Computação Visual e Multimédia
10504: Mestrado em Engenharia Informática
Chap. 1 — Digital Signal Processing: Basics
Module Introduction
http://en.wikipedia.org/wiki/Frequency
What is a signal?
Chapter 1: Digital Signal Processing: Basics
Sinusoidal waves of various frequencies; the bottom waves have higher frequencies
than those above. The horizontal axis represents time.
Chapter 1: Digital Signal Processing: Basics
http://www.bbc.co.uk/schools/gcsebitesize/science/aqa/radiation/anintroductiontowavesrev2.shtml
Amplitude, wavelength, frequency, velocity, period
Analogical vs. Digital Signals
Chapter 1: Digital Signal Processing: Basics
http://en.wikibooks.org/wiki/Digital_Signal_Processing/Sampling_and_Reconstruction
http://www.cs.cf.ac.uk/Dave/Multimedia/node149.html
Sampling
Chapter 1: Digital Signal Processing: Basics
http://mathworld.wolfram.com/SamplingTheorem.html
Chapter 1: Digital Signal Processing: Basics
Nyquist’s sampling theorem
f (t)
€
f (t)
€
s(t)
∞
s(t) =
∑δ (t − nt )
0
http://www.cs.cf.ac.uk/Dave/Multimedia/node149.html
n =−∞
t0
€
f s (t)
€
∞
f s (t) = f (t)s(t) = f (t) ∑δ (t − nt 0 )
n =−∞
€
€
€
http://www.cs.cf.ac.uk/Dave/Multimedia/node149.html
Example: playing piano on telephone?
Chapter 1: Digital Signal Processing: Basics
Humans hear frequencies from 20Hz up to 20kHz.
Chapter 1: Digital Signal Processing: Basics
http://www.cs.cf.ac.uk/Dave/Multimedia/node149.html
Example: more about aliasing in music…
Chapter 1: Digital Signal Processing: Basics
http://en.wikipedia.org/wiki/Aliasing#Folding
Aliasing
Aliasing example of the A letter in Times New
Roman. Left: aliased image, right: antialiased image.
Quantization
Chapter 1: Digital Signal Processing: Basics
analog signal
http://en.wikipedia.org/wiki/Aliasing#Folding
sampled signal
quantized signal
Quantization levels
Chapter 1: Digital Signal Processing: Basics
analog signal
http://en.wikipedia.org/wiki/Aliasing#Folding
sampled signal
quantized signal
http://en.wikipedia.org/wiki/Aliasing#Folding
Noise
Chapter 1: Digital Signal Processing: Basics
http://en.wikipedia.org/wiki/Aliasing#Folding
2
Psignal ⎛ Asignal ⎞
SNR =
= ⎜
⎟
Pnoise ⎝ Anoise ⎠
€
Psignal – power of signal
Pnoise – power of noise
http://en.wikipedia.org/wiki/Signal-to-noise_ratio
Signal-to-noise ratio (SNR)
Chapter 1: Digital Signal Processing: Basics
Chapter 1: Digital Signal Processing: Basics
Noise models
http://en.wikipedia.org/wiki/Aliasing#Folding
h(x, y) = d(x, y) ⊗ f (x, y) + n(x, y)
€
convolution
http://en.wikipedia.org/wiki/Aliasing#Folding
Noise types
http://en.wikipedia.org/wiki/White_noise
Chapter 1: Digital Signal Processing: Basics
What is DSP?
Digital Signal Processing
Chapter 1: Digital Signal Processing: Basics
Analysing and changing information which is measured as
discrete sequences of numbers
Chapter 1: Digital Signal Processing: Basics
http://en.wikipedia.org/wiki/Aliasing#Folding
DSP Implementation
Analog
Signal
sampling
Digital
Signal
DSP
Digital
Signal
Analog
Signal
reconstruction
Main limitations of DSP
Chapter 1: Digital Signal Processing: Basics
http://en.wikipedia.org/wiki/Aliasing#Folding
Sampling signals that are analog in nature leads to …
Loss of Information!
http://www-sigproc.eng.cam.ac.uk/~op205/3F3_1_Introduction_to_DSP.pdf
http://en.wikipedia.org/wiki/Aliasing#Folding
Chapter 1: Digital Signal Processing: Basics
Advantages of Digital over Analog Signal Processing
DSP Applications: Radar and Sonar
Chapter 1: Digital Signal Processing: Basics
DSP Applications: Biomedical Devices
Person wearing
electrodes for ECG
Chapter 1: Digital Signal Processing: Basics
Person wearing
electrodes for EEG
DSP Applications: Speech
Chapter 1: Digital Signal Processing: Basics
DSP Applications: Music
Chapter 1: Digital Signal Processing: Basics
DSP Applications: Communications
Chapter 1: Digital Signal Processing: Basics
DSP Applications: Image Processing
Chapter 1: Digital Signal Processing: Basics
Summary
Chapter 1: Digital Signal Processing: Basics