EEE 420 Digital Signal Processing

1
EEE 420 Digital Signal Processing

• Instructor Erhan A. Ince
• E-mail erhan.ince_at_emu.edu.tr
• Web page address
• http//faraday.ee.emu.edu.tr/eee420
• http//faraday.ee.emu.edu.tr/eaince

2
Digital Signal Processing And Its Benefits

• By a signal we mean any variable that carries or
  contains some kind of information that can be
  conveyed, displayed or manipulated.
• Examples of signals of particular interest are
• speech, is encountered in telephony, radio, and
  everyday life
• biomedical signals, (heart signals, brain
  signals)
• Sound and music, as reproduced by the compact
  disc player
• Video and image,
• Radar signals, which are used to determine the
  range and bearing
• of distant targets

3

• Attraction of DSP comes from key advantages such
  as
• Guaranteed accuracy (accuracy is only
  determined by the number of bits used)
• Perfect Reproducibility Identical
  performance from unit to unit
• ie. A digital recording can be copied or
  reproduced several times with no
• loss in signal quality
• No drift in performance with temperature and
  age
• Uses advances in semiconductor technology to
  achieve
• (i) smaller size
• (ii) lower cost
• (iii) low power consumption
• (iv) higher operating speed

4

• Disadvantages of DSP
• Speed and Cost
• DSP designs can be expensive, especially
  when large bandwidth signals
• are involved. ADC or DACs are either to
  expensive or do not have sufficient
• resolution for wide bandwidth
  applications.
• DSP designs can be time consuming plus need
  the necessary resources
• (software etc)
• Finite word-length problems
• If only a limited number of bits is
  used due to economic considerations
• serious degradation in system
  performance may result.

5
Application Areas

• Image Processing Instrumentation/Control Spee
  ch/Audio Military
• Pattern recognition spectrum analysis
  speech recognition secure
  communications
• Robotic vision noise reduction
  speech synthesis radar processing
• Image enhancement data compression
  text to speech sonar processing
• Facsimile position and rate digital
  audio missile guidance
• animation control equalization
• Telecommunications Biomedical Consumer
  applications
• Echo cancellation patient monitoring cellular
  mobile phones
• Adaptive equalization scanners UMTS
• ADPCM trans-coders EEG brain mappers digital
  television
• Spread spectrum ECG Analysis digital cameras
• Video conferencing X-Ray storage/enhancement
  internet phone
• etc.

6
Key DSP Operations

• Convolution
• Correlation
• Digital Filtering
• Discrete Transformation
• Modulation

7
Convolution

• Convolution is one of the most frequently used
  operations in DSP. Specially in digital filtering
  applications where two finite and causal
  sequences xn and hn of lengths N1 and N2 are
  convolved

where, n 0,1,.,(M-1) and M
N1 N2 -1 This is a multiply and accumulate
operation and DSP device manufacturers have
developed signal processors that perform this
action.
8
Correlation

• There are two forms of correlation
• 1. Auto-correlation
• 2. Cross-correlation
• The cross-correlation function (CCF) is a measure
  of the similarities or shared properties between
  two signals. Applications are cross-spectral
  analysis, detection/recovery of signals buried in
  noise, pattern matching etc.
• Given two length-N sequences xk and yk with
  zero means, an estimate of their
• cross-correlation is given by

Where, rxy(n) is an estimate of the cross
covarience
9

• The cross-covarience is defined as

10

• An estimate of the auto-correlation
  of an length-N sequence xk with zero mean is
  given by

11
Digital Filtering

• The equation for finite impulse response (FIR)
  filtering is

Where, xk and yk are the input and output
of the filter respectively and hk
for k 0,1,2,,N-1 are the filter coefficients
12
Filter structure

• A common filtering objective is to remove or
  reduce noise from a wanted signal.

13

(a) (b)
(c)
(d) (e)
(f)
Figure Reconstructed bi-level text images for
degradation caused by h1 and AWGN. (a) Original,
(b) 2D Inverse, (c) 2D Wiener, (d)PIDD, (e) 2D
VA-DF, (f) PEB-FCNRT

14
Discrete Transformation

• Discrete transforms allow the
  representation of discrete-time signals in the
  frequency domain or the conversion between time
  and frequency domain representations.
• Many discrete transformations exists but the
  discrete Fourier transform (DFT) is the most
  widely used one.
• DFT is defined as

IDFT is defined as
15
MATLAB function for DFT

• function Xk dft (xn,N)
• Computes Discrete Fourier Transform
• ------------------------------------------------
  -------
• Xk DFT coefficient array over 0lt k lt N-1
• xn N-point finite duration sequence
• N Length of DFT
• n 01N-1
• k 01N-1
• WN exp(-j2pi/N)
• nk n.k
• WNnk WN . nk
• Xk xn WNnk

16
Matlab Function for IDFT

• function xn idft(Xk,N)
• Computes the Inverse Discrete Transform
• n 01N-1
• k 01N-1
• WN exp(-j2pi/N)
• nknk
• WNnk WN .(-nk)
• xn (Xk WNnk) / N

17
Example

• Let xn be a 4-point sequence

gtgtx1, 1, 1, 1 gtgtN 4 gtgtX
dft(x,N) gtgtmagX abs(X) gtgtphaX angle(X)
180/pi magX 4.0000 0.0000 0.0000
0.0000 phaX 0 -134.981 -90.00 -44.997
18
Modulation

• Discrete signals are rarely transmitted over
  long distances or stored in large quantities in
  their raw form.
• Signals are normally modulated to match their
  frequency characteristic to those of the
  transmission and/or storage media to minimize
  signal distortion, to utilize the available
  bandwidth efficiently, or to ensure that the
  signal have some desirable properties.
• Two application areas where the idea of
  modulation is extensively used are
• 1. telecommunications
• 2. digital audio engineering
• High frequency signal is the carrier
• The signal we wish to transmit is the modulating
  signal

19

• Three most commonly used digital modulation
  schemes for transmitting
• Digital data over bandpass channels are
• Amplitude shift keying (ASK)
• Phase shift keying (PSK)
• Frequency shift keying (FSK)

When digital data is transmitted over an all
digital network a scheme known As pulse code
modulation (PCM) is used.