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”