Draw the block diagram architecture of TMSC6000 series Digital Signal Processor. Briefly describe each block functions.
[7 marks]Define ROC for z-transform? List the properties of the ROC.
[7 marks]Determine the z-transform of the following signals.
[ marks]1 x ( n ) u ( n ) (3-Marks) ii) x ( n ) ( c o s0 n ) u ( n ) 07 (4-Marks)
[ marks]State and prove Time Shifting and Scaling in z domain properties for z- transform.
[7 marks]State and prove convolution theorem and the correlation theorem for Fourier transform
[7 marks]Determine the spectra of the signals
[ marks]The impulse response of a linear time invariant system is h ( n ) 1 , 2 , 3 , 1 Determine the response of the system to the input signal x ( n ) 1 , 2 , 1 , 1 07
[ marks]Determine the inverse z-transform of X ( z ) 1 1 .5 z 1 1 0 .5 z if
[2 marks]ROC: z (ii) ROC: z 0 .5 (iii)ROC: 0 .5 z 107
[ marks]Determine the range of value of a and b for which the liner time-invariant system with impulse response h ( n ) a b n n , , n n 0 is stable.
[ marks]x ( n ) c o s 2 n (3-marks) ii) x ( n ) c o s n / 3 07 (4-marks)
[ marks]State the Sampling theorem. Consider the analog signal x a ( t ) 3 c o s 2 0 0 0 t 5 s i n 6 0 0 0 t 1 0 c o s 1 2 0 0 0 t 07 .
[ marks]How many numbers of additions, multiplications and memory locations will be required to realize a system H(z) having Mzeros and Npoles in (i) Direct-form Iand Direct-form-II realization?. (ii) Give direct form-Iand Direct form-II structures of second order system realization.
[7 marks]Compute the DFT of the four-point sequence x ( n ) { 0 1 2 3 }
[7 marks]Obtain direct form-Iand direct form-II structures for the system311 y(n) y(n1) y(n2)x(n) x(n1).483
[7 marks]What is the Nyquist rate for this signal? ii) Assume now that we sample this signal using a sampling rate Fs=5000samples/s. What is the discrete-time signal obtained after sampling?
[ marks]Classify the discreate time signals. Give one example of each class.
[7 marks]Explain the Decimation in Time FFT algorithm.
[7 marks]Perform the circular convolution of the following two sequences: x x1 ( n ( n ) ) 2 1 , ,1 , , , 1 , 07
[4 marks]Differentiate IIR and FIR systems.
[7 marks]