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EEE 4510: Introduction To Digital Signal Processing

tag 0 Download 5 Pages / 1,068 Words tag 14-09-2020

Question:

1.Given the signal x(t) = 2cos(2π ⋅2000t − π 6), the discrete-time signal x[n] = Acos ω! ( n +φ ) is obtained from x(t) by sampling at a rate of fS Hz . For each part below, determine the values of A,φ,ω! ( ) with 0 ≤ω! ≤ π . Has the signal been oversampled or undersampled? Verify your results using MATLAB.
 
a) fS = 16 kHz
b) fS = 10 kHz .
c) fS = 2.5 kHz .
d) fS = 1.5 kHz .
 
2.Determine which of the following discrete-time signals are equal; that is, their plots vs. n will be identical. Verify your results using the “stem” command in MATLAB.
 
x1 [n] = cos(0.7πn + π 3)
x2 [n] = cos(1.3πn − π 3)
x3 [n] = cos(1.3πn + π 3)
x4 [n] = cos(1.5πn − π 4)
x5 [n] = cos(−1.5πn − π 4)
x6 [n] = cos(2.5πn − π 4)
 
3.The following discrete-time signals are applied to an ideal D-to-A converter with a sampling rate fS = 4 kHz. In each case, determine the output signal in the range 0 ≤ω! ≤ π and use MATLAB to verify your results.
 
a) y1 [n] = 3cos(0.7πn + π 6)
b) y2 [n] = 2cos(1.7πn − π 3)
c) y3 [n] = 4 cos(2.2πn + π 4)
 
4.The A/D and D/A converters shown below share a common sampling frequency fS and the input signal is given by x(t) = 3cos(2π ⋅ 400t + π 4) + 2cos(2π ⋅1200t − π 3). 
                                      

 

  1. a)

If y(t) = x(t) what can you say about fS ?

  1. b)

If fS = 1.8 kHz what is x[n] ? Be sure 0 ≤ω

! ≤ π for all signal

components.

  1. c)

Sketch the frequency spectrum of the signal in (b).

  1. d)

Now assume that y(t) = 1+ 3cos(2π ⋅ 400t + π 4). What is fS ?

Due date: Wednesday, February 21

 
 
 
 
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