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Signals and Systems

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UNIT- I SIGNAL  ANALYSIS :
Analogy between vectors and signals, Orthogonal signal space, Signal approximationusing orthogonal functions, Mean square error, Closed or complete set of orthogonal functions,Orthogonality in complex functions, Exponential and sinusoidal signals, Concepts of Impulse function, Unit step function, Signum function.

UNIT- II FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS :
Representation of Fourier series, Continuous time periodic signals, properties of Fourier series, Dirichlet’s conditions, Trigonometric Fourier series and Exponential Fourier series, Complex Fourier spectrum

UNIT- III FOURIER TRANSFORMS :
Deriving Fourier transform from Fourier series, Fourier transform of arbitrary signal, Fourier transform of standard signals, Fourier transform of periodic signals, properties of Fourier transforms, Fourier transforms Involving
impulse function and Signum function. Introduction to Hilbert Transform.

UNIT-IV SIGNAL TRANSMISSION THROUGH LINEAR SYSTEMS :
Linear system, impulse response, Response of a linear system, Linear time invariant (LTI) system, Linear time variant (LTV) system, Transfer function of a LTI system. Filter characteristics of linear systems. Distortion less transmission through a system, Signal bandwidth, system bandwidth, Ideal LPF, HPF and BPF characteristics, Causality and Poly-Wiener criterion for physical realization, relationship between bandwidth and rise time.

UNIT-V CONVOLUTION AND CORRELATION OF SIGNALS :
Concept of convolution in time domain andfrequency domain, Graphical representation of convolution, Convolution property of Fourier transforms.Cross correlation and auto correlation of functions, properties of correlation function, Energy density spectrum, Parseval’s theorem, Power density spectrum, Relation between auto correlation function and energy/power spectral density function. Relation between convolution and correlation, Detection of periodic signals in the presence of noise by correlation, Extraction of signal from noise by filtering.

UNIT-VI SAMPLING :
Sampling theorem – Graphical and analytical proof for Band Limited Signals, impulse sampling, Natural and Flat top Sampling, Reconstruction of signal from its samples, effect of under sampling – Aliasing, Introduction to Band Pass sampling.

UNIT-VII LAPLACE TRANSFORMS :
Review of Laplace transforms, Partial fraction expansion, Inverse Laplace transform, Concept of region of convergence (ROC) for Laplace transforms, constraints on ROC for various classes of signals, Properties of L.T’s relation between L.T’s, and F.T. of a signal. Laplace transform of certain signals using waveform synthesis.

UNIT-VIII Z–TRANSFORMS :
Fundamental difference between continuous and discrete time signals, discrete time signal representation using complex exponential and sinusoidal components, Periodicity of discrete time using complex exponential signal, Concept of Z- Transform of a discrete sequence. Distinction between Laplace, Fourier and Z transforms. Region of convergence in Z-Transform, constraints on ROC for various classes of signals, Inverse Z-transform, properties of Z-transforms.

Speech recognition technology is used more and more for telephone applications like travel booking and information, financial account information, customer service call routing, and directory assistance. Using constrained grammar recognition, such applications can achieve remarkably high accuracy. Research and development in speech recognition technology has continued to grow as the cost for implementing such voice-activated systems has dropped and the usefulness and efficacy of these systems has improved. For example, recognition systems optimized for telephone applications can often supply information about the confidence of a particular recognition, and if the confidence is low, it can trigger the application to prompt callers to confirm or repeat their request. Furthermore, speech recognition has enabled the automation of certain applications that are not automatable using push-button interactive voice response (IVR) systems, like directory assistance and systems that allow callers to "dial" by speaking names listed in an electronic phone book.

Speaker identity is correlated with the physiological and behavioral characteristics of the speaker. These characteristics exist both in the spectral envelope (vocal tract characteristics) and in the supra-segmental features (voice source characteristics and dynamic features spanning several segments). The most common short-term spectral measurements currently used are Linear Predictive Coding (LPC)-derived cepstral coefficients and their regression coefficients. A spectral envelope reconstructed from a truncated set of cepstral coefficients is much smoother than one reconstructed from LPC coefficients.

Therefore it provides a stabler representation from one repetition to another of a particular speaker's utterances. As for the regression coefficients, typically the first- and second-order coefficients are extracted at every frame period to represent the spectral dynamics. These coefficients are derivatives of the time functions of the cepstral coefficients and are respectively called the delta- and delta-delta-cepstral coefficients.

Speech recognition technology is used more and more for telephone applications like travel booking and information, financial account information, customer service call routing, and directory assistance. Using constrained grammar recognition, such applications can achieve remarkably high accuracy. Research and development in speech recognition technology has continued to grow as the cost for implementing such voice-activated systems has dropped and the usefulness and efficacy of these systems has improved. For example, recognition systems optimized for telephone applications can often supply information about the confidence of a particular recognition, and if the confidence is low, it can trigger the application to prompt callers to confirm or repeat their request. Furthermore, speech recognition has enabled the automation of certain applications that are not automatable using push-button interactive voice response (IVR) systems, like directory assistance and systems that allow callers to "dial" by speaking names listed in an electronic phone book.

Speaker identity is correlated with the physiological and behavioral characteristics of the speaker. These characteristics exist both in the spectral envelope (vocal tract characteristics) and in the supra-segmental features (voice source characteristics and dynamic features spanning several segments). The most common short-term spectral measurements currently used are Linear Predictive Coding (LPC)-derived cepstral coefficients and their regression coefficients. A spectral envelope reconstructed from a truncated set of cepstral coefficients is much smoother than one reconstructed from LPC coefficients.

Therefore it provides a stabler representation from one repetition to another of a particular speaker's utterances. As for the regression coefficients, typically the first- and second-order coefficients are extracted at every frame period to represent the spectral dynamics. These coefficients are derivatives of the time functions of the cepstral coefficients and are respectively called the delta- and delta-delta-cepstral coefficients.

TEXT BOOKS :
1. Signals, Systems & Communications - B.P. Lathi, BS Publications, 2003.
2. Signals and Systems - A.V. Oppenheim, A.S. Willsky and S.H. Nawab, PHI, 2nd  Edn.

REFERENCES :
1. Signals & Systems - Simon Haykin and Van Veen, Wiley, 2nd Edition.
2. Network Analysis - M.E. Van Valkenburg, PHI Publications, 3rd Edn., 2000.
3. Fundamentals of Signals and Systems Michel J. Robert, MGH International Edition, 2008.
4. Signals, Systems and Transforms - C. L. Philips, J.M.Parr and Eve A.Riskin, Pearson education.3rdEdition, 2004.

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