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”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”