ELEC 470, Spring 2004
Prof. Rich Kozick

Homework 5


Date Assigned: Tuesday, February 17, 2004
Date Due: Tuesday, February 24, 2004

  1. Reading: Please begin reading Chapter 4 of the Lathi text on amplitude modluation, particularly Sections 4.1 - 4.3.

  2. Consider a linear, time-invariant system with impulse response h(t) shown below.


    \begin{figure} \centerline{ \epsfxsize=5.5in \epsfysize=2in \epsfbox{hw4fig.eps}}\end{figure}

    (a) What is the expression for h(t) in terms of the rect function?

    (b) Sketch the output signal y(t) from the system when the input signal is x(t) as shown above.

    (c) What is the frequency response H(omega) of this system? Sketch the amplitude response |H(omega)|.

    (d) Find the steady-state system output y(t) when the input is

    \begin{displaymath} x(t) = 2 \cos (2 \pi 50 t) + 0.5 \sin (2 \pi 100 t), \,\, -\infty < t < \infty.\end{displaymath}

    Hint: Is it simpler to find the output in the time domain or the frequency domain?

  3. Consider the RC circuit shown below with R = 1000 ohms and C = 1e-6 farads. Please find the frequency response H(omega), and sketch the amplitude and phase response of the filter for frequencies in the range 0 Hz to 10,000 Hz.

    \begin{figure} \centerline{ \epsfxsize=2.5in \epsfysize=1.7in \epsfbox{hw4rc.eps}}\end{figure}

  4. You are given two data files, sig1.dat and sig2.dat, which can be downloaded from the Web page for this assignment. These are both ASCII files, and they can be loaded into Matlab with the command
    load sig1.dat -ascii
    after which a variable named sig1 will be available. (The same can be done with sig2.dat.) Both files were recorded by sampling a signal at a rate of 60 samples per second.

    Analyze the frequency content of these data files using the FFT in MATLAB. For each data file, how many sine waves appear to be present? What are the frequencies of the sine waves? Can you say anything about the relative amplitudes of the various sine wave components?

Thank you.