10.1 The Complex Sinusoid10.2 Complex Math Review10.3 Time Delay as a Math Operator10.4 The Sampled Sinusoid10.5 1st Order Feed-Forward Filter Revisited10.5.1 Negative Frequencies10.6 Evaluating the Transfer Function H(ω)10.6.1 DC (0 Hz)10.6.2 Nyquist (π)10.6.3 ½ Nyquist (π/2)10.6.4 ¼ Nyquist (π/4)10.7 Evaluating e jω10.8 The z Substitution10.9 The z Transform10.10 The z Transform of Signals10.11 The z Transform of Difference Equations10.12 The z Transform of an Impulse Response10.13 The Zeros of the Transfer Function10.14 Estimating the Frequency Response: Zeros10.15 Filter Gain Control10.16 1st Order Feedback Filter Revisited10.16.1 Step 1: Take the z Transform of the Difference Equation10.16.2 Step 2: Fashion the Difference Equation into a Transfer Function10.16.3 Step 3: Factor out a0 as the Scalar Gain Coefficient10.17 The Poles of the Transfer Function10.17.1 Step 4: Estimate the Frequency Response10.17.2 Step 5: Perform Direct Evaluation of the Frequency Response10.17.3 DC (0 Hz)10.17.4 Nyquist (π)10.17.5 ½ Nyquist (π/2)10.17.6 ¼ Nyquist (π/4)10.18 2nd Order Feed-Forward Filter10.18.1 Step 1 and Step 2: Take the z Transform of the Difference Equation
and Fashion it into a Transfer Function10.18.2 Step 3: Factor Out a0 as the Scalar Gain Coefficient10.18.3 Step 4: Estimate the Frequency Response10.18.4 Step 5: Direct Evaluation10.18.5 DC (0 Hz)10.18.6 Nyquist (π)10.18.7 ½ Nyquist (π/2)10.18.8 ¼ Nyquist (π/4)10.18.9 z Transform of Impulse Response10.19 2nd Order Feedback Filter10.19.1 Step 1, Step 2, and Step 3: Take the z Transform of the Difference
Equation to Get the Transfer Function, Then Factor Out a0 as the Scalar Gain Coefficient10.19.2 Step 4: Estimate the Frequency Response10.19.3 Step 5: Direct Evaluation10.19.4 DC (0 Hz)10.19.5 Exercise10.20 1st Order Pole/Zero Filter: The Shelving Filter10.20.1 Step 1, Step 2, and Step 3: Take the z Transform of the Difference
Equation to Get the Transfer Function, Then Factor Out a0 as the Scalar Gain Coefficient10.20.2 Step 4: Estimate the Frequency Response10.20.3 Step 5: Direct Evaluation10.20.4 DC (0 Hz)10.20.4.1 Exercise10.21 The Biquadratic Filter10.21.1 Step 1, Step 2, and Step 3: Take the z Transform of the Difference
Equation to Get the Transfer Function, Then Factor Out a0 as the Scalar Gain Coefficient10.21.2 Step 4: Plot the Poles and Zeros of the Transfer Function10.21.3 The aN and bM Coefficient Naming Conventions10.22 Other Biquadratic Structures10.23 C++ DSP Object: Biquad10.23.1 Biquad: Enumerations and Data Structure10.23.2 Biquad: Members10.23.3 Biquad: Programming Notes10.24 Homework10.25 Bibliography