MEHRAN UNIVERSITY OF ENGINEERING AND TECHNOLOGY,
JAMSHORO
Due Dated: 09-03-2018 Marks: 10
Note: SOLVE ALL QUESTIONS.
1. Given a DSP system in which a sampling rate of 8,000 Hz is used and the anti-
aliasing filter is a Butterworth low pass filter with a cutoff Frequency of 3.2 kHz,
determine the order of the Butterworth low pass filter for the percentage of
aliasing level at the cutoff frequency required to be less than 10%.
2. Consider a digital sequence sampled at the rate of 20,000 Hz. If we use the
8,000-point DFT to compute the spectrum, determine
a. the frequency resolution
b. The folding frequency in the spectrum.
3. Given the following data sequence with a length of 6,
x(0)=0, x(1)=1, x(2)=0, x(3)= -1, x(4)= 0, x(5)=1
Compute the windowed sequence xw(n) using the
a. Triangular window function.
b. Hamming window function.
c. Hanning window function.
4. Given a sequence x(n) for 0 ≤ n ≥ 3,where x(0) -4, x(1)=3, x(2)=3, and x(3)=1,
evaluate its DFT X(k)using the decimation-in-frequency FFT method, and
determine the number of complex multiplication.
5. A system is described by the difference equation
( ) ( ) ( ) ( ) ( )
Determine the solution when initial conditions are y(-1) =1 and y(-2)= 3.
6. Given the following difference equation with the input-output relationship of a
certain initially relaxed DSP system( all initial conditions are zero),
ASSIGNMENT DIGITAL SIGNAL PROCESSING
