Notes on Signals & Systems

These notes were created by Dr. Fred DePiero , et. al. of the CalPoly Electrical Engineering Dept and are used in EE 228, 302/342, 328/368, 419/459, 515, 525 and 528, at CalPoly.

General

Analog Signals and Transforms

Discrete Signals, Sampling, and Transforms

Analog Filters

Digital Filters

Advanced DSP

Analog Control Systems

Probability & Random Signals

Kalman Filter

Applied Math

Convolution Demo

This demo illustrates the process of evaluating a convolution integral to obtain y(t) = h(t)*x(t). Shows intermediate signals, including "flip & slide" version of x(), and its product with h(). User can select various signals for x() and h(), and vary the wave shape (duration, for example). The 'User' menu animates the calculation of the convolution integral, which can also be observed by moving the lower slider. User menu also provides a choice of adjusting either x(t) or h(t) using the sliders.

This demonstration illustrates a number of concepts in signals and systems including:

Download the ZIP File and extract to any convenient location, such as the desktop. Open the extracted folder named 'SIPTool 1D Convolution', and run the 'SIPTool' executable.

Click on the 'x(l)', 'x(t-l)', and' h(l)x(t-l)' tabs to see intermediate signals. The lower slider adjusts 't', shifting the input and changing the overlapping functions. The product of 'h(l)x(t-l)' appears in blue. The 'y(t)' tab shows the output, as computed up to time 't'. See the 'User' menu to select which signal (x or h) the sliders affect. Left-click on the waveform names appearing in the 'x(t) Type' and 'h(t) Type' tabs to alter the type of signal.

Notch Filter Demo

This demo processes signals from the microphone in real-time. Input and output signals are displayed in both the time and frequency domains. The notch filter is described by its frequency response, a pole-zero plot, and the impulse response. The center frequency and pole radius of the filter are adjustable by sliders.

This demonstration illustrates a number of concepts associated with digital filters:

Download the ZIP File and extract to any convenient location, such as the desktop. Open the extracted folder named 'Audio Notch', and run the 'Audio Notch SIPTool' executable.

To activate on-line processing, select on of the 'User' -> 'Process Mic' menu options. The signal that initially appears was from a whistle. Have Fun!

Short-Time Fourier Transform Demo

This demo uses WAV files for input and plots the Short-Time Fourier Transform, as well as a standard Fourier Transform and a time-domain plot. A plot similar to that of a spectrum analyzer is also shown.

This demonstration illustrates a number of concepts associated with digital signals:

Download the ZIP File and extract to any convenient location, such as the desktop. Open the extracted folder named 'STFT for WAV', and run the 'SIPTool.exe' executable.

The 'STFT Magnitude' tab depicts the energy content of the signal as a function of time (horizontally) and frequency (vertically, lower frequencies at the top). Left-click in the tab windows and select 'Playback' to hear the WAV file played. You will also see a cursor sweep the STFT display (roughly) in time with the audio. Other left-click options are also available. Drag and drop a WAV file into the tab window to load a new file. Have Fun!

Root Locus Demo

This demonstration package addresses fundamental concepts in control systems, including contruction of root locus, transfer functions, construction of a Bode plot and deeterminiation of gain and phase margin. Nyquist plots are also illustrated. The step response is shown in a traditional format (output versus time) and via an X-Y plotter. In the X-Y display two independent positioners are animated. The horizontal positioner has dynamics and gain set by the input file and sliders. The vertical positioner has the same poles and zeros but half the gain value.

Further info and a download are available.

All materials on this site are copyright by Professor DePiero, and others.