A. Design a minimum order FIR filter for the following specifications (Use the r

Question

A. Design a minimum order FIR filter for the following specifications (Use the remez filter): the relative specification is provided as below, where Rp=1 dB, Rs=20 dB .

Use a trial and error process to figure out the minimum order of the filter that satisfies the given specifications. To help you in your process you must use the line command in MATLAB. Line(x,y) will plot lines on your filter plot, where x and y are vectors of the x and y coordinates of the points that are to be joint using lines. Use this command to draw the lines representing the specifications as shown in the attached picture.

B. Use the filter to remove the noise component from a signal that is sampled at 1000 Hz, and has a combination of 200 Hz signal (Amplitude 100) and a 450 Hz signal (Amplitude 10). Fs=1000; t= 0:(1/Fs):1; s=100*sin (2*pi*t*200) + 10*sin (2*pi*t*450);

C. Show the signal before and after filtering.

D. Show the normalized FFT of the signal before and after filtering.

Please include all MATLab code used to create this

Explanation / Answer

1

1. Introduction

The Digital Filter Design problem involves the determination of a set of filter coefficients tomeet a set of design specifications. These specifications typically consist of the width of thepassband and the corresponding gain, the width of the stopband(s) and the attenuation therein; theband edge frequencies (which give an indication of the transition band) and the peak rippletolerable in the passband and stopband(s).Two types of digital filters exist – the IIR (Infinite Impulse Response) and the FIR (FiniteImpulse Response). FIR filters were studied in an earlier project. They possess certain properties,which make them the preferred design choices in numerous situations over IIR filters. Mostnotably, FIR filters (all zero system function) are always stable, with a realization existing foreach FIR filter. Another feature exclusive to FIR filters is that of a linear phase response.The content of this project is the design of IIR filters using MATLAB

. The design of IIRfilters proceeds through a vastly different set of steps than those followed by FIR filter designalgorithms. The design of IIR filters is closely related to the design of analog filters, which is awidely studied topic. An analog filter is usually designed and a transformation is carried out intothe digital domain. Two transformations exist – the

impulse invariant

transformation and the

bilinear

transformation. In this project, the focus is on designing minimum order IIR filters tomeet a set of specifications using MATLAB functions. The bilinear transformation has been used.The designed IIR filters are characterized by significantly lower order than the correspondingFIR filters. This comparison is brought about in Section I of the design where FIR filters aredesigned along with the IIR filters. There it is shown that the best IIR filter is less complex thanthe optimum FIR filter. The price to pay is the non-linear phase of the IIR filters, which isunavoidable.The rest of this report is organized as follows. The next section describes the IIR digital filterdesign process. Then the design is presented in two sections. In the first, a low pass filter isdesigned for four IIR and two FIR realizations and various comparisons are drawn from theresults. The second section deals with the design of a high pass Elliptic filter and a band passChebyshev Type I filter. Each design is accompanied by a plot of its frequency response, impulseresponse and pole-zero diagram. The MATLAB code is presented as appendix with anaccompanying appendix with a glossary of the key functions for filter design.

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