System analysis and signal processing

Size: px

Start display at page:

Download "System analysis and signal processing"

Eustace Parks
5 years ago
Views:

System analysis and signal processing with emphasis on the use of MATLAB PHILIP DENBIGH University of Sussex ADDISON-WESLEY Harlow, England Reading,

1 System analysis and signal processing with emphasis on the use of MATLAB PHILIP DENBIGH University of Sussex ADDISON-WESLEY Harlow, England Reading, Massachusetts Menlow Park, California New York Don Mills, Ontario Amsterdam Bonn Sydney Singapore Tokyo # Madrid San Juan : Milan Mexico City Seoul Taipei

1. Getting started in MATLAB and an introduction to systems and signal processing 1 1.1 Preview 1 1.2 Getting started in MATLAB 1 1.2.1 Variables 2 1.2.2 Sequences, arrays and vectors 3 1.2.3 Generating vectors 4 1.

2 1. Getting started in MATLAB and an introduction to systems and signal processing Preview Getting started in MATLAB Variables Sequences, arrays and vectors Generating vectors Addressing vectors Array mathematics Multiple commands on one line and comments Element indexing and time indexing Augmenting a vector with zeros to correspond with an extended timing index vector Linear algebra and matrix operations Plotting data values Hardcopy Transfer of a figure to a word processor document M-files Some signals and systems terminology Some examples of analogue systems and analogue signal processing Some examples of digital systems and digital signal processing Justification for the digital processing of signals Some signals of special importance Summary Problems Impulse functions, impulse responses and convolution Preview The unit sample function (or discrete-time unit impulse function) Discrete-time impulse responses and the convolution sum Alternative forms and interpretations of the convolution sum Convolution using MATLAB Continuous-time impulse functions Continuous-time impulse responses and the convolution integral A graphical interpretation of the convolution integral Convolution of analogue signals using MATLAB Some examples of convolution not related to networks 50 V

vi Contents 2.11 Some properties of convolution 53 2.12 Deconvolution 53 2.13 Summary 54 2.14 Problems 54 3.

3 vi Contents 2.11 Some properties of convolution Deconvolution Summary Problems The steady state response of analogue networks to cosinusoids and to the complex exponential e >cot Preview The properties of network elements The difficulty of solving network equations The use of the complex exponential waveform exp(jwt) Impedance functions Inductance Resistance Capacitance Admittance functions Elements in series and in parallel Frequency transfer functions and Bode plots Summary Problems Phasors Preview Vector representation of cosinusoids Phasors and phasor diagrams Phasors in network analysis The use of phasors in power calculations The application of MATLAB to network analysis Phasors not related to network analysis Contra-rotating phasors Summary Problems Line spectra and the Fourier series Preview One-sided frequency domain descriptions of sinusoids and cosinusoids Two-sided frequency domain descriptions of cosinusoids Negative frequencies Periodic signals and the trigonometric Fourier series The exponential Fourier series Plotting line spectra using MATLAB Further properties and examples of Fourier series Summary Problems Spectral density functions and the Fourier transform Preview Energy signals and power signals 110

vii 6.3 The Fourier transform of an aperiodic energy signal 111 6.4 The Fourier transform of a rectangular pulse 112 6.5 The Fourier transform of an impulse 114 6.

4 vii 6.3 The Fourier transform of an aperiodic energy signal The Fourier transform of a rectangular pulse The Fourier transform of an impulse Symmetry in Fourier transforms Some physical insight into the evaluation of Fourier transforms The inverse Fourier transform Reconstruction of a waveform from its Fourier transform Fourier transforms of power signals Fourier transforms of periodic signals Cyclic frequency versus radian frequency Signal transmission through linear networks The importance of the Fourier transform in network analysis The energy density spectrum Power spectral density (PSD) The equivalence of convolution in one domain to multiplication in the other domain Some other properties of Fourier transforms Superposition Duality Compression and expansion The effect of a time shift on the Fourier transform The effect of a frequency shift on the inverse Fourier transform Differentiation and integration A selection of some important Fourier transforms Summary, Problems The sampling and digitization of signals Preview Overview of sampling and digitization Binary codes Analogue to digital and digital to analogue converters The 'flash'adc The weighted-resistor-network DAC The «-2«DAC The successive-approximation ADC Distortion due to sampling, and the sampling theorem Ideal sampling and the Fourier transform approach to the spectra of sampled signals Anti-aliasing filters The effect of holding sample amplitudes Dynamic range and quantization errors An introduction to the sampling of bandpass signals Summary Problems The discrete Fourier transform Preview An introduction to basis functions 167

8.3 Alternative sets of basis functions and orthogonality 169 8.4 Trigonometric basis functions for discrete signals 172 8.5 Digital frequency 176 8.6 The inverse discrete Fourier transform 178 8.

5 8.3 Alternative sets of basis functions and orthogonality Trigonometric basis functions for discrete signals Digital frequency The inverse discrete Fourier transform Notation and symbols Evaluating the coefficients of complex exponential basis functions The discrete Fourier transform The discrete Fourier transform pair Interpretation of the DFT Differences in the definitions of the continuous and discrete Fourier transforms The effect of sampling and windowing the waveform The effect of sampling and windowing the spectrum Summary of the relationship between the DFT and the continuous Fourier transform Reordering of DFT coefficients An alternative interpretation scheme Summary Problems The fast Fourier transform and some applications Preview Computational demands of the discrete Fourier transform Computational demands of the fast Fourier transform Spectral analysis Window functions for improving spectral estimates Zero-padding Spectrograms Linear convolution and periodic (or circular) convolution using the FFT Summary Problems The steady state response of analogue systems by consideration of the excitation e st Preview Impedance and admittance when the excitation is e 5t Transfer functions Further justification for the use of e 5t Pole-zero plots Frequency response from the pole-zero plot Frequency response using MATLAB The order of a transfer function, some examples of second-order systems, and Q Conjugate pole and conjugate zero pairs Impedance functions for non-electrical components and systems Transfer functions for electromechanical components and systems Summary Problems 258

ix 11. Natural responses, transients and stability 259 11.1 Preview 259 11.2 Natural response 259 11.3 The natural response of first-order systems 260 11.3.1 The natural current response of a series RC network 260 11.

6 ix 11. Natural responses, transients and stability Preview Natural response The natural response of first-order systems The natural current response of a series RC network The natural current response of a series RL network The complete response Transients Relationship between the natural response and the system poles and zeros The natural response of second-order systems The natural response of hybrid electrical and mechanical systems Stability Summary Problems The Laplace transform Preview The bilateral Laplace transform The unilateral Laplace transform Convergence A physical interpretation of the Laplace transform Applications of the Laplace transform to system analysis justification of the Laplace transform and a comparison with the Fourier transform s-plane plots and some more Laplace transforms The step function The exponentially decaying step function The ramp function At Sine and cosine functions Functions modified by an exponential decay Exponentially decaying sines and cosines Delayed functions Inverse Laplace transformation Interpreting signal waveforms from pole-zero plots The step function response of first-order systems The step function response of second-order systems System responses using MATLAB An introduction to automatic control Laplace transforms used directly for the solution of differential equations Laplace transforms used directly for the solution of integro-differential equations A comparison of Laplace transforms and phasors for system analysis Summary Problems Synthesis of analogue filters Preview Basic approach to filter design 323

13.3 Amplitude and delay distortion 324 13.4 Selecting a frequency response 327 13.5 Transfer functions and frequency responses of analogue filters using MATLAB 329 13.

7 13.3 Amplitude and delay distortion Selecting a frequency response Transfer functions and frequency responses of analogue filters using MATLAB Obtaining the transfer function corresponding to a desired frequency response Translating a transfer function into a filter design Design of passive lowpass filters using tables Impedance scaling Frequency scaling of lowpass filters Lowpass to bandpass transformation Lowpass to highpass transformation Passive bandstop filters Active lowpass filters Active highpass filters Active bandpass filters Delay equalizers Summary Problems An introduction to digital networks and the z transform Preview Structure of digital networks and the difference equation The impulse responses of digital networks - FIR and HR systems Other configurations of digital networks The hardware realization of digital networks An s-plane treatment of digital networks A z-plane treatment of digital networks Mapping between the s-plane and the z-plane The frequency response of a digital network from a geometrical interpretation of z-plane poles and zeros An analytical approach to the frequency response of a digital network Frequency responses and pole-zero plots using MATLAB The z transform Some important z transforms The unit step function The unit ramp The decaying exponential The damped cosinusoid f The damped sinusoid A direct derivation of the z transfer function The inverse z transform Discrete-time convolution using the z transform The responses of digital systems using MATLAB Transfer functions of sampled analogue systems An introduction to digital control systems The relationship between the z transform, the Fourier transform and the DFT 394

xi 14.21 Summary 397 14.22 Problems 397 15 Synthesis of digital filters 399 15.1 Preview 399 15.2 Filter design by pole-zero placement 399 15.

8 xi Summary Problems Synthesis of digital filters Preview Filter design by pole-zero placement Design of recursive digital filters based on the frequency response characteristics of analogue filters The impulse invariant technique The bilinear transformation technique Highpass, bandpass and bandstop filters Designing recursive digital filters with MATLAB Effect of coefficient quantization inmr filters Cascading low-order IIR filters for improved stability Design of non-recursive digital filters The Fourier (or window) method The design of optimal linear phase FIR filters Summary Problems Correlation Preview Covariance and the correlation coefficient The cross-correlation function for finite-duration signals Correlation using MATLAB The cross-correlation function for power signals Autocorrelation functions Some applications of cross-correlation and autocorrelation Determination of time delays System identification Pattern recognition Detection of signals in noise by cross-correlation Detection of signals in noise by autocorrelation The chirp pulse Time domain correlators and matched filters Frequency domain correlation The output waveform from a matched filter, and the processing gain Doppler effects in correlators Summary Problems Processing techniques for bandpass signals Preview Bandpass signals Baseband representations of bandpass signals and the complex envelope Generation of in-phase and quadrature components 478

17.5 Envelope detection using quadrature components 479 17.6 An example of quadrature channels for measuring Doppler shifts in radar 483 1 7.

9 17.5 Envelope detection using quadrature components An example of quadrature channels for measuring Doppler shifts in radar An example of quadrature channels in narrowband FFT beamforming Filtering bandpass signals with lowpass filters Correlators for bandpass signals The physical reality of complex envelopes Analytic signals Summary Problems 496 Appendix A Listings of selected MATLAB programs 498 Bibliography 504 Index 505 Trademark notice The following are trademarks or registered trademarks of their respective companies: Macintosh MATLAB Windows Apple Computer, Inc. The Mathworks, Inc. Microsoft Corporation

Signals and Systems Using MATLAB

Signals and Systems Using MATLAB Second Edition Luis F. Chaparro Department of Electrical and Computer Engineering University of Pittsburgh Pittsburgh, PA, USA AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK