{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ELEC442-6601 chapter 4 examples, solution_2

ELEC442-6601 chapter 4 examples, solution_2 - Sampling...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Sampling Theorem Examples Concordia University 1 Question 1) Determine the condition on the sampling interval s T so that each ) ( t x is uniquely represented by the discrete-time sequence ) ( ] [ s nT x n x = . a) ) 4 sin( ) 2 sin( 3 ) cos( ) ( t t t t x π π π + + = b) t t t t t t t x π π π π π π ) 2 sin( ) 6 sin( 3 ) sin( ) 2 cos( ) ( + = c) The signal ) ( t x with FT given in the figure. Solution 1) Part a: The signal ) 4 sin( ) 2 sin( 3 ) cos( ) ( t t t t x π π π + + = has frequencies of π , π 2 and π 4 radians/sec. Therefore the maximum frequency of the signal is π 4 = Ω m and therefore the sampling frequency should be π 8 > Ω s . The sampling period is 4 1 < s T . Part b: The first term has a square spectrum which is extended up to frequency of π due to t t π π ) sin( and is shifted π 2 due to ) 2 cos( t π and therefore the overall spectrum has maximum of π π π 3 2 = + . The second term has a square spectrum which is extended up to frequency of π 2 due to t t π π ) 2 sin( and is shifted π 6 due to ) 2 sin( t π and therefore the overall spectrum has maximum of π π π 8 6 2 = + . Therefore π 8 = Ω m and 8 1 < s T . Part c:
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Sampling Theorem Examples Concordia University 2 The maximum frequency in this signal as shown in the frequency spectrum is about π 5 . 4 = Ω m radians/sec and therefore the sampling frequency should be π 9 > Ω s . The sampling period is 9 2 < s T Question 2) Consider the signal < Ω < - Ω = Ω otherwise j X 0 1000 1000 ) ( π π a) Clearly sketch the signal in the frequency domain include all relevant points and values. b) If the signal is fed into an ideal sampler with sampling frequency 3000π (rad/sec), clearly sketch the output of the sampler in the frequency domain include all relevant points and values. c) If the sampled signal is fed into an ideal low pass filter with a cut-off frequency of 1500π (rad/sec), clearly sketch the output of the filter in the frequency domain. In your drawing include all relevant points and values. d) If the ideal low pass filter had a cut-off frequency of 2500π (rad/sec), clearly sketch the output of the filter in the frequency domain. In your drawing include all relevant points and values.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern