Digital signal processing
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This document covers digital signal processing (DSP) and its applications, highlighting the architecture and components of DSP processors, particularly the TMS320C54x. It explains key concepts like the short-time Fourier transform (STFT) and wavelet transform, including their definitions, applications, and the trade-offs in resolution. The document details various addressing modes, applications of DSP in different industries, and the fundamentals of signal transformation methods.
Digital signal processing
- 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.
- 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
- 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.
- 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
- 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