit. The final assignment is a written summary with embedded graphs of their findings. Students will need to have preloaded mp3 files 60Hz_White_Noise.mp3 and 800Hz_White_Noise.mp3 into their ipods or a computer with an audio jack. Students are given the freedom to develop a means for estimating noise in the sinusoidal signal based on their previous experiences with the directed radio example. Depending on the students’ background with superposition of waves, Vernier’s Fast Fourier Transform (under insert / additional graph) is a possible means to analyze the more complex 800 hz sample. Sample graphs for the prompts can be found here Sample Graphs for Signal and Noise Op Amp Activity. In the extension section below is a link to a number of possible investigations as well as additional mp3 files.