Aims & Learning Objectives:
Aims: To introduce students to the fundamentals of signal processing and provide illustrations of their practical applications.
At the end of this unit students should be able to: (i) explain the sampling theorem and appreciate the implications of aliasing distortion, (ii) use the DFT and its fast implementation in the form of the FFT for spectral analysis, (iii) describe the reasons for spectral leakage and utilise windowing techniques for its mitigation, (iv) explain the types of ideal filter and how prescribed functions are used for their approximation, (v) employ FIR design techniques to implement linear phase and Fourier transform filters, (vi) design simple IIR digital filters and exploit different structures for their realisation, (vii) exploit pole-zero diagrams in the implementation of filters, (viii) describe the key components of a multirate filter and their role in sample rate conversion.
Review: sampling theorem and aliasing distortion, spectra and spectral descriptions.Digital spectral analysis: principles of DFT and FFT, effect of finite time window, spectral leakage and its reduction with prescribed windows. Analogue filters: approximation functions, Butterworth/Chebyshev/Bessel/Elliptic implementations. Digital filtering: z-transforms, FIR filters, properties, linear phase and Fourier transforms, design techniques; IIR filters, properties, allpass filters, realisations; pole-zero diagrams, minimum/maximum phase, stability. Multirate filtering: decimation, interpolation, polyphase realisation. Applications: signal analysis, filtering and sample rate conversion.