DSP
What is DSP?
• DSP: Digital Signal Processing---Using a
digital process (e.g., a program running on a
microprocessor) to modify a digital
representation of a signal
• DSP: Digital Signal Processor---a
specialized microprocessor designed for
handling DSP tasks.
Types of Signals
• Analog signal: A continuous signal in both
value (magnitude) and time
• Digital: A signal that is discrete in both
value and time (or other dimension such as
space)
Transducers convert analog signals to
time-varying electrical voltages
• P3 fig1-1
Source of analog signals and how they
are converted to digital ones
• P20 table 2-1
Nyquist’s Sampling Theorem
• Analog to digital conversion: the analog
signal must be sampled at twice the highest
frequency component of the signal to avoid
distortion.
• Example, for digital audio CD, the sampling
rate is 44.1 kHz (based on the highest
human audible frequency of around 20
KHz)
Illustration of the Sampling
Process
• P4 fig 1-2
Speed of DSP Critical for RealTime Applications
• Example: sampling rates are 44.1 kHz for
audio CD and 48 kHz for digital audio tape
(DAT) unit. A DSP CD-to-tape converter
must be ready to accept a new sample every
22.6 sec (or 1/44100 sec) from the CD
source and produce a new output sample for
the DAT every 20.8 sec (1/48000 sec).
Advantages of DSP over analog signal
processing (ASP)
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Insensitive to environment
Insensitive to component tolerances
Predictable, repeatable (exact) behavior
Programmability (flexibility)
Size: small than analog counterpart in general
Continued rapid advancement of VLSI technology
Capacity utilization of high BW transmission links
Design tools are available
Applications of DSP
• P8 tab 1-1
Major DSP Vendors
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Analog Devices
AT&T
Lucent
Motorola
NEC
Texas Instruments
Zoran
Fourier Analysis
Fourier Analysis (continued)
Fourier Analysis (continued)
Fourier Analysis (continued)
Fourier Analysis (continued)
Fourier Analysis (continued)
Sinusoidal components (continued):
1 Hz square wave
• P30 fig 2-9, 10
Frequency components of 1 Hz
squarewave
Visualization of a signal (Dual Tone Multiple
Frequency) in time and frequency domain
• P23 fig 2-3, 4
Fourier series: sinusoidal
components of a signal
• P 28 fig 2-7, 8
Filters
• Filter is used to “shape” (selectively change
or modify the magnitude and phase of the
input signal as a function of frequency) the
signals.
Functions of Filters
• Remove noise/interference
• Spectral analysis: analyze the frequency
contents of a signal
• Synthesis: generate simple tones to human
voice
• …
Types of filters
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Low-pass
High-pass
All-pass (amplifier)
Band-pass
Band-stop (notch)
Arbitrary pass-band
comb
Ideal versus real filter: low-pass
• P67 fig 3-3
The meaning of db or decibel
• P45 tab 2-3
Bassband and bandpass filters
• P38 fig 2-18
Types of filters
• High pass & bandpass
• p70
Types of filters (continued)
• Bandpass & bandstop
• P71 fig 3-8
Types of filters (continued)
• Comb filter
• p74 fig 3-12
The characteristics of a real
baseband (lowpass) filter
• P41 fig 2-21
Implementation of filters
• Analog filters
• Digital filters: one of the major applications
of DSP; offer many advantages over their
analog counterpart as described earlier.
Example of filter (notch filter)
application: removal of noise
• P66 fig 3-2
Correlation: compare earlier sections of
signals with current section (autocorrelation); special case of filtering.
A typical DSP chip (IC)
• P11 tab 1-2
Limitations of DSP
• Speed: being programmable means 10 to
100 times slower than the hardwired tech.
• Processing: program is simple but needs be
done quickly (lots of MAC instructions)
• Precision: use fixed point format with
limited precision to save chip space
• Digital signal required more BW than the
corresponding analog signal
Visualizing analog signals in time
domain
• P22 figs 2-1 & 2-2
Human Speech Spectrum
Describing a system in time domain:
the impulse response
• An impulse (math.) excites a system equally
at all frequencies.
• P47 fing 2-23
Labeling a system in time domain
• P49 fig 2-25
Impulse response of an elliptical filter
• P48 fig 2-24
The frequency response function
• H(j), where  ( or ) is signal frequency;
it is also known as the transfer function
• H(j) can be generalized to H(s), the
system function, where s =  + j, a
quantity known as complex frequency.
Depending on whether  is positive or
negative, the signal strength increases or
decreases in time, as show in the following
example.
Example of complex frequency
• P54 fig 2-30
The complex frequency s-plane
• P57 fig 2-31
Properties of a linear system
• P59 fig 2-33
Poles and zeros of the transfer function
• P85 equations
Poles and zeros (continued)
• P86 equation & fig 3-22
Poles and zeros example
Poles and zeros (continued)
• P88 fig 3-24
Poles and zeros (continued)
• P89 fig 3-25
Analog, discrete-time, and digital signals
• P94 fig 4-1
Sampling: 1st step to convert an analog
signal to digital one
• Nyquist rate: minimum sampling frequency
to avoid undesirable effect (aliasing)
• p96 fig 4-2
Sampling theorem
Sampling theorem (continued)
Sampling theorem (continued)
Describing discrete-time system
• H(z): the system or transfer function, where
z is the complex frequency in polar
coordinates
The polar coordinate and z-plane
• P110 fig 4-14
More on H(z) and z-plane
• P111 equations, p112 fig 4-15
More on H(z)
Example for a simple system
• P113 fig 4-16
H(z) and the difference equations
• H(s): Laplace transformation of h(t)
• H(z): z-transformation of the DT (discrete
time) impulse response of h(n)
• h(t) is a differential equation
• h(n) is described using difference equations,
meaning current output of the system is a
linear combination of current input samples,
past input samples, and past output samples.
The difference equations
• General form:
• p116 equation 4-14
• Difference equations can be translated
easily into computer programs (run on DSP)
Digital filters
• The IIR (infinite impulse response) filter
• p148 fig 4-33
The FIR (finite impulse response) filter
• P149 fig 4-34
IIR versus FIR digital filters
• P152 tab 4-6
DSP implementation of filters
• DSP architecture: