Deck 3: Fundamental Concepts in Video and Basics of Digital Audio

Question 1

Why is YUV (or YIQ) used for TV signal transmission instead of RGB or CMY?

Answer 1

Bandwidth reduction. Human vision has lower acuity in color perception, hence UV or IQ can be sent with lower bandwidth than $Y$ .

Question 2

Recall that for historical reasons NTSC uses a frame rate of $29.97 \mathrm{fps}$ .
But usually we capture video at 30 (or sometimes just 15) fps. To make these values jibe, a "drop frame" format is used. Naturally, however, one does not like to physically drop actual frames, so instead a few time codes are dropped per several minutes: we skip one time code assigned to frames every so often.
Devise a scheme for doing this so that we end up dropping an integer number of time codes per an integer number of minutes.

Answer 2

In 5 minutes, use not $5 * 60 * 30=9000$ , but just $5 * 60 * 29.97=8991=9000-9$ frames. This is sometimes phrased in terms of $10 \mathrm{~min}$ : in 10 minutes, use not $10 * 60 * 30=18000$ , but just $10 * 60 * 29.97=17982=18000$ 18 frames.

Question 3

When we view video on a computer, analog video is digitized and stored in the frame buffer of the video "frame grabber" card.
Suppose that the video is digitized at NTSC frame rate, has resolution $640 \times 480$ pixels, and is stored with a bit depth of 24 bits.
We're interested in displaying the captured video.
(a) What must be the minimal data rate of the system bus when data is moved from the video frame grabber to the memory for video display?
(b) How much storage capacity is required to store 1 minute of this video?

Answer 3

(a) Minimal Data Rate $=640$ x 480 pixels/frame $\times 24$ bits/pixels $\times 30$ frames $/ \mathrm{sec}=210.93 \mathrm{Mbps}$
(b) $210.93 \mathrm{Mbps} \times 60 \mathrm{sec}=1.545 \mathrm{~GB}$

Question 4

An original $8 \times 8$ color "checkerboard" CMY image is shown below in which the two colors are $\mathrm{C} 1:(\mathrm{C}=255, \mathrm{M}=155, \mathrm{Y}=255)$ and $\mathrm{C} 2:(\mathrm{C}=\mathrm{M}=\mathrm{Y}=100)$ , where $[0 . .255]$ is the range for the three color components.
You are asked to convert the color CMY image to YIQ images using 4:1:1 chroma subsampling. (In subsampling, you should use an averaging method so you are not selectively throwing away information from certain pixels.)

(a) Show all pixel values of each of the YIQ images generated from the given CMY color image.
(b) Besides their low resolution, do the chrominance images maintain enough information in this case? What does this tell?
Note: The relationship between RGB and YIQ is approximately:
$\left[\begin{array}{c}Y \\I \\Q\end{array}\right]=\left[\begin{array}{rrr}0.3 & 0.6 & 0.1 \\0.6 & -0.3 & -0.3 \\0.2 & -0.5 & 0.3\end{array}\right]\left[\begin{array}{l}R \\G \\B\end{array}\right]$

Question 5

We wish to develop a new Internet service, for doctors. Medical ultrasound is in the range 2-10 MHz; what should our sampling rate be chosen as?

Question 6

If a tuba is $20 \mathrm{~dB}$ louder than a singer's voice, what is the ratio of intensities of the tuba to the voice?

Question 7

Suppose we mistakenly always use the 0.75 point instead of the 0.50 point in a quantization interval as the decision point, in deciding to which quantization level an analog value should be mapped. Above, we have a rough calculation of SQNR. What effect does this mistake have on the SQNR?

Question 8

State the Nyquist frequency for the following digital sample intervals. Express the result in Hertz in each case.
(a) 1 millisecond
(b) 0.005 seconds
(c) 1 hour

Question 9

In an old Western movie, we notice that a stagecoach wheel appears to be moving backwards at $5^{\circ}$ per frame, even though the stagecoach is moving forward.
To what is this effect due? What is the true situation?

Question 10

The Pitch Bend opcode in MIDI is followed by two data bytes specifying how the control is to be altered. How many bits of accuracy does this amount of data correspond to? Why?

Question 11

The note "A above Middle C" (with frequency $440 \mathrm{~Hz}$ ) is note 69 in General MIDI. What MIDI bytes (in hex) should be sent to play a note twice the frequency of (i.e., one octave above) "A above Middle C" at maximum volume on channel 1? (Don't include start/stop bits.)
Information: An octave is 12 steps on a piano, i.e., 12 notes up.

Question 12

We have suddenly invented a new kind of music: "18-tone music", that requires a keyboard with 180 keys. How would we have to change the MIDI standard to be able to play this music?

Question 13

Suppose you wish to transmit a stereo audio signal through a 1 mega-bit/s connection in real time. Consider the following scenarios:
i) You are using a sampling frequency of 44.1 kHz. What is the maximum average number of bits can you use to represent an audio sample?
ii) You want to use 16 bit/sample/channel representation. What is the maximum sampling frequency? What will you need to do in order to avoid aliasing?
iii) You want to use a sampling frequency of 44.1 KHz, and also want use 16 bit/sample/ channel representation. What is the minimum compression ratio you need in order to transmit the audio signal?