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This development of these labs was supported by the National Science Foundation under Grant No. DUE-0511635. Any opinions, conclusions orrecommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Introduction

In this lab, we will look at the effect of filtering signals using a frequency domain implementation of an LTI system, i.e., multiplying the Fourier transform of the input signal with the frequency response of the system. In particular, we will filter sound signals, and investigate both low-pass and high-pass filters. Recall that a low-pass filter filters out high frequencies, allowing only the low frequencies to pass through. A high-pass filter does the opposite.

Matlab commands and resources

  • help<command> , online help for a command.
  • fft , Fast Fourier Transform.
  • ifft , Inverse Fourier Transform.
  • sound , plays sound unscaled (clips input to [-1,1]).
  • soundsc , plays sound scaled (scales input to [-1,1]).
  • wavread , reads in WAV file. The sampling rate of the WAV file can also be retrieved, for example, [x, Fs] = wavread('filename.wav') , where x is the sound vector and Fs is the sampling rate.

All of the sounds for this lab can be downloaded from the Sound Resources page.

Transforming signals to the frequency domain and back

When working in MATLAB, the continuous-time Fourier transform cannot be done by the computer exactly, but a digital approximation is done instead. The approximation uses the discrete Fourier transform (more on that in EE 341). There are a couple important differences between the discrete Fourier transforms on the computer and the continuous Fourier transforms you are working with in class: finite frequency range and discrete frequency samples. The frequency range is related to the sampling frequency of the signal. In the example below, where we find the Fourier transform of the "fall" signal, the sampling frequency is Fs=8000 , so the frequency range is [-4000,4000] Hz (or 2*pi times that for w in radians). The frequency resolution depends on the length of the signal (which is also the length of the frequency representation).

The MATLAB command for finding the Fourier transform of a signal is fft (for Fast Fourier Transform (FFT)). In this class, we only need the default version. >>load fall %load in the signal>>x = fall;>>X = fft(x); The fft command in MATLAB returns an uncentered result. To view the frequency content in the same way as we are used to seeing it in class, you need to plot only the first half of the result (positive frequencies only) OR use the MATLAB command fftshift which toggles between centered and uncentered versions of the frequency domain. The code below will allow you to view the frequency content both ways. >>N = length(x);>>pfreq = [0:N/2]*Fs/N; % index of positive frequencies in fft>>Xpos=X(1:N/2+1); % subset of fft values at positive frequencies>>plot(pfreq,abs(Xpos)); % plot magnitude of fft at positive frequencies>>figure;>>freq = [-(N/2-1):N/2]*Fs/N; % index of positive AND negative freqs>>plot(freq,abs(fftshift(X))); % fftshift actually SWAPS halves of X here. See help. % Convince yourself of why it does this to match up with freq! Note that we are using abs in the plot to view the magnitude since the Fourier transform of the signal is complex valued. (Type X(2) to see this. Note that X(1) is the DC term, so this will be real valued.)

Questions & Answers

An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Source:  OpenStax, Continuous time linear systems laboratory (ee 235). OpenStax CNX. Sep 28, 2007 Download for free at http://cnx.org/content/col10374/1.8
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