1. Multimedia Processing
Chapter 2.
Digital Data Acquisition

2. Introduction
Introduction

3. Issues
Issues
Sampling
Quantization
Bit Rate

4. Sampling xs (n )= x (nT) , where T is the sampling period
f=1/T is the sampling frequency
In reality, more complex, as sampling comes with filtering
Surprisingly, we may not lose information in sampling

5. Quantization
Quantization
quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively-small set of discrete symbols or integer values.
Irreversible and lossy.

6. 24-bit RGB color 16 colors Quantization 6 bits 5 bits 4 bits 3bits

7. Bit Rate Bit Rate = Sampling rate × Quantization per sample
Audio (MP3)
32 kbit/s — MW (AM) quality
96 kbit/s — FM quality
128–160 kbit/s — Standard Bitrate quality; difference can sometimes be obvious (e.g. bass quality192 kbit/s — DAB (Digital Audio Broadcasting) quality. Quickly becoming the new 'standard' bitrate for MP3 music; difference can be heard by few people
224–320 kbit/s — Near CD quality. Sound is nearly indistinguishable from most CDs.

8. 8 kbit/s — telephone quality (using speech codecs)
Bit Rate
Other audio
800 bit/s — minimum necessary for recognizable speech (using special-purpose FS-1015 speech codecs)
8 kbit/s — telephone quality (using speech codecs)
500 kbit/s–1 Mbit/s — lossless audio
1411 kbit/s — PCM sound format of Compact Disc Digital Audio

9. 128 – 384 kbit/s — business-oriented videoconferencing system quality
Bit Rate
Video (MPEG2)
16 kbit/s — videophone quality (minimum necessary for a consumer-acceptable "talking head" picture)
128 – 384 kbit/s — business-oriented videoconferencing system quality
1.25 Mbit/s — VCD quality
5 Mbit/s — DVD quality
15 Mbit/s — HDTV quality
36 Mbit/s — HD DVD quality
54 Mbit/s — Blu-ray Disc quality

10. Signals and Systems Continuous and smooth Continuous and not smooth
Neither smooth nor continuous
Odd/Even
Periodic: f(x+T)=f(x)
Compact support: 0 outside finite interval
g(t) periodic version of f(t): g(t)=Σkf(t-kT)

11. Linear Time Invariant Systems Linearity:
Signals and Systems
Linear Time Invariant Systems
Linearity:
yk(t) is the output resulting from the sole input xk(t).
Time invariance means that whether we apply an input to the system now or T seconds from now, the output will be identical, except for a time delay of the T seconds. If the output due to input x(t) is y(t), then the output due to input x(t − T) is y(t − T). More specifically, an input affected by a time delay should effect a corresponding time delay in the output, hence time-invariant.

12. Signals and Systems
Time/frequency

13. The convolution theorem states that
Signals and Systems
Convolution
The convolution of  f   and   g    is written  f*g  . It is defined as the integral of the product of the two functions after one is reversed and shifted.
The convolution theorem states that

14. Signals and Systems
Useful signals
The Dirac delta or Dirac's delta is a mathematical construct introduced by the British theoretical physicist Paul Dirac. Informally, it is a function representing an infinitely sharp peak bounding unit area: a function δ(x) that has the value zero everywhere except at x = 0 where its value is infinitely large in such a way that its total integral is 1.

15. Signals and Systems
Sifting property

16. Signals and Systems
Comb
A Dirac comb is an infinite series of Dirac delta functions spaced at intervals of T.

17. Signals and Systems
Step function

18. Signals and Systems
Box

19. Signals and Systems
Sinc Function

20. The Fourier Transform
The Fourier Transform
Fourier series are named in honor of Joseph Fourier ( ), who made important contributions to the study of trigonometric series, after preliminary investigations by Euler, d'Alembert, and Bernoulli. He applied this technique to find the solution of the heat equation, publishing his initial results in 1807, and publishing his Théorie analytique de la chaleur in 1822.

21. This could not be solved analytically before!
The Fourier Transform .
Fourier
This could not be solved analytically before!

22. What he said The Fourier Transform Multiplying both sides by
and then integrating from y = − 1 to y = + 1 yields:
For periodic functions of period T=1
Harmonic decomposition

23. Lagrange, Laplace, Legendre, :
The Fourier Transform
What they said
Lagrange, Laplace, Legendre, :
...the manner in which the author arrives at these equations is not exempt of difficulties and [...] his analysis to integrate them still leaves something to be desired on the score of generality and even rigour.
Existence?
Convergence?
Why exponentials?
Finite support functions?

24. Fourier thought any function would work (not true)
The Fourier Transform
Properties
Fourier thought any function would work (not true)
Discontinuities (Gibbs effect)

25. The Fourier Transform
Examples

26. Finite support  Infinite support Delta  constant Sinc  box
The Fourier Transform
Properties: duality
|F(ω)|2 =|f(t)| 2
Periodic  Periodic
Finite support  Infinite support
Delta  constant
Sinc  box
Gaussian  Gaussian
Comb  Comb

27. The Uniform Sampling Theorem
A bandlimited signal f(t) with max frequency ωF is fully determined from its samples f (nT) is 2π/T > 2 ωF
The continuous signal can then be reconstructed from its samples f (nT) by convolution with the filter r(t)=sinc(ωF(t-nT)/2π)

28. The Uniform Sampling Theorem
Illustration

29. The Uniform Sampling Theorem
Aliasing
Artifacts resulting from an improper sampling frequency.
Sound
Images (Moire)
Video (wagon wheel)

30. The Uniform Sampling Theorem

31. The Uniform Sampling Theorem
Anti Aliasing
In practice: smooth the data with a low-pass filter before sampling
Issues: ideal filters cannot be realized

32. Homework
Homework
Read Text Chapter 3.
Prepare Presentation