Course reviews and continues the study of differential equations with the objective of introducing classical methods for solving boundary value problems. This course serves as a basis of the applications for differential equations‚ Fourier series and Laplace transform in various branches of engineering and sciences. This course emphasizes the role of orthogonal polynomials in dealing with Sturm-Liouville problems. 2. Text Book: Simmons G.F.‚ Differential Equations with Applications and Historical
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APPLICATION NOTE AN014 Understanding FFT Windows The Fast Fourier Transform (FFT) is the Fourier Transform of a block of time data points. It represents the frequency composition of the time signal. Figure 2 shows a 10 Hz sine waveform (top) and the FFT of the sine waveform (bottom). A sine wave is composed of one pure tone indicated by the single discrete peak in the FFT with height of 1.0 at 10 Hz. Introduction FFT based measurements are subject to errors from an effect known as leakage
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Frequency-Division Multiple Access) modulator and demodulator. The aim is to create a high level implementation of a high performance FFT for OFDM Modulator and Demodulator. This project concentrates on developing Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT). The work also includes in designing a mapping module‚ serial to parallel and parallel to serial converter module. The design uses 8point FFT and IFFT for the processing module which indicate that the processing
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02XXX-WTP-001-A March 28‚ 2003 NRZ Bandwidth (-3db HF Cutoff vs SNR) How Much Bandwidth is Enough? White Paper Introduction A number of customer-initiated questions have arisen over the determination of the optimum bandwidth for any transimpedance amplifier and subsequent filter employed in a fiber optic receiver module using NRZ coding. When asked what the optimum bandwidth for such a system‚ most engineers will respond with a number between 0.7 and 0.75 times the NRZ bitrate. The real answer
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2 Fundamental of signal processing Figure 1-10: The continuous-time unit step function The discrete-time unit-step function The discrete-time unit-step function is denoted as u [ n ] ‚ and is defined mathematically by: 0 u [ n] = 1 and its plot is shown in Figure 1-11. for n = −1‚ −2‚ −3‚ for n = 0‚1‚ 2‚3‚ 4‚ u (n) 1 • • • • • −4 −3 −2 −1 0 1 2 3 n Figure 1-11: The discrete-time unit step function The amplitude scaling If A ‚ is an arbitrary nonzero real number‚ than
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Circuits & Signals EEE/ INSTR C272 BITS Pilani Pilani Campus p ANU GUPTA EEE Time-domain analysis BITS Pilani Pilani Campus p Response of a LTIC system time-domain analysis linear‚ time-invariant‚ continuous-time (LTIC) systems--Total response = zero-input response + zero-state response zero-input response component that results only from the initial i t t th t lt l f th i iti l conditions at t = 0 with the input f(t) = 0 for t ≥ 0‚ zero-state zero state response component that
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IEEE SIGNAL PROCESSING LETTERS‚ VOL. 21‚ NO. 7‚ JULY 2014 829 Discrete Anamorphic Transform for Image Compression Mohammad H. Asghari‚ Member‚ IEEE‚ and Bahram Jalali‚ Fellow‚ IEEE Abstract—To deal with the exponential increase of digital data‚ new compression technologies are needed for more efficient representation of information. We introduce a physics-based transform that enables image compression by increasing the spatial coherency. We also present the Stretched Modulation Distribution‚ a
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Q-A. Find the Laplace transform of the following functions 1. f (t) = t − 1‚ 0 < t < 3; 7‚ t > 3. 2. f (t) = cos t − 0‚ 2π 3 ‚ 0 2π . 3 2π ; 3 4‚ 0 < t < 1; −2‚ 1 < t < 3; 3. f (t) = 5‚ t > 3. 5. f (t) = 3t3 + e−2t + t 3 7. f (t) = cos3 2t 9. f (t) = sin (3t + 5) 11. f (t) = e−3t sin2 t 13. f (t) = 7T 15. f (t) = e−3t (cos (4t) + 3 sin (4t)) 17. f (t) = teat 19. f (t) = t sin2 3t 21. f (t) = t2 e−2t cos t 23. f (t) = t cos (7t + 9) 25. f (t) = 27. f (t) = sin2 t t e−t sin t t 1 2
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at ) sin ( at ) - at cos ( at ) cos ( at ) - at sin ( at ) sin ( at + b ) sinh ( at ) e at sin ( bt ) e at sinh ( bt ) t ne at ‚ n = 1‚ 2‚3‚K uc ( t ) = u ( t - c ) Heaviside Function F ( s ) = L { f ( t )} 1 s n! s n +1 Table of Laplace Transforms f ( t ) = L -1 {F ( s )} F ( s ) = L { f ( t )} 1 s-a G ( p + 1) s p +1 1 × 3 × 5L ( 2n - 1) p 2n s 2 s 2 s + a2 s2 - a2 2 n+ 1 2. 4. 6. 8. 2 e at t p ‚ p > -1 t n- 1 2 p 2s a 2 s + a2 2as 2 3 2 ‚ n = 1‚ 2‚3‚K cos ( at
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Submitted To The Department of Electronics and Computer Engineering Submitted By Dhruba Adhikari Familiarization with Basic CT/DT functions Objective The basic objective of this lab was to be familiar with MATLAB‚ one of the most famous tools used in Signal Analysis and Processing. Theory Impulse Signal The impulse function‚ also known as Dirac delta function or Dirac impulse‚ is defined by |
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