Lab 4: FIR & IIR Filter Design Report - University of Guelph ENGG 3390

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University of Guelph School of Engineering ENGG*3390: Signal Processing Lab 4: FIR & IIR Filter Design Tables of Contents: Introduction: Digital filters are comprised of a system that performs m... athematical operations on a discrete time signal. The basic premise is to perform a computation to of one sequence of numbers (input) and generate a new sequence of numbers (output).The purpose of this lab was to program a Texas Instrument’s TMS320C5505 eZdsp USB Stick (DSP) as a signal processor to implement and evaluate the performance of FIR and IIR filters . A window function is a mathematical function that is a zero valued outside of a chosen interval (window). Windowing reduces amplitude of discontinuities at the boundaries of a finite sequence. When a coefficients are zero this is a Finite impulse response (FIR) filters. Types of window functions include rectangular window, hamming window and blackman window. A general equation for radian frequency is given by: (1) Where ω is radian frequency, n is size and N represents the width, in samples, of a discrete time window function. Rectangular windows (ω[n] = 1) occur when a function is constant inside the interval and zero elsewhere giving a rectangular shape and is equivalent to no window at all. The hamming window is optimized to minimize the maximum side lobe which results in a wide peak and low sidelobes. Hamming are useful for noise measurements when better frequency resolutions are desired. The blackman is similar to hamming with wide peak but has good side lobe compression. Network synthesis is a method of designing Infinite impulse response (IIR) signal processing filters. The basis of the method is to obtain component values of a filter from a rational function that represents a transfer function. Types of network synthesis include low pass bessel filter given by the the transfer function: (2) where n is the reverse bessel polynomial and ωo is the frequency chosen to give the desired Ө cutoff frequency. Bessel filters give a maximally linear phase response preserving wave shape of filter signals in passband. A second type of IIR signal processing filter is Butterworth filter. This filter is designed to give a flat frequency response as possible in the passband. It is given by the butterworth polynomial and has the transfer function: (3) Where G is the gain, Bn is normalized butterworth polynomial and a is s/ωc. ωc is the cutoff frequency assumed to be 1 to give maximal flatness. Third type is a chebyshev filter which has a steeper roll-off and more ripple in passband than butterworth. Understanding the system behind the different types of FIR window functions and IIR filters are important to find the best one for application purpose. Applications of digital filters include sound filtering, communications, audio crossovers and digital conversions of audio files. Methods: The lab consisted of two parts; FIR Filtering and IIR Filtering. Both filtering were done with the use of a switch statement in C. The number of times the LED on the board flashed was used as the expression for the switch statement. The first part of the lab dealt with FIR Filtering. This involved using the FIR filter coefficients calculated in matlab for the Rectangular and Blackman window FIR Filters of window sizes M = 8 and M = 32. The coefficients for these FIR filters were put in the FIR_filters.h header file in the Lab [Show More]

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