Z Transform, Sampling and the DTFT.
• Sampling and Definition of Z transform.
• Z transform, Convergence.
• Z transform of step and related functions.
• Z transform of ramp and parabola.
• Z transform of exp and sinusoid.
• Table of Z transforms.
• Properties of Z transforms.
• Inverse Z transform by listing terms.
• Inverse Z transform by partial fraction expansion.
• Roots of cubic and quartic polynomials.
• Roots of polynomials order 3 to 14.
• Inverse Z transform using inversion integral.
• Z transforms and difference equations.
• Inverse Z transform using Division.
• Relation of Z transform to Laplace transform.
• Mapping s plane semiellipse to Z plane.
• Z plane and Stability
• Relation between Z transform, the Fourier transform and the DTFT.
• DTFT, 2 Negative Exponents.
• DTFT, Time Limited Unit Step
• DTFT, Time Limited Square Wave
• DTFT, Damped Sine.
• DTFT, 2 Sinusoids
• DTFT, Time Limited Cosine.
• Sampling, Frequencies in Sampled Signal.
• Sampling, Reconstruction of Sampled Signal.
• Sampling, Reconstruction of Presampled Signal.
• Sampling, Triangular Spectrum and Aliasing.
• Sampling, Sample Width and Signal Spectrum.
• Z Transform and Discrete Convolution.
• Z Transform and System Response.
• DeConvolution.
• System identification.
• Matched Filter.
• Correlation 1.
• Correlation 2.
• RC Step Response by Convolution.
• RC Step Response by Difference Equation.

Basic Filter Concepts, Poles, Zeros and Frequency response.



• Introduction
• 1 Pole Frequency Response.
• 1 Pole Impulse, Step and Ramp Response.
• 1 Pole Magnitude and Phase in unit Circle.
• 1 Pole Sine, Square, Triangle Signal Response.
• 1 Pole/1 Zero Frequency Response.
• 1 Pole/1 Zero Impulse, Step and Ramp Response.
• 1 Pole/1 Zero Magnitude and Phase in unit Circle.
• 2 Poles Frequency Response.
• 2 Poles Impulse, Step and Ramp Response.
• 2 Poles Magnitude and Phase in unit Circle.
• 2 Poles Sine, Square. Triangle Wave Response.
• 2 Poles/2 Zeros Frequency Response.
• 2 Poles/2 Zeros Impulse, Step and Ramp Response.
• 2 Poles/2 Zeros Magnitude and Phase Surface.
• 3 Poles Frequency Response.
• 3 Poles Impulse, Step and Ramp response.
• 3 Poles Magnitude and Phase in unit Circle.
• 4 Poles Frequency Response.
• 4 Poles Impulse, Step and Ramp Response.
• 4 Poles Magnitude and Phase Surface.
• 4 CC Poles, 2 CC Zeros Frequency Response.
• 4 CC Poles, 4 CC Zeros Frequency Response.
• First order AllPass Filter.
• Second Order AllPass Filter.
• Linear Phase Filter.
• 4 CC Zeros, Impulse and Frequency response.
• 6 CC Zeros, Impulse and Frequency response.
• 8 CC Zeros, Impulse and Frequency response.
• Comb Filter.
• Inverse Comb Filter.
• Inverse Comb with Cancelled Zeros.

DFT
• DFT, Definition and Properties.
• DFT, Calculations.
• DFT, Transform for simple signals 1.
• DFT, Transform for simple signals 2.
• DFT, Transform for simple signals 3.
• DFT and the DTFT.
• DFT and the Fourier Series.
• DFT, 8 Samples Even Odd.
• DFT, 32 Samples.
• DFT, Time Shift.
• DFT, Rectangle/Ramp/Triangle/Cosine Pulse.
• DFT, Square to Triangle and related signals.
• DFT, Sine, Real, Imag.
• DFT, 1 Sine Nonlinear.
• DFT, 1 Sinusoid and related signals, Range and Resolution.
• DFT, 1 Sine Hamming, Kaiser Windows.
• DFT, Sinc.
• DFT, 2 Sines.
• DFT, 2 Sines Window.
• DFT, 2 Sines Nonlinear.
• DFT, 2 Sines Parseval.
• DFT, Complex Signal, Gabor Wavelet.
• DFT, AM, FM.
• DFT, 3 Sines Band Pass Sampling.
• DFT, 3 Sines Short Time.
• DFT, 8 Samples Zero Padding.
• DFT, 8 Samples, Sinusoid, Resampling and interpolation.
• DFT, Effect of Quantisation on Spectrum.
• DFT, Quantisation error.
• DFT, Van Der Pol.
• DFT, Chaos.
• DFT, 2 Sines Random Noise.
• DFT, Sinusoid with Noise, Frequency domain filtering.
• DFT, Rec Pulse and RC Circuit, Frequency Domain I/O.
• DFT, Rectangle Pulse Bilinear, 2nd order Circuit, Frequency Domain I/O.

FFT
• Introduction
• DIT, Butterfly diagram, 8 Samples, Natural Input, Scrambled output.
• DIT, Butterfly diagram, 8 Samples, Scrambled Input, Natural output.
• DIT, Butterfly diagram, 8 Samples, Natural Input, Natural output.
• DIF, Butterfly diagram, 8 Samples, Natural Input, Scrambled output.
• DIF, Butterfly diagram, 8 Samples, Scrambled Input, Natural output.
• DIF, Butterfly diagram, 8 Samples, Natural Input, Natural output.
• DIT, Butterfly diagram, 8 Samples, Complex Natural Input, Natural output.
• FFT, Sinusoid, Square, Triangle, Range and Resolution.
• FFT, 2 Sinusoids.
• FFT, 2 Sinusoids with Hamming Window.
• FFT, Other Waveforms.
• FFT, AM.
• FFT, FM.
• FFT, FM, NonSinusoidal.
• FFT, Phase Modulation.
• FFT, Pulse Amplitude Modulation.
• FFT, Pulse Position Modulation.
• FFT, Amplitude Shift Keying.
• FFT, Frequency Shift Keying.
• FFT, Phase Shift Keying.
• Spectrogram, Damped exponent, Gauss.
• Spectrogram, Chirp, FM.
• FFT, Diffraction and Interference.
• 2D FFT Diffraction Patterns.
• 2D FFT bit mapped aperture.

Infinite Impulse Response Filters
• Infinite Impulse Response Filters, Introduction
• Impulse Invariant Response, Introduction
• Impulse Invariant Response, 2nd Order Butterworth Lowpass
• Impulse Invariant Response, 2nd Order Butterworth Lowpass, Impulse Response
• Impulse Invariant Response, 2nd Order Butterworth Lowpass, Magnitude Surface
• Impulse Invariant Response, 3rd Order Butterworth lowpass
• Step Invariant Response, Introduction
• Step Invariant Response, 2nd Order Butterworth Lowpass
• Step Invariant Response, 2nd Order Butterworth Lowpass, Impulse, Step Response
• Step Invariant Response, 2nd Order Butterworth Lowpass, Magnitude Surface
• Step Invariant Response, 3rd Order Butterworth lowpass
• Matched Z, Introduction
• Matched Z, 2nd Order Butterworth Lowpass
• Matched Z, 2nd Order Butterworth Lowpass. Impulse Response
• Matched Z, 2nd Order Butterworth Lowpass. Magnitude Surface
• Matched Z, 3rd Order Butterworth lowpass
• Matched Z with zeros, 2nd Order Butterworth Lowpass
• Matched Z with zeros, 3rd Order Butterworth lowpass
• Matched Z, 2nd,3rd Order Butterworth highpass
• Bilinear Transformation, Introduction
• Bilinear Transformation, 2nd Order Butterworth Lowpass
• Bilinear Transformation, 2nd Order Butterworth Lowpass, Impulse Response
• Bilinear Transformation, 2nd Order Butterworth Lowpass, Magnitude Surface
• Bilinear Transformation without prewarping, 2nd Order Butterworth Lowpass
• Bilinear Transformation, 3rd Order Butterworth lowpass
• Bilinear Transformation, 3rd Order Butterworth, Magnitude Surface
• Bilinear Transformation, 2nd,3rd Order Butterworth highpass
• Comparison of approximations for third order Butterworth Filter.
• IIR Realization.
• Bilinear Approximation to nth order Low Pass Butterworth Filter.
• Bilinear Approximation to nth order High Pass Butterworth Filter.
• Bilinear Approximation to nth order Low Pass Chebychev Filter.
• Bilinear Approximation to nth order High Pass Chebychev Filter.
• Bilinear Approximation to nth order Low Pass Elliptic Filter.
• Bilinear Approximation to nth order High Pass Elliptic Filter.
• Mirror Image Polynomials, Intro.
• Mirror Image Polynomials, Sin, Low Pass
• Mirror Image Polynomials, Sin, High Pass
• Mirror Image Polynomials, Tan, Low Pass
• Mirror Image Polynomials, Tan, High Pass

FIR Filters
• Fourier Series Intro.
• Fourier Series, LP, HP, BP, BS Filters.
• Fourier Series low pass, Phase.
• Fourier Series low pass, Zeros.
• Low Pass FIR Filters and Zero Placement.
• High Pass FIR Filters and Zero Placement.
• Windows Intro.
• LP/HP/BP/BS Filters with Hamming/Hanning/Blackman Windows.
• LP/HP/BP/BS Filters with the Blackman Harris Window.
• Low Pass with Various Windows.
• Low Pass with Bl/Hn/Hm/Rec Window, Zeros.
• Low Pass with Kaiser Window.
• High Pass with the Kaiser Window.
• Band Pass with the Kaiser Window.
• Band Stop with the Kaiser Window.
• Low Pass with the Dolph-Chebyshev Window.
• Low Pass Comparison of Kaiser and Hamming/Blackman/Blackman Harris Window.
• Low Pass Comparison of Dolph-Chebyshev and Hamming/Blackman/Blackman Harris Window.
• Low Pass Comparison of Kaiser and Dolph-Chebyshev Window.
• High Pass with Dolph-Chebyshev Window.
• Band Pass with Dolph-Chebyshev Window.
• Band Stop with Dolph-Chebyshev Window.
• FIR filter 'design' with the Fourier Series and the Kaiser Window.
• FIR Filter 'design' with the Fourier Series and the Dolph-Chebyshev Window.
• Effect of Quantizing the Impulse Response.
• DFT Frequency Sampling Intro.
• DFT Frequency Sampling Linear Samples.
• DFT Frequency Sampling Log Samples.
• DFT Frequency Sampling, Kaiser Window.
• DFT Frequency Sampling, Transition Samples.
• DFT Frequency Sampling, Transition Samples 2.
• Introduction to Equiripple Filters.
• Low Pass Equiripple Filters.
• Comparison of Equiripple Approximation and Kaiser Window.
• Comparison of Equiripple Approximation and Chebychev Window.
• High Pass Equiripple Filters.
• Band Pass Equiripple Filters.
• Band Stop Equiripple Filters.
  
  If the screen resolution is greater than 1200(H) x 900(V), then the following may be tried.
  
  
• Low Pass Equiripple Filter.
• High Pass Equiripple Filter.
• Band Pass Equiripple Filter.
• Band Stop Equiripple Filter.
  
  
• DSP References..

For Analog Signal Processing see:- cnyack
For Circuits see:- circuits-can
For Control see:- control-can