Wave form generation,sampling and aliasing

1)    To know how to generate a square wave.
2)    To investigate the sampling process and the aliasing phenomena.
3)    To learn how to use anti-alias using Matlab.
Equipment Required
A PC having Code Composer Studio and Matlab, a Picoscope and DSK6713 kit.
Sampling and aliasing
Sampling is the process of converting a continuous time signal into discrete time signal. As we know from the sampling theory, the sampling frequency must be at least greater than twice the bandwidth of the analog signal as explained by the sampling theory
Where  is the maximum frequency content of the analog signal.
In this experiment a simple program for sampling a signal from the function generator will be considered.

Part One: Basic sampling and aliasing effects
1.     Write a c program to read a signal from the LINE IN input of the DSK6713 and write the data back to the line out. You can use the code shown in Figure 4to help you performing this task
1.     After compiling and running your program, connect a signal from the function generator to the LINE IN terminal 
2.     Set the function generator to sine wave, the amplitude of the signal to 1 VPP, and the frequency to 1 kHz and plot the signal as it appears on the screen of the oscilloscope  
1.     Increase the frequency of the square wave from 1 kHz to 4 kHz in steps of 1 kHz then plot the signal as it appears on the oscilloscope. Explain the signal shape you see on the screen of the oscilloscope repeat step 5 for sinusoidal signal
We notice that when we increase the frequency of the signal, the period will decrease according to the equation  , until we reach 4kHz. at 4 kHz aliasing will occur since the sampling frequency should be   and after 4kHz the signal will disappear.

Q1) Determine the frequency of the reconstructed signal if the input signal frequency is  and the sampling frequency is 8 kHz.

Part Two: Down Sampling and anti-alias filtering

  1.     Open new MATLAB Simulink design
  2.     Connect the system as shown in Figure 7
   1.     Set the frequency of the sine signal to 1 kHz with sampling frequency of 16 kHz.
   2.     Set the sampling frequency of DAC to 8kHz saturate mode.
   3.     Choose low pass filter with cut off frequency of the filter to 3.9 kHz and sampling frequency 8 kHz .plot the signal as it appears on CRO.