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### Simulate the System in Python for the Spectral Analysis Case Study

To finish off this case study, simulate the system in Python. To give you a feel for sinusoidal spectrum analysis and window selection, here’s a Python simulation that utilizes the test signal: [more…]

### Examine the Open-Loop System Function

Before getting into the closed-loop system function of the CD/DVD case study, consider a few attributes of the open-loop system function by writing it out, leaving [more…]

### Investigate the Closed-Loop System Function

With the simplification to the open-loop system function in place, you can dive in and find the closed-loop system function of the CD/DVD case study, with full variable substitution. Here’s the closed-loop [more…]

### Create a System Block Diagram for the Cruise Control Case Study

After the system has been linearized, a system block diagram utilizing Laplace transform (LT) techniques for feedback control of the vehicle velocity can be constructed. The differential equation can now [more…]

### Simulate the Time Domain for the Cruise Control Case Study with Pylab

In this cruise control case study, you can use Pylab and the SciPy function lsim() to evaluate the cruise control performance with a 4 percent grade. Note that a grade of 4 percent means rise over run [more…]

### Working across Domains Example: Take the RC Low-Pass Filter to the Z-Domain

Working across domains is a fact of life as a computer and electronic engineer. Solving real computer and electrical engineering tasks requires you to assimilate the vast array of signals and systems concepts [more…]

### How to Work and Verify Convolution Integral and Sum Problems

Mastering convolution integrals and sums comes through practice. Here are detailed analytical solutions to one convolution integral and two convolution sum problems, each followed by detailed numerical [more…]

### How to Characterize the Peaking Filter for an Audio Graphic Equalizer

A peaking filter for an audio graphic equalizer provides gain or loss (attenuation) at a specific center frequency *f** _{c}*. A peaking filter has unity frequency response magnitude, or 0 dB gain, at frequencies [more…]

### 10 Signals and Systems Properties You Never Want to Forget

A big wide world of properties is associated with signals and systems — plenty in the math alone! Here are ten unforgettable properties related to signals and systems work. [more…]

### 11 Common Mistakes to Avoid When Solving Problems

Here are eleven common mistakes students make when trying to solve problems and how to avoid them. Slow down enough to think through solutions, and make sure your fundamental understanding of the core [more…]

### How to Relate Signals and Systems Domains

To successfully apply the various signals and systems concepts as part of practical engineering scenarios, you need to know what analysis tools are available. The figure shows the mathematical relationships [more…]

### How to Use PyLab for LCC Differential and Difference Equations

Computer tools play a big part in modern signals and systems analysis and design. LCC differential and difference equations are a fundamental part of simple and highly complex systems. Fortunately, current [more…]

### Real-World Signals and Systems Case: Analog Filter Design with a Twist

You’re given the task of designing an analog (continuous-time) filter to meet the amplitude response specifications shown. You also need to find the filter step response, determine the value of the peak [more…]

### Real-World Signals and Systems Case: Solving the DAC ZOH Droop Problem in the *z*-Domain

The zero-order-hold (ZOH), which is inherent in many digital-to-analog converters (DACs), holds the analog output constant between samples. The action of the ZOH introduces [more…]

### The Two-Sided z-Transform

The *z-*transform (ZT) is a generalization of the discrete-time Fourier transform (DTFT) for discrete-time signals, but the ZT applies to a broader class of signals than the DTFT. The [more…]

### The Significance of the Region of Convergence (ROC)

The ZT doesn’t converge for all sequences. When it does converge, it’s only over a region of the *z-*plane. The values in the *z-*plane for which the ZT converges are known as the [more…]

### Continuous-Time Signals and Systems

Continuous-time signals and systems never take a break. When a circuit is wired up, a signal is there for the taking, and the system begins working — and doesn’t stop. Keep in mind that the term [more…]

### Discrete-Time Signals and Systems

Discrete-time signals and systems march along to the tick of a clock. Mathematical modeling of discrete-time signals and systems shows that activity occurs with whole number [more…]

### Signal Classifications

Signals, both continuous and discrete, have attributes that allow them to be classified into different types. Three broad categories of signal classification are periodic, aperiodic, and random. [more…]

### Testing Product Concepts with Behavioral Level Modeling

Computer and electrical engineers work through a process that allows them to test, or *model,* potential solutions to find out whether the idea is likely to work in the real world. For products that rely [more…]

### Signals and Systems of 3 Familiar Devices

You probably have some level of familiarity with consumer electronics, such as MP3 music players, smartphones, and tablet devices, and realize that these products rely on signals and systems. But you may [more…]

### Deterministic and Random Signal Classifications

A signal is classified as *deterministic* if it’s a completely specified function of time. A good example of a deterministic signal is a signal composed of a single sinusoid, such as [more…]

### Periodic and Aperiodic Signal Classifications

A type of signal classification you need to be able to determine is *periodic* versus *aperiodic.* A signal is periodic if *x*(*t*) = *x*(*t* + *T*_{0}), where *T*_{0}, the period, is the largest value satisfying the equality [more…]

### Power and Energy Signal Classifications

To classify a signal *x*(*t*) according to its power and energy properties, you need to determine whether the energy is finite or infinite and whether the power is zero, finite, or infinite. The measurement [more…]

### Even and Odd Signals

Signals are sometimes classified by their symmetry along the time axis relative to the origin, *t* = 0. *Even* signals fold about *t* = 0, and *odd* signals fold about [more…]