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Summary of Book
A detail description on Discrete Fourier Transforms (DFT) : Frequency domain sampling and reconstruction of discrete time signals. DFT as a linear transformation, Its relationship with other transforms. Properties of DFT, Multiplication of two DFTs - The circular convolution, Additional DFT properties. Use of DFT in linear filtering, Overlap-save and overlap-add method. Direct computation of DFT, Need for efficient computation of the DFT (FFT algorithms). Radix-2 FFT algorithm for the computation of DFT and IDFT decimation in time and decimation-in-frequency algorithms. Goertzel algorithm and chirp z-transform. IIR Filter Design : Characteristics of commonly used analog filters - Butterworth and Chebysheve filters, Analog to analog frequency transformations. Implementation of Discrete Time Systems : Structures for IIR and FIR systems - Direct form I and direct form II systems, Cascade, Lattice and parallel realization. FIR Filter Design : Introduction to FIR filters, Design of FIR filters using rectangular, Hamming, Bartlet and Kaiser windows, FIR filter design using frequency sampling technique. Design of IIR filters from analog filters (Butterworth and Chebyshev) - Impulse invariance method. Mapping of transfer functions : Approximation of derivative (backward difference and bilinear transformation) method, Matched z-transforms, Verification for stability and linearity during mapping.
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