数字信号处理综合练习题及答案.docVIP

《数字信号处理》课程综合练习题 Let and , Determine the linear convolution sum of and ; Determine the 4-point circular convolution sum of and ; Determine the 7-point circular convolution sum of and . Plot the DFT-based implementation of determining. Solution: Linear convolution sum the 4-point circular convolution sum the 7-point circular convolution sum (d)the DFT-based implementation of determining linear convolution sum is shown below: 2. Prove the Parseval’s Relation Where, and are the N-point DFT of and, respectively. Proof: 3. Construct a flow graph for a 4-point radix-2 DIT FFT algorithm. Label all multipliers in terms of power . Label the input and output nodes with the appropriate values of the input and DFT sequences, respectively. Determine the number of real multiplications and the number of real additions required to implement the flow graph. solution: Flow graph of the 4-point radix-2 DIF FFT algorithm is shown below: 图略 the number of complex multiplications: the number of complex additions: As 1 complex multiplication consists of 2 real additions and 4 real multiplications, 1 complex addition of 2 real additions, hence, there are 2*4+2*8=24 real additions and 4*4=16 real multiplications totally. 4. A discrete-time system is characterized by the following difference equation: Given the input and initial condition and , determine the total solution using MATLAB or classical method. Solutions: p=1;d=[1,1,-6]; ys=[1,-1]; xn=8 * ones(1,8); si=filtic(p,d,ys); yn=filter(p,d,xn,si); Notes: Using classical method, the total solution is 5. The transfer function of a FIR digital filter is (a) Determine the impulse response of the FIR digital filter. (b) Is it a linear-phase FIR filter? Prove the answer. (c) Develop a minimum-multipliers realization. (d) Let the input sequence be , determine the output sequence . Solutions: Applying inverse Z-transform