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A/D converter aliasing analog signal autocorrelation autocorrelation sequence cascade causal complex computation Consequently continuous-time convolution corresponding decimation Determine difference equation digital filter digital signal processing direct form discrete-time signal equivalent example expressed factor FFT algorithm FIGURE filter coefficients filter design finite FIR filter FIR system Fourier series Fourier transform frequency domain frequency response frequency response characteristics given Hence illustrated in Fig implementation impulse response impulse response h(n input sequence input signal interpolation inverse linear time-invariant system linear-phase FIR filter lowpass filter LTI system magnitude and phase matrix method multiplications noise obtain parameters passband periodic signal phase response pole-zero poles polynomial power spectrum estimate quantization errors random process realization recursive result sampling rate second-order sequence x(n shown in Fig signal x(n Solution specifications spectral state-space stopband structure subroutine system described unit circle unit sample response V-point values variable variance xa(t z-transform zero