## Fundamentals of digital signal processing |

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algorithm aliasing analog filter analog frequency analog signal bandpass BIBO stable bilinear transformation Butterworth filter calculated causal coefficient difference equation complex multiplications constant coefficient difference convolution sum corresponding cutoff frequency defined difference equation digital filter digital frequency Digital Signal Processing direct form discrete Fourier transform discrete-time filter discrete-time signals discrete-time system elliptic filter evaluation EXAMPLE Figure filter design finite FIR filter frequency response gives H(eJ Ha(s input signal input x(n inverse transform linear constant coefficient linear phase linear shift invariant low-pass filter number of complex obtained output y(n Passband ripple plot poles prefilter rad/sec region of convergence sample response h(n samples/sec sampling rate sequence x(n shift invariant system shown in Fig signal xa(t sinusoidal sequence Solution specified steady state output stopband attenuation stopband gain structure summation system function H(z taking the inverse theorem transfer function transform of x(n unit sample response values z-plane zero