1 of 6

ELEN0450 · MULTIMEDIA SYSTEMS

Sampling and quantization

Lecture 1 — Part B · Exercises

​

Gavage Cédric

2 of 6

REMINDER

Formula sheet

Sampling condition f_s ≥ 2 · f_max

Nyquist frequency f_N = 1 / (2 · T_s) = f_s / 2

Quantization levels N bits → 2^N levels

Dither levels n×n matrix → n² + 1 levels

Raw audio bit rate f_s × N × n_channels

Raw video bit rate W × H × bpp × fps

Unit conversion 1 byte = 8 bits

3 of 6

EXERCISE 1

Give the minimum sampling frequency for:

a) A telephone signal band-limited to 4 kHz

b) Music covering the full range of human hearing,

up to 20 kHz

c) A medical ultrasound signal occupying

the 2 – 10 MHz band

The same second of signal

a) Telephone speech

4 kHz

b) Music

20 kHz

c) Medical ultrasound

10 MHz

4 of 6

EXERCISE 2

A sunset sky fades smoothly from orange to blue. Store it on too few bits

and the gradient breaks into visible bands.

a) How many distinct levels for 1, 8, 10 and 16 bits?

b) A grayscale image has 4096 shades.

On how many bits is it coded?

c) A colour image is coded on 24 bits, 8 per channel.

How many colours can it represent?

What “N bits” actually means

1 bit

2 bits

3 bits

4 bits

5 of 6

EXERCISE 3

Call a friend and their voice sounds noisy. Put the same voice on a CD

and it sounds like they are in the room.

  • Digital telephony samples speech at 8 kHz on 8 bits, in mono.

​

  • CD audio samples at 44.1 kHz on 16 bits, in stereo.

Compute the raw bit rate of each one.

What factor separates them, and where does it come from?

Two devices, two sets of numbers

Digital telephone

8 kHz

8 bits

mono

CD audio

44.1 kHz

16 bits

stereo

6 of 6

EXERCISE 4

A YouTube video is nothing but a stack of still pictures, thirty of them

every second. Let us open one up and count what is inside.

For a 640 × 480 video, colour at 8 bits per channel, 30 frames per second:

a) How many pixels does the frame contain in total, and how many bytes are required to store this single frame?

b) What is the video bit rate, expressed in MB/s and in Mb/s

c) How many bytes is it for an hour ?

Three sampling axes

W × H

space

fps

time