Digital signal processing is a specialized microprocessor with its architecture optimized for operational needs of digital signal processing Application's of DSP like STFT and Wavelet transform has been explained in detail with images.

1. DIGITAL SIGNAL PROCESSING
AND IT’S APPLICATION

2. CONTENT
I. 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

3. 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.

4. 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 DAC
Analog
input

5. Microprocessor DSP processor
Microprocessor are typically
built for a range of general
purpose functions and
DSP chips are primarily built for
real time number crunching
normally
run large blocks of software
like LINUX Windows etc.
They have dual memories (data
and program)
They are not often called for real
time 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.

6. 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.

7. Functional Block diagram

8. Basic building blocks
• Central processing
unit(CPU)
• Arithmetic logical unit(ALU)
• Accumulators
• Barrel shifter
• Multiplier/adder
• CSSU

9. 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

10. Addressing modes
• Immediate addressing mode
• Direct addressing mode
• In-direct addressing mode
• Absolute addressing mode
• MMR addressing mode

11. 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

12. Applications
• Automation and process
control
• Automotive transportation
• Consumer & portable
electronics
• Health tech & industrial
• Security and safety
• Space avionics and defense

13. Short-time Fourier Transform
(STFT)

14. WHAT IS STFT????
• Fourier-related transform used to determine
the sinusoidal frequency and phase content of
local sections of a signal as it changes over
time.

15. Types of STFT
STFT
Continuo
us-time
STFT
Discrete-
time STFT

16. 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 of
the signal over time and frequency.)

17. Discrete-time STFT
The data to be transformed is broken up into chunks or frames and
each chunk is Fourier transformed.

18. 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.

19. 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.

20. 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

21. • Each FT provides the spectral
information of a separate time-slice of
the signal, providing simultaneous time
and frequency information.

22. 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

23. Wavelet Transform

24. 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,

25. History and Introduction
• what is a wavelet…?
• A wavelet is a waveform of effectively limited
duration that has an average value of zero.

26. 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

27. 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

28. Wavelet's properties
• Short time localized waves with zero integral
value.
• Possibility of time shifting.
• Flexibility.

29. Scaling
 Scale factor works exactly the same with
wavelets:
f t a
f t a
f t a
t
t
t
( )
( )
( )
( )
( )
( )
 
 
 



;
;
;
1
2 1
2
4 1
4

30. Discrete Wavelet Transform
We can construct discrete WT via iterated (octave-band) filter banks

31. 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:

32. Wavelet Transform
 And the result of the CWT are Wavelet
coefficients .
 Multiplying each coefficient by the
appropriately scaled and shifted wavelet
yields the constituent wavelet of the original
signal:

33. Wavelet function
   a
by
a
bx
a
bba
yx
yxyx

 ,1
, ,,
• b – shift
coefficient
• a – scale
coefficient
• 2D function
  a
bx
xba

 a
1
,

34. 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

35. THANK YOU