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### Signals & Systems For Dummies Cheat Sheet

Signals and systems is an aspect of electrical engineering that applies mathematical concepts to the creation of product design, such as cell phones and automobile cruise control systems. Absorbing the [more…]

### How to Verify a Convolution Integral Problem Numerically

Here is a detailed analytical solution to a convolution integral problem, followed by detailed numerical verification, using PyLab from the IPython interactive shell [more…]

### Application Example: Frequency Tripler

The Fourier series is a powerful mathematical tool, and it applies to multiple branches of engineering and mathematics. The design of a *frequency tripler* [more…]

### 11 Signals and Systems Concepts Used to Design an Audio Graphic Equalizer

Following are eleven signals and systems concepts that apply to the design of a signal processing system known as an *audio graphic equalizer*. When you listen to music on a portable music player or a computer [more…]

### Use an Antialiasing Filter to Avoid Aliasing at the ADC

The great attributes of discrete-time signals and systems rely on the ability to interface with the continuous-time domain. Analog-to-digital converters [more…]

### Implement a Real-World System: Karaoke Machine

Here’s a system-level look at the signals and systems model of a karaoke machine — an audio playback system with a powerful speaker that allows a person to sing over recorded music. A multimedia interface [more…]

### Conduct Performance Testing on an Audio Graphic Equalizer

The real deal with a ten-band equalizer is that you can graphically visualize the spectral shaping you provide to the signal passing through the equalizer by just looking at the positions of slider gain [more…]

### Signals and Systems Math Comes to Life with Animation Apps

You may not fully appreciate the mathematics of signals and systems on your first encounter. To enhance your understanding, you can use computer animation to bring to life some of the more difficult concepts [more…]

### Simplify the Analysis with Complex Baseband Signals

The block diagram is a hybrid of discrete-time and continuous-time signals and systems. When studying the performance of a digital communications scheme, working with the [more…]

### AM Broadcast Frequency Spectrum

For many people in the United States, AM radio — a legacy modulation scheme known as *amplitude modulation* (AM) — is the place to go for talk radio and sports. But AM is more than just commercial broadcasting [more…]

### Test the AM Radio Design with a Voice Message

You can test the AM receiver by using an actual voice message. The value of this test lies in actually listening to the speech before and after it goes through the communications link. Your ears hear differences [more…]

### Start the Cruise Control Case Study with Physics

This case study begins with model construction, starting from basic physics. Special consideration is given to incorporate wind resistance and include as a system [more…]

### Define the Problem for the Signal Processing Case Study

The block diagram of a system that uses a digital filter to remove an SNOI and retain the SOI is shown. This system assumes that the signals originate in continuous time and, after filtering, are returned [more…]

### Analysis and Design of the FIR and IIR Notch Filters

*Option**s* *a* and *b* are the fixed FIR and IIR notch filters, respectively. The simplicity of these filters is a major draw. But how well do they work? Characterizing the filters in the frequency domain is [more…]

### Simulate the System in Python for the Signal Processing Case Study

Simulate *O**ptions a, b,* and *c* by using a speech file of a male voice reading phrases. The file enters the simulation as a wav file: [more…]

### Define the Problem for the Spectral Analysis Case Study

A basic digital spectrum analyzer is shown in the figure. The default window, *w*[*n*], is a constant of one over the capture interval of *N** _{r}* samples. The FFT works with a finite length discrete-time signal [more…]

### Perform Analysis and Design for the Spectral Analysis Case Study

Increasing the data record length, denoted *N** _{r}* in this case study, improves spectral resolution, but the decay rate of the spectral leakage still needs to be addressed. Many window choices are available [more…]

### CD/DVD Electromechanical System

This case study focuses on the *sled* position control system, which moves the read/write laser assembly radially under the spinning CD. Check out the figure for a close-up of a CD/DVD electromechanical [more…]

### Create a System Block Diagram for the CD/DVD Case Study

The system block diagram for the sled (coarse laser position) control system on a CD/DVD drive is composed of several subsystems. Start with a continuous-time linear time-invariant [more…]

### Simulate the Time Domain for the CD/DVD Case Study with PyLab

You can simulate the complete CD/DVD drive control system by using a step function input for *r*(*t*), which is the commanding signal for the sled positioner. The output should be scaled in millimeters for [more…]

### Connecting Pole-Zero Geometry and Frequency Response: A Video

In the study of both continuous-time and discrete-time systems, the frequency response and its relationship to pole and zero locations in the *s**-* and *z**-* [more…]

### Diagram the System to Transmit Binary Data

The various blocks of a digital communication system are a hybrid of discrete-time signal generation and filtering, continuous-time signal processing at baseband frequencies, and continuous-time radio [more…]

### Simulate the System for Transmitting Binary Data in Python

As a simple experiment, this case study generates three tightly packed SRC shaped BPSK signals. The signal of interest is centered at *f* = 0, while the cochannel signals — those that are nearest neighbors [more…]

### Create a System Block Diagram for the AM Radio Design

Visualize the big picture of the AM radio transmitter, receiver, and interfering signals with a system block diagram. Each block in the diagram has an underlying mathematical model. [more…]

### Adjacent-Channel Interference for the AM Radio Design

In reality, multiple radio stations operate in the same metro area, or *market**.* When you tune in a signal at 750 kHz, another signal may be at 760 kHz. To find out whether the adjacent signal impacts the [more…]