Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Filter Programming Assignment - Signals and Systems | ECE 3640, Assignments of Signals and Systems

Utah State University (USU)Signals and Systems

Material Type: Assignment; Class: Signals and Systems; Subject: Electrical & Computer Engr; University: Utah State University; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 07/31/2009

koofers-user-kqj
koofers-user-kqj 🇺🇸

5

(1)

10 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
ECE 3640
Filter Programming Assignment
Objective and Background
In this programming assignment you will design both IIR and FIR filters. The IIR filter is “designed” by
pole placement. The FIR filter is designed with the help of a Matlab design tool. You will then implement
the filters in C++. You will test the filter response by providing sinusoidal inputs at a variety of frequencies
and comparing the actual magnitude response with the theoretical magnitude response.
The signals you are to deal with are sampled at a rate of Fs= 8000 samples/sec.
One of the algorithms you will use for the filter design uses the Matlab routine remez. (Note: most
recent versions of Matlab call this function firpm. However, since there may be older versions of Matlab
still in use, we will refer to the function as remez. You should check the help function in Matlab.) The
remez routine is an implementation of the algorithm known as the Parks-McClellan algorithm for digital
filter design, after its inventors. (The name “remez” comes from a particular numerical algorithm, known as
the “Remez exchange” which forms part of the Parks-McClellan algorithm.) The Matlab manual pages for
the remez function are provided with this assignment. (For example, do help remez in Matlab. To use
the remez routine, you specify the lower and upper frequencies and the desired magnitude response at those
frequencies. The frequencies are given as a fraction of the Nyquist frequency for the system (the maximum
frequency representable in the sampled system). For example, if you are sampling at Fs= 8000 samples/sec,
the Nyquist frequency is 4000 Hz. The continuous-time frequency frequency of 4000 Hz. corresponds in the
remez algorithm, to a digital frequency of 1.
Assignment
Design of the filters
1. Design a filter using the remez routine. (See the notes below.)
(a) Using the remez routine and the sampling rates described above, design a linear-phase FIR
digital filter with the following characteristics:
•100 coefficients
•Lowpass filter
•Passband frequency of 1000 Hz with unit gain.
•Stopband frequency of 1500 Hz with zero gain.
(b) Plot the desired magnitude response and the actual magnitude response.
(c) Make a plot of the phase response of the filter (see freqz in Matlab). In your writeup,
comment on whether the phase response is actually linear (as it should be). Note: the
Matlab command unwrap may be helpful here.
(d) Save your filter coefficients to a file that you can later read in to your C++ program.
2. Design a filter using pole-zero placement.
(a) Design a lowpass digital filter with the same passband and stopband as before using pole-zero
placement. That is, place some poles and zeros, make a plot using freqz, and see if it works.
You decide where and how many poles and zeros to place. This may take several iterations,
and you will probably not obtain the same quality of design as you did using remez.
Helpful functions to be aware of: roots, poly, zplane, freqz. Look up Matlab help on
these. Also, it would probably be very helpful to write a Matlab script (i.e., program), so
that all you need to do is change some numbers to have the results computed for you.
(b) Scale the result so the DC frequency response has magnitude 1.
(c) Make a plot of the desired magnitude response and the actual magnitude response of your
filter.
(d) Make a plot of the phase response of the filter (see freqz).
1
pf3
pf4
pf5

Partial preview of the text

Download Filter Programming Assignment - Signals and Systems | ECE 3640 and more Assignments Signals and Systems in PDF only on Docsity!

ECE 3640

Filter Programming Assignment

Objective and Background

In this programming assignment you will design both IIR and FIR filters. The IIR filter is “designed” by pole placement. The FIR filter is designed with the help of a Matlab design tool. You will then implement the filters in C++. You will test the filter response by providing sinusoidal inputs at a variety of frequencies and comparing the actual magnitude response with the theoretical magnitude response. The signals you are to deal with are sampled at a rate of Fs = 8000 samples/sec. One of the algorithms you will use for the filter design uses the Matlab routine remez. (Note: most recent versions of Matlab call this function firpm. However, since there may be older versions of Matlab still in use, we will refer to the function as remez. You should check the help function in Matlab.) The remez routine is an implementation of the algorithm known as the Parks-McClellan algorithm for digital filter design, after its inventors. (The name “remez” comes from a particular numerical algorithm, known as the “Remez exchange” which forms part of the Parks-McClellan algorithm.) The Matlab manual pages for the remez function are provided with this assignment. (For example, do help remez in Matlab. To use the remez routine, you specify the lower and upper frequencies and the desired magnitude response at those frequencies. The frequencies are given as a fraction of the Nyquist frequency for the system (the maximum frequency representable in the sampled system). For example, if you are sampling at Fs = 8000 samples/sec, the Nyquist frequency is 4000 Hz. The continuous-time frequency frequency of 4000 Hz. corresponds in the remez algorithm, to a digital frequency of 1.

Assignment

Design of the filters

  1. Design a filter using the remez routine. (See the notes below.) (a) Using the remez routine and the sampling rates described above, design a linear-phase FIR digital filter with the following characteristics: - 100 coefficients - Lowpass filter - Passband frequency of 1000 Hz with unit gain. - Stopband frequency of 1500 Hz with zero gain. (b) Plot the desired magnitude response and the actual magnitude response. (c) Make a plot of the phase response of the filter (see freqz in Matlab). In your writeup, comment on whether the phase response is actually linear (as it should be). Note: the Matlab command unwrap may be helpful here. (d) Save your filter coefficients to a file that you can later read in to your C++ program.
  2. Design a filter using pole-zero placement. (a) Design a lowpass digital filter with the same passband and stopband as before using pole-zero placement. That is, place some poles and zeros, make a plot using freqz, and see if it works. You decide where and how many poles and zeros to place. This may take several iterations, and you will probably not obtain the same quality of design as you did using remez. Helpful functions to be aware of: roots, poly, zplane, freqz. Look up Matlab help on these. Also, it would probably be very helpful to write a Matlab script (i.e., program), so that all you need to do is change some numbers to have the results computed for you. (b) Scale the result so the DC frequency response has magnitude 1. (c) Make a plot of the desired magnitude response and the actual magnitude response of your filter. (d) Make a plot of the phase response of the filter (see freqz).

(e) Convert the pole-zero representation to a rational transfer function representation (the routine zp2tf might be helpful). (f) Save the filter coefficients to a file you can use.

Implementation Write a C++ class that implements digital filtering. The class might have the following form:

class filter { // private data double *numcoeff; // pointer to numerator coefficients double *dencoeff; // pointer to denominator coefficients int type; // IIR or FIR? public: // public interface filter(int n, double *numcoeff); // FIR constructor filter(int n, double *numcoeff, int m, double *dencoeff); // IIR constructor ~filter(); // destructor -- make sure you de-allocate memory double filt(double input); // the actual filter function // whatever other functions you might want };

Your constructor functions need to allocate space for the filter coefficients and the filter storage, copy the filter coefficients passed in into their appropriate storage arrays. Your filter function should do filtering as appropriate, whether IIR or FIR. (To be really fancy, you might want to use some sort of virtual function to select whether you are doing FIR or IIR filtering, but this level of sophistication is not really necessary.) You could use this filter class in your program as follows:

#include "filter.h" // <-- you write this #include <math.h> ... // other stuff

main( ... ) { // ...

int n = 100; // number of FIR filter coefficients // ... // read the FIR filter coefficients into an array called y // ...

filter FIR(n,y); // instantiate the FIR filter // ...

// Here is how to use it: x = ... // x = the input function y = FIR.filt(x); // "pass" x into the filter, then y is the output

// read the IIR coefficients into a numerator array called num, and a // denominator array called den. int n = ... // number of numerator coefficients int m = ... // number of denominator coefficients

// determine the amplitude of the output signal (think carefully!) // ... outamplitude = ...; } } // end for t ratio = outamplitude/inamplitude; // write the frequency F and the ratio to a file // ... } // end for t

// close the output file // ... } // end main

To plot the results, you will need to get into Matlab, plot the desired magnitude response with freqz, load in your actual results using the load command, then plot these on the same axes. For example, you might have the following:

% Let a and b represent the numerator and denominator polynomials % of the designed filter [h,f] = freqz(a,b); clf; % clear current figure (remove existing plots) subplot(2,1,1); % plot in part of the available window plot(f/(2pi),20log10(abs(h))); % plot the magnitude response in dB hold on; % make it so that the plot can be overlaid xlabel(’discrete frequency’) % label the axes ylabel(’magnitude response, dB’)

% read in your data, say into the arrays fa and ha % ...

% Now plot your results on top of the theoretical results plot(fa,20*log10(ha),’:’); % plot your computed response with % dotted line

Turn In the following:

  • Plots of filter magnitude and phase response (and the ideal magnitude response) for the FIR filter.
  • Listings of your filter class code.
  • Listings of your testing code.
  • Plots comparing the actual magnitude response with the tested magnitude response (overlay the actual values with the design values on a single plot). For the FIR filter, also overlay the desired frequency response. Also include a discussion on whether the phase response of the FIR filter is linear.
  • The transfer function for your IIR filter in both pole-zero and polynomial form. Also a plot of the pole and zero locations you used in your design
  • Plot showing the actual IIR-filtered magnitude response for the given frequencies. Also a descrip- tion of how you chose the normalizing factor.
  • A discussion of of what you learned and comparisons between FIR and IIR filters (e.g., which runs faster, and why, which does a better job of filtering, and why, etc.)

Notes on the remez function

The remez function is invoked as

h = remez(n,f,m)

(See the help remez in Matlab.) The following information comes from the manual for The Student Edition of Matlab, v. 4.

  • The filter computes the coefficients for an FIR filter with n + 1 coefficients.
  • The argument f is a vector of pairs of frequency points expressed in normalized frequency: the frequency of 1 corresponds to half the sampling frequency, and 0 corresponds to 0 Hz (DC). The frequencies in f must be listed in increasing order.
  • m is a vector containing the desired magnitude response at the points specified in f. The vectors m and f must be the same length.
  • The desired magnitude function at frequencies between pairs of points f(k),f(k+1) for k odd is the line segment connecting the points f(k),m(k) and f(k+1),m(k+1).
  • The desired magnitude function at frequencies between pairs of points f(k),f(k+1) for k even is unspecified. These correspond to transition bands or “don’t care” regions.
  • If you use the form

h = remez(n,f,m,w)

then w is a weight vector, which uses the weights to fit in each frequency band. The length of w is half the length of f or m, so there is exactly one weight per band.

Here is an example of a bandpass filter: We desire a filter to pass signals between f = 0.4 and f = 0. 6 (normalized frequency) with an amplitude of 1, and to attenuate other signals. A plot of the desired frequency response is

f = [0 0.3 0.4 .6 0.7 1]; m = [0 0 1 1 0 0]; % bands: 0-0.3 is a stop band (at 0) % 0.3-0.4 is a transition band % 0.5-0.6 is the pass band % 0.6-0.7 is a transition band % 0.7-1 is a stop band (at 0) clf; % clear previous plot, if any plot(f,m,’:’); % a plot of the desired frequency response h = remez(17,f,m); % create a filter with 18 coefficients [response,freq] = freqz(h,1,512); % compute the frequency response hold on; % overlay the plots plot(freq/pi,abs(response)); % freq/pi converts to this normalized % freq. scale % abs(response) is the magnitude response xlabel(’f (normalized)’); ylabel(’Magnitude response’); legend(’Desired frequency response’,’Actual frequency response, 18 coefs.’)

The plot below shows the results: