3.1  To Learn in This Chapter
3.2  Contrasting Signals and Systems
3.3  A Quick Discussion About Filters
3.3.1  Cutoff and natural frequencies
3.4  Linear Time-Invariant Systems
3.4.1  Impulse response and convolution for LTI systems
3.4.2  Advanced: Convolution properties
3.4.3  Advanced: Convolution via correlation and vice-versa
3.4.4  Advanced: Discrete-time convolution in matrix notation
3.4.5  Approximating continuous-time via discrete-time convolution
3.4.6  Frequency response: Fourier transform of the impulse response
3.4.7  Fourier convolution property
3.4.8  Circular and fast convolutions using FFT
3.5  Advanced: Sampling and Signal Reconstruction Revisited
3.5.1  A proof sketch of the sampling theorem
3.5.2  Energy and power of a sampled signal
3.5.3  Energy / power conservation after sampling and reconstruction
3.5.4  Sampling theorem uses a strict inequality
3.5.5  Undersampling or passband sampling
3.5.6  Sampling a complex-valued signal
3.5.7  Signal reconstruction and D/S conversion revisited
3.6  Advanced: First and Second-Order Analog Systems
3.6.1  First-order systems
3.6.2  Second-order systems
3.7  Advanced: Bandwidth and Quality Factor
3.7.1  Bandwidth and Quality Factor of Poles
3.7.2  Bandwidth and Quality Factor of Filters
3.8  Importance of Linear Phase (or Constant Group Delay)
3.9  Advanced: Filtering technologies: Surface acoustic wave (SAW) and others
3.10  Introduction to Digital Filters
3.10.1  Designing simple filters using specialized software
3.10.2  Distinct ways of specifying the “ripple” / deviation in filter design
3.10.3  LCCDE digital filters
3.10.4  FIR, IIR, AR, MA and ARMA systems
3.10.5  Filter frequency scaling
3.10.6  Filter bandform transformation: Lowpass to highpass, etc.
3.11  IIR Filter Design
3.11.1  Direct IIR filter design
3.11.2  Indirect IIR filter design
3.11.3  Methods to convert continuous into discrete-time system functions
3.11.4  Summary of methods to convert continuous-time system function into discrete-time
3.12  Bilinear Transformation: Definition and Properties
3.12.1  Bilinear mapping between s and z planes and vice-versa
3.12.2  Non-linear frequency warping imposed by bilinear
3.12.3  Tracking the frequency warping provoked by bilinear
3.12.4  Advanced: Properties of the bilinear transformation
3.13  System Design with Bilinear Transformation
3.13.1  Bilinear for IIR filter design
3.13.2  Bilinear for matching a single frequency
3.13.3  Bilinear for mimicking G(s)
3.14  FIR Filter Design
3.14.1  A FIR filter does not have finite poles
3.14.2  The coefficients of a FIR coincide with its impulse response
3.14.3  Algorithms for FIR filter design
3.14.4  FIR design via least-squares
3.14.5  FIR design via windowing
3.14.6  Two important characteristics: FIRs are always stable and can have linear phase
3.14.7  Examples of linear and non-linear phase filters
3.14.8  Zeros close to the unit circle may impact the phase linearity
3.14.9  Four types of symmetric FIR filters
3.15  Realization of Digital Filters
3.15.1  Structures for FIR filters
3.15.2  Structures for IIR filters
3.15.3  Running a digital filter using filter or conv
3.15.4  Advanced: Effects of finite precision
3.16  Advanced: Minimum phase systems
3.17  Advanced: Multirate Processing
3.17.1  Upsampler and interpolator
3.17.2  Downsampler and decimator
3.18  Applications
3.19  Comments and Further Reading
3.20  Exercises
3.21  Extra Exercises