Discussions are listed by chapter. Scroll down to see the current chapter discussion.

Discussions on chapter 1:

Class/Group Discussion
Discussion or assign Lab Overview Questions:
How many blocks are used in the "Object Tracker" Worksheet? What is the input and output of this system?
Answer: There are 10 blocks in the coin counter worksheet (even the video displays are actual blocks). The input to this system is the video camera and the output is a video display with a green cross-hair in it.

What does the "Object Tracker" do? By looking at the VAB worksheet, can you determine how it operates? How can you move across the video screen without the object tracker finding you?
Answer: The object tracker attempts to place a green cross-hair over the object in the video stream that is moving. If multiple objects are moving - the system tends to lock on the brightest object that is moving. The system looks for changes in position of elements of the video stream over time - that is, it looks for changes from one picture in the video stream to the next. If you move very slowly, there won't be a noticeable change between adjacent picture in the video stream - so it won't be able to identify that you are moving. (By double clicking on the image delay block you can modify the system to delay by more images. It is currently set to one - so the system looks for changes between adjacent images. Changing it to 5, would have the system look for changes between images separated by five snapshots, which would identify items moving five times as slowly as the original system.)

What does the "coin counter" engineering design do? What does each slider control?
Answer: The coin counter attempts to count the number of circles of a give size. If the slider bars are set properly, you can count quarters, nickels, pennies, or dimes. The slider bars control the minimum and maximum area of the circles. One also adjusts the contrast to take into account various lighting levels. Is the "coin counter" easy to fake out? If so, how would you do it? Answer: Since the coin counter looks for circles (not coins), it is easy to fake out. You can just cut out a paper circle and it will work as well as a real coin.

Class/Group Discussion cont.
How does the "echo lab" work? What are its inputs and outputs? Does it seem to give you an effect that could be useful in applications such as music production?
Answer: The "echo lab" just delays a sound and adds it back to the original. This delay is physically similar to someone yelling into a canyon and hearing a delay in the sound that reflects off the edge of the opposite wall of the canyon. The input is a microphone and the output is sound played through the speaker. This is very useful since most modern vocalists sound better with a little echo (generally very short in duration).

In addition, discuss the questions listed on Chapter 1 Slide 39

Summary

By now you should have a good feeling for how to load, run, and "read" VAB worksheets.
You are now ready to start using them in some real and interesting engineering applications.

Discussions on chapter 2: 2.2

• How are the functions cos(x) and sin(x) related to the motion of a rotating dot around a circle?
Answer: If sin(x) controls the x-axis of the dot's position, cos(x) controls the y-axis of the dot's position, and x is made a function of time such as x = c t where c is a constant, then the result is a dot that goes around the origin in a circle with a constant angular velocity. The distance of this dot away from the origin is always one.

• What do the sine and cosine functions look like when they are plotted as a function of time?
Answer: The functions go up and down in an oscillatory manner. They are fairly smooth, too.

• What happens to the shape of the function when you double the fundamental frequency of a sine or cosine signal? How does this action change the sound of these signals?
Answer: Doubling the fundamental frequency of a sine or cosine signal causes it to oscillate twice as fast as before. The sounds of these signals become higher in pitch, too.

• What are the names of the three numbers that define a sinusoidal signal?
Answer: The three numbers that control the shape of a sinusoidal signal are: frequency, amplitude, and phase.

• Of these three numbers, which one changes the sound of the sinusoid the most? Which one changes the sound of the sinusoid the least?
Answer: Changing the frequency of the sinusoid changes its sound the most, because the pitch changes. Changing the phase of a sinusoid causes almost no audible change in the sinusoid.

• How can the spectrum be used to figure out the fundamental frequency of a sinusoid?
Answer: The peak of the spectrum is located at the fundamental frequency of the sinusoid.

• How is amplitude related to the loudness of a sinusoidal signal?
Answer: Amplitude is directly related to loudness; increase the amplitude, and the sound of the sinusoid gets louder.

• What type of signal does a tuning fork sound most resemble?
Answer: A tuning fork's signal most resembles a sinusoid--either a cosine signal or sine signal.

• If you were to describe a tuning fork by the sound that it makes, which property is more important to describe--amplitude or frequency?
Answer: A tuning fork is best described by the fundamental frequency of the sound it makes.

• Suppose you wanted to make a digital tuning fork. What would you need?
Answer: The VAB worksheet is literally a digital tuning fork--no other parts are needed.

• State the difference between the spectrum of a signal and the spectrogram of a signal.
Answer: The spectrum of a signal is indicative of the frequency components of the signal or rather is a plot of the signal's sinusoidal components while the spectrogram is a two-dimensional image describing the spectrum of the signal over time.

• Can you synthesize (create) any signal using just cosines? How many would you need to recreate a given random noise waveform?
Answer: Yes, given sufficient number of cosines, we can create virtually any waveform. Since the random noise w/f contains a many frequencies, we would need a large number of tones perfectly recreate the noise signal. We can approximate the signal by using only those tones which have a big amplitude, and neglecting those with small ones.

• Given a spectrogram of a signal, could you obtain its time waveform? (Using your knowledge of VAB, modify the design so that the cosine generator frequency is a sinusoid itself, say with f=50Hz around a base frequency of 800Hz. You will need to add the cosine wave to the frequency slider output. Look at the spectrogram, what do you see?
Answer: Sure you can. The spectrogram and the time w/f are simply two representations of the same signal. Given one, we can find out the other.

• What will a signal sound like if the spectrogram consisted of just one horizontal line?
Answer: You have just designed a simple FM system!. The spectrogram will show you a sinusoid centered about 800Hz.

• How would the spectrogram of a sinusoid at 300Hz look like? How about the spectrogram of: s(t) = 3 cos (2pi 100t) +1.3 sin (2pi 50t) - 10 cos (2pi 150t)?
Answer: The horizontal line indicates that the signal consists of just one frequency and the frequency content of the signal is not changing over time. Hence it will just be a pure tone.

SECTION 2.4

• The length of the buffer is 95 samples. What frequency uses all of the samples once and only once?
Answer: 8000/95 = 84.21 Hz

• How does the performance of the system change when more samples are added to the buffer? When samples are taken away?
Answer: When more samples are added to the buffer, we are able to come closer to using an integer as the index in each channel. As the buffer becomes shorter, the system is less able to recreate the wave exactly, and it tuning will become worse.

• Why does this player sound a little out of tune? How can this be fixed?
Answer: The player sounds out of tune because we are approximating the sampling period. This causes error in the frequency.

• Design Project: Try to modify the basic MIDI player to use the envelope portion of Sketch Wave.
Answer: Open for Discussion.

• How will you make the synthesized music sound richer? Will adding another tone help? Why?
Answer: By adding more sinusoids. As you keep on adding tones, you get a closer and closer approximation to the true sound.

• Can this sketch wave VAB that you built be used to play standard MIDI files? How would you modify the design of the sketch wave VAB to incorporate MIDI?
Answer: No, this sketch wave that you built cannot be used to play standard MIDI files. But it can be modified in a manner such that it can be used to read standard MIDI files. For the design of the sketch wave which incorporates MIDI, look up the MIDI Sketch Wave VAB.

Chapter 3 Discussions 3.1 Introduction 3.2 Digitizing Images (Quantization)

• In the Image Quantization Grayscale worksheet you dealt with quantizing images to 8 bits/pixel or less. How many gray value steps an you have with 8 bits? Could you have gray values exceeding 1024 or 4096? How many bits would you need for 4096 gray value steps? Would the human eye be able to resolve these gray values in an image?
Answer: We can have 28 = 256 gray value steps with 8 bits. Yes we could have gray values exceeding 1024 or 4096. We would need m = log2 (4096) = 12 bits for 4096 gray value steps. No, the human eye would not be able to resolve 4096 gray values in an image.

• Can you think of a simple way to reduce the file size of an image? Assume that you can afford to lose a little sharpness in the image in return for decreased storage space.
Answer: You could use fewer bits to represent each pixel (color quantization) and/or reduce the resolution of the image. If color is not very important for the particular picture and application, you could even store the image as just a gray scaled picture.

• In this lab (3.1/3.2), we saw one way of reducing the number of pixels in an image i.e. by throwing away all but one of many pixels. Can you think of other ways to reduce the number of pixels?
Answer: Yes! One way can be to replace the pixels by their average value. Yet another could be to replace them by their maximum or minimum value. Results will vary depending upon the type of image.

Chapter 4 discussions.

Discussions in Chapter 4 Discuss or assign these Lab Overview Questions:

• Where have you seen image thresholding in use?
Answer: There are many places…the first one that comes to mind is a weatherman being placed in front of a map.

• Consider a system using two images. The first is a picture with containing object that you would like to separate from the background and the second picture if only the background with some noise added to it. How could you thresholding to remove the background from the object of interest?
Answer: Here is an idea: subtract the two and threshold just above the level. This results in a mask, which can be used to remove the object of interest. Note that the color that will be left out of the object of interest will be black or white (depending on the order of subtraction).

• Design a system which will separate out your portrait from the background your school ID. What additional blocks will you require for a colored image? How about separating objects from a video stream?
Answer: Open discussion. For the color image separation, you might use parallel masks for the 3 color planes or use them jointly with an appropriate threshold.

• Can you think of a practical real-world application where subtracting images is useful? Answer: How about a security camera? Image subtraction could be used to tell when the image changed--for example, when an intruder came into the room. Have the students build this worksheet in VAB?

• Can you think of a practical real-world application where adding images is useful? Answer: How about special effects? Did you ever wonder how Hollywood movie ghosts were made? Simple, by adding an image to its background. Summary Since images are just groups of numbers, anything we can do to a group of numbers, we can do to an image. In this lab we added two images, and subtracted two images. These kinds of operations make up a huge chunk of the tools engineers use to manipulate images. There is nothing complex or magical about them, just simple mathematical operations such as adding, subtracting, and multiplying.

• Can you think of a practical real-world application where adding a shifted image to itself is useful?
Answer: Sometimes, we want to blur an image to get a cool effect. Adding several shifted but otherwise identical images creates a blurring effect that is quite useful in some scenarios.

• Can you think of a practical real-world application where subtracting a shifted image from itself is useful?
Answer: What about planetary astronomy? In astronomy, we look at energy patterns (light, X-rays, gamma ray, infrared) in the sky and try to see what has changed, if anything, from previous nights. Sometimes, we can't get the picture positioned in an identical place in the sky. By shifting and subtracting images, we can register the two images and figure out what has changed. Maybe we can discover a new comet or asteroid this way!
Summary: This lab has introduced you to an important concept: the shifting of images. Image shifting (also called image translation) is an important processing tool in manipulating images. In later labs, you'll learn how we can use image shifts to empmasize edges in images, create more interesting image blurs, and remove noise from images.

• Why is image sharpening useful? Describe situations where you would want to use image sharpening.
Answer: Besides blurry photos of friends, image sharpening is used in exploration (astronomy), medicine (making X-ray images sharper), and entertainment (giving an enhanced effect to a movie scene).

• What problems might you come across by using image sharpening?
Answer: If the image is noisy, then sharpening the image usually increases the effective noise level. Sometimes, the noisier image is harder to look at or read. In such cases, it is more useful to process parts of the image that need enhancement, especially if these parts are less noisy than others.
Summary: Image sharpening is a useful procedure for making blurry pictures clearer. But beware: it can make noise in images larger, too.

• How might edge detection be used in practice?
Answer: It could be used to help a robot pick up and manipulate objects in its environment.

• What defines an edge in a digital image?
Answer: An edge is defined by a change in color or gray scale, usually at the boundaries of objects.
Summary: Edge detection is a basic building block of image processing systems. As you can see, the methods for edge detection are pretty simple and easy to do.