digital signal processing
TRANSCRIPT
DIGITAL SIGNAL PROCESSINGAND IT’S APPLICATION
CONTENTI. Introduction
II. Architecture of processor
III. Basic building blocks
IV. Addressing modes
V. Differences between controller and processor
VI. Short time Fourier transform
VII.Types of STFT
VIII.Applications
IX. Wavelet transform
X. Types of wavelet transform
XI. Application
DSP Processor-TMS320C54x
• It is a specialized microprocessor with its
architecture optimized for operational needs of digital
signal processing
• We will have overview of the central processing unit (CPU) architecture, bus structure, memory structure, on-chip peripherals, and the instruction set.
Why DSP processor?
• DSP algorithm often require a large number of
mathematical operations to be performed quickly and
repeatedly on series of data samples, signals.
Analog Input
ADC DSP DACAnalog input
Microprocessor DSP processor
Microprocessor are typicallybuilt for a range of generalpurpose functions and
DSP chips are primarily built forreal time number crunching
normallyrun large blocks of softwarelike LINUX Windows etc.
They have dual memories (dataand program)
They are not often called for realtime computation
Sophisticated address generators
They lack a hardware multiplier Efficient external interface
Lack high memory bandwidth Powerful functional unit
Cost advantages Such as adder shift register etc.
Architecture
• Advanced, modified Harvard architecture that
maximizes processing power by maintaining one
program memory bus and three data memory buses.
• These DSP Families also provide a highly
specialized instruction set.
• Two reads and one write operation can be performed
in a single cycle.
• Instructions with parallel store and application-
specific instructions can fully utilize this architecture.
Functional Block diagram
Basic building blocks
• Central processing unit(CPU)
• Arithmetic logical unit(ALU)
• Accumulators
• Barrel shifter
• Multiplier/adder
• CSSU
Registers
• Status registers(ST0-ST1)
• Auxiliary registers(AR0-AR7)
• Temporary registers(TREG)
• Stack-pointer registers(SP)
• Circular Buffer-size registers(BK)
• Transition registers(TRN)
• Block-repeat registers(BRC,RSC,REA)
• Interrupt registers(IMR,IFR)
• Processor-mode status registers(PMST)
Power down modes
Addressing modes
• Immediate addressing mode
• Direct addressing mode
• In-direct addressing mode
• Absolute addressing mode
• MMR addressing mode
Microcontroller
• There is programmable input/output, memory and processor code.
• There are designed for embedded applications
• They have non power off erasable program memory inside, with EPROM store capabilities
Digital signal processor
• Signal processing done on a digital signal
• It is specialized processor optimized for operational needs
• Absence of flash program memory. They need to load data
Applications
• Automation and process control
• Automotive transportation
• Consumer & portable electronics
• Health tech & industrial
• Security and safety
• Space avionics and defense
Short-time Fourier Transform(STFT)
WHAT IS STFT????
• Fourier-related transform used to determinethe sinusoidal frequency and phase content oflocal sections of a signal as it changes overtime.
Types of STFT
STFT
Continuo
us-time
STFT
Discrete-
time STFT
Continuous-time STFT
Where w(t) is the window function (“Hann window or Gaussian
window”) x(t) is the signal to be transformed X(τ,ω) is essentially the Fourier Transform of x(t)w(t-τ),
(a complex function representing the phase and magnitude ofthe signal over time and frequency.)
Discrete-time STFTThe data to be transformed is broken up into chunks or frames and
each chunk is Fourier transformed.
Resolution Issues
“One of the pitfalls of the STFT is that it has a fixed
resolution.”
The width of the windowing function relates to how the signal
is represented—it determines whether
there is good frequency resolution (frequency components
close together can be separated)
or good time resolution (the time at which frequencies
change).
Better frequency resolution, but poor time resolution.
Better time resolution, but poor frequency resolution.
25ms window, precise time at which the signals change but the precise frequencies are difficult to identify.
1000ms window, allows the frequencies to be precisely seen but the time between frequency changes is blurred.
How to calculate?
• Steps :1. Choose a window function of finite length
2. Place the window on top of the signal at t=0
3. Truncate the signal using this window.
4. Compute the FT of the truncated signal, save the results.
5. Incrementally slide the window to the right
6. Go to step 3, until window reaches the end of thesignal
• Each FT provides the spectral information of a separate time-slice of the signal, providing simultaneous time and frequency information.
Applications of STFT
STFTs as well as standard Fourier transforms
and other tools are frequently used to analyse
music.
Audio engineers use this kind of visual to
gain information about an audio sample, such
as locating the frequencies of specific noises
(especially when used with greater frequency
resolution)..
Finding frequencies which may be more or
less resonant in the space where the signal
was recorded. This information can be used
for equalization or tuning other audio effects. A STFT used to analyze an audio signal across time
Wavelet Transform
History and Introduction
• The first recorded mention of what we now call a "wavelet" seems to be in 1909, in a thesis by Alfred Haar.
• The methods of wavelet analysis have been developed mainly by Y. Meyer and his colleagues,
History and Introduction
• what is a wavelet…?
• A wavelet is a waveform of effectively limited duration that has an average value of zero.
Wavelets vs. Fourier Transform
• In Fourier transform (FT) we represent a signal in terms of sinusoids
• FT provides a signal which is localized only in the frequency domain
• It does not give any information of the signal in the time domain
Wavelets vs. Fourier Transform
• Basis functions of the wavelet transform (WT) are small waves located in different times
• They are obtained using scaling and translation of a scaling function and wavelet function
• Therefore, the WT is localized in both time and frequency
Wavelet's properties
• Short time localized waves with zero integral value.
• Possibility of time shifting.
• Flexibility.
Scaling
Scale factor works exactly the same with wavelets:
f t a
f t a
f t a
t
t
t
( )
( )
( )
( )
( )
( )
;
;
;
1
2 12
4 14
Discrete Wavelet Transform
We can construct discrete WT via iterated (octave-band) filter banks
The Continuous Wavelet Transform (CWT)
The CWT is a complex-valued function of scale and position. If the signal is real-valued, the CWT is a real-valued function of scale and position. For a scale parameter, a>0, and position, b, the CWT is:
Wavelet Transform
And the result of the CWT are Wavelet coefficients .
Multiplying each coefficient by the appropriately scaled and shifted waveletyields the constituent wavelet of the original signal:
Wavelet function
a
by
abx
abba
yxyxyx
,1, ,,
• b – shift coefficient
• a – scale coefficient
• 2D function
abx
xba
a
1,
Applications
• Image compression
• Noise reduction by wavelet shrinkage
• Discontinuity Detection
• Automatic Target Reorganization
• Metallurgy for characterization of rough surfaces
• In internet traffic description for designing the service size
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