A Visual Interactive approach to
Digital Signal Processing.
Page Index.
Cuthbert Nyack
Java Applets.
Because of events over the last few years, Java applets no
longer have a future on the web for the kind of application used here.
Work is currently in progress to replace the java applets that were on these pages with javascripthtmlcss.
This has the advantage that it is possible to have the result look and work the same way
in any browser and on any device. To date the ones that have been completed have been
tested with different browsers on windows and apple pc's, android and windows tablets and android phones.
Because of time commitments to other issues, it will take a while to complete
the conversion from java applets to javascript.
Cuthbert Nyack. 20150726.
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 DolphChebyshev Window.

Low Pass Comparison of Kaiser and Hamming/Blackman/Blackman Harris Window.

Low Pass Comparison of DolphChebyshev and Hamming/Blackman/Blackman Harris Window.

Low Pass Comparison of Kaiser and DolphChebyshev Window.

High Pass with DolphChebyshev Window.

Band Pass with DolphChebyshev Window.

Band Stop with DolphChebyshev Window.

FIR filter 'design' with the Fourier Series and the Kaiser Window.

FIR Filter 'design' with the Fourier Series and the DolphChebyshev 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: circuitscan
For Control see: controlcan
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Copyright © 1996, 2008 Cuthbert A. Nyack.