Signals and Systems - Electrical Engineering

704 C H A P T E R 11: Introduction to the Design of Discrete Filters 11.12. Butterworth versus Chebyshev filtering—MATLAB If we ...

Problems 705 11.15. IIR comb filters—MATLAB Consider a filter with transfer function H(z)=K 1 +z−^4 1 +( 1 / 16 )z−^4 (a) Find t ...

706 C H A P T E R 11: Introduction to the Design of Discrete Filters 11.20. Down-sampling transformations—MATLAB Consider down s ...

Problems 707 11.25. Realization of IIR filters Given the realization in Figure 11.35: FIGURE 11.35 Problem – 11.25: IIR realizat ...

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CHAPTER 12 Applications of Discrete-Time Signals and Systems................................. Nullius in verba (Take nobody’s wo ...

710 CHAPTER 12: Applications of Discrete-Time Signals and Systems indicated before, digital communications began with the introd ...

12.2 Application to Digital Signal Processing 711 12.2.1 Fast Fourier Transform Comparing the equations for the DFT and the inve ...

712 CHAPTER 12: Applications of Discrete-Time Signals and Systems Decimation-in-Time Algorithm Applying the divide-and-conquer p ...

12.2 Application to Digital Signal Processing 713 whereIN/ 2 is a unit matrix andN/ 2 is a diagonal matrix with entries{WNk,k=0 ...

714 CHAPTER 12: Applications of Discrete-Time Signals and Systems which requires 16 multiplications (8 if multiplications by 1 a ...

12.2 Application to Digital Signal Processing 715 which in matrix form is       Y[0] Y[1] ··· Z[0] Z[1]       =   ...

716 CHAPTER 12: Applications of Discrete-Time Signals and Systems the same locations. Since X[k]is typically complex, to have id ...

12.2 Application to Digital Signal Processing 717 transformed. Sincek=k 1 p+k 0 the final equation isY[k]+WNkZ[k], which we obta ...

718 CHAPTER 12: Applications of Discrete-Time Signals and Systems FIGURE 12.2 Lattice forn 0 =0, 1andn 1 =0,..., 3(the values in ...

12.2 Application to Digital Signal Processing 719 G[k]= ∑^1 n 1 = 0 y[1,n 1 ]Wn 21 k= ∑^1 n 1 = 0 y[2n 1 +1]W 2 n^1 k= ∑^1 n 1 = ...

720 CHAPTER 12: Applications of Discrete-Time Signals and Systems FIGURE 12.3 CPU times for thefftand the dftfunctions used in c ...

12.2 Application to Digital Signal Processing 721 andy[n] of lengthsNandMis obtained in the frequency domain by following these ...

722 CHAPTER 12: Applications of Discrete-Time Signals and Systems M = 2∗NN-1; t0 = cputime; y = conv(x,x); % convolution using c ...

12.3 Application to Sampled-Data and Digital Control Systems 723 FIGURE 12.5 Digital implementation of a continuous-feedback sys ...