Please do Problem 2 (Problem 1 is below). 2. (20 points) Use problem 1 to find t
ID: 2083349 • Letter: P
Question
Please do Problem 2 (Problem 1 is below).
2. (20 points) Use problem 1 to find the following: a. Show the Autocorrelation evaluated at t 0 is the same as your result in part 1b. b. What is the Nyquist frequency in Hz so that this waveform does not experienced aliasing? c. What are the frequency components located between 0 Hz and 64 Hz, if the waveform IS IMPULSE sampled at 36 Hz and is an input to an ideal low pass filter having a cutoff frequency of Hz. d. The above waveform is sampled and uniformly quantized. The maximum signal distortion is 10 microvolts. How many binary digits are required to represent the sampled signal to the required accuracy? e. Given your answer in part 2d, what is the required bit rate to transmit this signal?Explanation / Answer
Autocorrelation function is getting the deviation of the signal with respect to its mean and then normalising it. At t=0, Autocorrelation is smae as the energy function. Hence, prooved.
The signal includes 40 Hz and 60 Hz frequency components. So Nyquist frequency will be twice the highest component of frequency in it. Hence, Nyquist sampling fequency should be equal to 120 Hz in order to avoid aliasing.
If the waveform is sampled at 36 Hz, it will be under-sampled, it will include frequencies 40-36 = 4 Hz and its multiples. Since the cut of frewuency is 72 Hz, the frequency components between 0 and Hz will be multiples of 4 and 36 till 72 Hz.