Digital signal processing

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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