1) a)Test the following systems for Time invariance.
i) y(n) =x(n) +C
ii) y(n) =nx2
b) Test the stability of the following system.
i) y (n) =Cos [x(n)]
2) Calculate the 8 point DFT of x (n) by radix-2 in DIT-FFT.
X (n) ={1,2,3,4,4,3,2,1}
3) Transform the analog filter with system function Ha(s) into the digital filter IIR filter by means of the impulse invariant method.
Ha(s) = S+0.1/(S+0.1)2+9 With T=1 SEC
4) Find the direct form-I, direct form-II and Cascade form realizations of the LTI system governed by the equation,
y(n) = - 0.1y(n-1) +0.2y(n-2)+3x(n)+3.6x(n-1)+0.6x(n-2).
5) Calculate the coefficients of the linear-phase FIR filter of length N=15. Which has a Symmetric unit sample response and a frequency response that satisfies the conditions?
H (2 π k/15) = 1: for k = 0,1,2,3
0.4: for k = 4
0: for k = 5, 6, 7
6) Develop the high pass filter using hamming window with a cut of frequency of 1.2 radians/sec and N=9.
7) For the second order IIR filter H(z) = 1/(1-0.5z-1) (1-0.45z-1). Study the effect of shift in pole location with 3-bit coefficient representation in direct form and cascade form.
8) Specify the characteristics of the limit cycle oscillation with respect to the System described by the difference equation y(n) =0.95y(n-1)+x(n). Find the dead band of the filter.
9) Sketch and describe the architecture of the TMS320C24 DSP Processor.
10) Describe the several addressing modes of the TMS 320C24 DSP Processor with the help of examples.