Filter Circuits: Frequency Response, Bode Plots, and Fourier Transform

  • Sergey N. Makarov
  • Reinhold Ludwig
  • Stephen J. Bitar


Knowledge of complex arithmetic


Analog filter RC filter RL filter Port Two-port network First-order high-pass filter First-order low-pass filter Filter termination Amplitude transfer function Phase transfer function Power transfer function Complex transfer function Frequency response Break frequency Half-power frequency 3-dB frequency Corner frequency Bode plot Decibel Roll-off High-frequency asymptote Low-frequency asymptote Frequency band Passband Stopband Decade Octave Power gain Open-loop amplifier gain Unity-gain bandwidth Gain-bandwidth product Internal compensation Open-loop AC gain Closed-loop AC gain Amplifier circuit bandwidth, Fourier transform continuous (direct inverse Fourier spectrum direct inverse Fourier spectrum bandlimited spectrum reversal property sinc function mathematical properties amplitude-modulated signal Parseval’s theorem energy spectral density), Fourier transform discrete (Fast digital signal processing (DSP) sampling points sampling interval sampling frequency sampling theorem Riemann sum approximation rectangle rule fundamental frequency direct (DFT) inverse (IDFT) standard form reversal property structure of discrete spectrum numerical differentiation filter operation for pulse signals) 

Supplementary material

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sergey N. Makarov
    • 1
  • Reinhold Ludwig
    • 2
  • Stephen J. Bitar
    • 3
  1. 1.ECE DepartmentWorcester Polytechnic InstituteWorcesterUSA
  2. 2.ECE DepartmentWorcester Polytechnic InstituteWorcesterUSA
  3. 3.Worcester Polytechnic InstituteWorcesterUSA

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