# Fourier transform of both discrete and continous signals

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There are two files which both need completed. Please see attached files for full problem description.

Please be sure to provide code and plots. Thanks.

Lab 2:

1. A discrete-time system has the following unit-pulse response:

h[n] = 0.5^n - 0.25^n, for n >= 0

Correspondingly, the following difference equation describes the behavior of the system:

y[n+2] - 0.75y[n+1] + 0.125y[n] = 0.25x[n+1]

A. Use the MATLAB command conv to calculate the response of the system to

a unit step input, x[n]=u[n]. Consider 0 =< n <= 20. Show what you type into

the MATLAB command window and submit a plot of the output. Please label the axes.

B Use the MATLAB script recur to calculate the response of the system to a

unit step input, x[n]=u[n]. Again consider 0 =< n <= 20. Show all that you type

into the MATLAB command window. Submit a plot of the output with the axes labeled.

Lab 3:

The continuous time function. This signal is a sinc function defined as y(t) = sinc(t). The Fourier transform of this signal is a

rectangle function.

1. Use the function linspace to create a vector of time values from -5 =<t <=5. Next, plot the function using the sinc function for y(t) = sinc(t).

2. Using MATLAB and the command fft, show that the Fourier transform pair is indeed a rectangle function. Use the command fftshift to center your plot.. Show both the m-file code and plot.

3. Using the same time values, plot the continuous time function defined as y(t) = sinc(2t).

4. Plot the transform pair for this signal.

Discussion:

1. What is the "ringing" caused from seen on top of the rectangular pulse?

2. In step 3 above, the sinc function gets compressed or smaller by a factor of 2. What happened to the rectangular pulse in the frequency domain? What property does this relate to?

#### Solution Preview

Please see the attached files.

You can paste the codes to Matlab to run the ...

#### Solution Summary

The first part of the solution concentrates on the explanation of the discrete time system and its unit-pulse response. The second part explains the Fourier transform of a continuous signal sinc(t). The codes are implemented in Matlab.