We know that ideal filters are not physically possible. Here we take our first steps toward practical–buildable–linear time-invariant systems.
Previous SPTK Post: The Laplace Transform Next SPTK Post: The Z Transform
Before we translate the Laplace transform from continuous time to discrete time, deriving the Z transform, let’s take a step back and look at practical filters in continuous time. Practical here stands in opposition to ideal as in the ideal lowpass, highpass, and bandpass filters we studied earlier in the SPTK thread.
Continue reading “SPTK: Practical Filters”An interesting paper on the true nature of the impulse function we use so much in signal processing.
The impulse function, also called the Dirac delta function, is commonly used in statistical signal processing, and on the CSP Blog (examples: representations and transforms). I think we’re a bit casual about this usage, and perhaps none of us understand impulses as well as we might.
Enter C. Candan and The Literature [R155].
Continue reading “Comments on “Proper Definition and Handling of Dirac Delta Functions” by C. Candan.”Some examples of random variables encountered in communication systems, channels, and mathematical models.
Previous SPTK Post: Random Variables Next SPTK Post: Random Processes
In this Signal Processing ToolKit post, we continue our exploration of random variables. Here we look at specific examples of random variables, which means that we focus on concrete well-defined cumulative distribution functions (CDFs) and probability density functions (PDFs). Along the way, we show how to use some of MATLAB’s many random-number generators, which are functions that produce one or more instances of a random variable with a specified PDF.
Continue reading “SPTK: Examples of Random Variables in Communication-Signal Contexts”Ideal filters have rectangular or unit-step-like transfer functions and so are not physical. But they permit much insight into the analysis and design of real-world linear systems.
Previous SPTK Post: Convolution Next SPTK Post: The Moving-Average Filter
We continue with our non-CSP signal-processing tool-kit series with this post on ideal filtering. Ideal filters are those filters with transfer functions that are rectangular, step-function-like, or combinations of rectangles and step functions.
Continue reading “SPTK: Ideal Filters”Convolution is an essential element in everyone’s signal-processing toolkit. We’ll look at it in detail in this post.
Previous SPTK Post: Interconnection of Linear Systems Next SPTK Post: Ideal Filters
This installment of the Signal Processing Toolkit series of CSP Blog posts deals with the ubiquitous signal-processing operation known as convolution. We originally came across it in the context of linear time-invariant systems. In this post, we focus on the mechanics of computing convolutions and discuss their utility in signal processing and CSP.
Continue reading “SPTK: Convolution and the Convolution Theorem”Real-world signal-processing systems often combine multiple kinds of linear time-invariant systems. We look here at the general kinds of connections.
Previous Post: Frequency Response Next Post: Convolution
It is often the case that linear time-invariant (or for discrete-time systems, linear shift-invariant) systems are connected together in various ways, so that the output of one may be the input to another, or two or more systems may share the same input. In such cases we can often find an equivalent system impulse response that takes into account all the component systems. In this post we focus on the serial and parallel connections of LTI systems in both the time and frequency domains. Much more complex interconnections can be constructed from these two basic kinds of connections.
Continue reading “SPTK: Interconnection of Linear Systems”