Demos - MATLAB

	Sinusoids	This is an introduction to plotting sinusoids (both sine and cosine waves) from equations. In addition, the tutorial reviews how to write the equation given a plot of the sinusoid.
	Rotating Phasors	Here are four movies showing rotating phasors and how the real part of the phasor traces out a sinusoid versus time. Two of the movies show how rotating phasors of different frequencies interact to produce complicated waveforms such as beat signals.
	Sine Drill	Sine Drill (sindrill) is a program that tests the users ability to determine basic parameters of a sinusoid. After a plot of a sinusoid is displayed, the user must correctly guess its amplitude, frequency, and phase.
	Tuning Fork	This demo shows how the size and stiffness of a tuning fork affect the tone produced by three different tuning forks.
	Clay Whistle	Here's a demo that shows the nearly sinusoidal waveforms produced by two clay whistles.
	ZDrill	ZDrill is a program that tests the users ability to calculate the result of simple operations on complex numbers. The program emphasizes the vectorial view of a complex number. The following six operations are supported: Add Subtract Multiply Divide Inverse Conjugate

3. Spectrum Representation

	FM Synthesis	This demo gives the mathematical derivation of how instrument sounds can be synthesized using the principles of frequency modulation. The example sounds include a bell and a clarinet.
	Rotating Phasors	Here are four movies showing rotating phasors and how the real part of the phasor traces out a sinusoid versus time. Two of the movies show how rotating phasors of different frequencies interact to produce complicated waveforms such as beat signals.
	Fourier Series	This MATLAB demo reconstructs a square, triangle, or sawtooth waveform, using a given number of Fourier Series coefficients.
	Spectrograms	This demo illustrates the connection between a variety of sounds and their spectrograms. Among the different sounds are simple tones and waveforms, real and synthesized music, and chirp signals.
	Vowel Synthesis	This demonstrates the idea of harmonic sinusoids. Five sinusoids with a common fundamental frequency are added together, one at a time.

4. Sampling and Aliasing

The collection of demos in Chapter 5 are designed to illustrate the concepts of sampling, aliasing and reconstruction.

	Aliasing and Folding	Here are some movies that illustrate the concepts of aliasing and folding when a sinusoid is sampled below the Nyquist rate.
	Continuous-Discrete Sampling	The Continuous-Discrete Sampling Demo (con2dis) is a program that shows the continuous and discrete spectra (and signals) during sampling. Features: Users can change the input frequency and sampling rate. Frequency axis can be labeled in hertz or radians/sec. Reconstruction through D/A is also shown.
	Reconstruction Movies	Here are some movies that illustrate the reconstruction process
	Sampling Theory Tutorial	These movies explain the basics of sampling rates and sampling periods. They also explain how to use Matlab to simulate a sinusoid of a given frequency and duration.
	Strobe Movies	These movies give an alternate view of the sampling process by using the strobing nature of a camcorder (30 frames per second) to show aliasing of a pattern on a rotating disk.
	Synthetic Strobe Movies	These movies were generated in MATLAB to show the strobe/sampling effect on a rotating disk. With MATLAB the rotation rate can be calibrated exactly, so that forward and backward movement of the spokes on the disk (due to aliasing) can be tracked.

5. FIR Filters

The Chapter 6 demos consist of block diagram examples designed to reinforce the ideas of linearity and time-invariance in FIR filtering.

Discrete Convolution Demo

The Discrete Convolution Demo (dconvdemo) is a program that helps visualize the process of discrete-time convolution.
Features:

Users can choose from a variety of different signals.
Signals can be dragged around with the mouse with results displayed in real-time.
Tutorial mode lets students hide convolution result until requested.
Various plot options enable the tool to be effectively used as a lecture aid in a classroom environment.

6. Frequency Response of FIR Filters

This collection of demos illustrates the effects of LTI filters on various types of signals. In the first demo the linearity of FIR filters is demonstrated by cascading filters and showing that the order of the cascade has no effect on the final output. The second demo explores the effects of low-pass filtering on signals. You will have an opportunity to listen to a composite chirp and speech signal before and after filtering.

	Cascading FIR Filters	LTI FIR filters are used to process images, thus demonstrating that low-pass filtering is blurring, while high-pass filtering will sharpen edges.
	DLTI Demo	DLTIDemo is a program that illustrates the relationship between the input and output of a discrete-time linear time-invariant (LTI) filter when the input is a sinusoidal function. The user is allowed to control the parameters of both the input sinusoid and the digital filter.
	Introduction to FIR Filtering	A brief introduction to FIR filters and how they can change the sound of speech signals.

7. Z-Transform

	Three Domains - FIR	The connection between the Z-transform domain of poles and zeros and the time domain, and also the frequency domain is illustrated with several movies where individual zeros or zero pairs are moved continuously.
	PeZ GUI	PeZ (pezdemo) is a MATLAB tool for pole/zero manipulation. Poles and zeros can be placed anywhere on a map of the z-plane. The corresponding time domain (n) and frequency domain (ω) plots will be displayed. When a zero pair (or pole pair) is dragged, the impulse response and frequency response plots will be updated in real time.
	PeZ Tutorial	These movies describe how to use the PeZ graphical user interface to place/move poles and zeros. They also show how to display the associated impulse and frequency response.
	Z to Freq	A demo that illustrates the connection between the complex Z-plane and the frequency response of a system. The frequency response is obtained by evaluating H(z) on the unit circle in the complex Z-plane.

8. IIR Filters

	Three Domains - IIR	The connection between the z-transform domain of poles and zeros and the time domain, and also the frequency domain is illustrated with several movies where individual poles, or zeros or pole pairs of IIR filters are moved continuously.
	PeZ GUI	PeZ (pezdemo) is a MATLAB tool for pole/zero manipulation. Poles and zeros can be placed anywhere on a map of the z-plane. The corresponding time domain (n) and frequency domain (ω) plots will be displayed. When a zero pair (or pole pair) is dragged, the impulse response and frequency response plots will be updated in real time.
	PeZ Tutorial	These movies describe how to use the PeZ graphical user interface to place/move poles and zeros. They also show how to display the associated impulse and frequency response.
	IIR Filtering	A short tutorial on first- and second-order IIR (infinite-length impulse response) filters. This demo shows plots in the three domains for a variety of IIR filters with different filter coefficients.
	Z to Freq	A demo that illustrates the connection between the complex Z-plane and the frequency response of a system. The frequency response is obtained by evaluating H(z) on the unit circle in the complex Z-plane.

9. Continuous-Time Signals and LTI Systems

	Continuous Convolution Demo	The Continuous Convolution Demo (cconvdemo) is a program that helps visualize the process of continuous-time convolution. Features: Users can choose from a variety of different signals. Signals can be dragged around with the mouse with results displayed in real-time. Tutorial mode lets students hide convolution result until requested. Various plot options enable the tool to be effectively used as a lecture aid in a classroom environment.
	Discrete Convolution Demo	The Discrete Convolution Demo (dconvdemo) is a program that helps visualize the process of discrete-time convolution. Features: Users can choose from a variety of different signals. Signals can be dragged around with the mouse with results displayed in real-time. Tutorial mode lets students hide convolution result until requested. Various plot options enable the tool to be effectively used as a lecture aid in a classroom environment.

10. Frequency Response

	CLTI Demo	CLTIDemo is a program that illustrates the relationship between the input and output of a continous-time linear time-invariant (LTI) filter when the input is a sinusoidal function. The user is allowed to control the parameters of both the input sinusoid and the filter.
	Fourier Series	This MATLAB demo reconstructs a square, triangle, or sawtooth waveform, using a given number of Fourier Series coefficients.

11. Continuous-Time Fourier Transform

	CLTI Demo	CLTIDemo is a program that illustrates the relationship between the input and output of a continous-time linear time-invariant (LTI) filter when the input is a sinusoidal function. The user is allowed to control the parameters of both the input sinusoid and the filter.
	Fourier Series	This MATLAB demo reconstructs a square, triangle, or sawtooth waveform, using a given number of Fourier Series coefficients.

12. Filtering, Modulation, and Sampling

	CLTI Demo	CLTIDemo is a program that illustrates the relationship between the input and output of a continous-time linear time-invariant (LTI) filter when the input is a sinusoidal function. The user is allowed to control the parameters of both the input sinusoid and the filter.
	Fourier Series	This MATLAB demo reconstructs a square, triangle, or sawtooth waveform, using a given number of Fourier Series coefficients.

13. Computing the Spectrum

	Wideband FM Signals	Four FM signals are presented via sound and spectrogram. Each signal chirps faster than the one before it.
	Music GUI	A MATLAB graphical user interface for composing music, listening to sinusoidal synthesis and viewing the spectrogram of the song.
	Resolution of the Spectrogram	These movies illustrate the inherent trade-offs between time and frequency resolution of the spectrogram when it is computed by a sliding-window FFT.

A. Complex Numbers

	Complex Numbers via Matlab	Examples of how complex numbers and complex exponentials can be handled by MATLAB.
	PhasorRaces	PhasorRaces began as a speed drill for testing complex addition. Now it includes many other related operations that can be tested in a "drill" scenario: adding sinusoids, z-transforms, etc. A timer starts as soon as the problem is posed, so that a student can try to solve questions quickly and accurately.
	ZDrill	ZDrill is a program that tests the users ability to calculate the result of simple operations on complex numbers. The program emphasizes the vectorial view of a complex number. The following six operations are supported: Add Subtract Multiply Divide Inverse Conjugate