Tag: Convolution

SPTK: The Matched Filter

Matchmaker, Matchmaker,
Make me a match,
Find me a find,
catch me a catch!
–“Matchmaker” from Fiddler on the Roof

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In this post, we take a look at a special linear time-invariant system called the matched filter. It is used to detect the presence of a known signal. In practice, it is often applied to the detection of a periodically repeated known portion of a communication signal, such as a channel-estimation frame or frequency-correction burst. It is also widely used in the detection of radar pulses, where the matched-filtering operation is renamed to pulse compression. Filtering, which implies a convolution operation, and correlation are nearly the same thing. Therefore applying a matched filter is sometimes referred to as applying a correlator.

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SPTK: Convolution and the Convolution Theorem

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.

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SPTK: Interconnection of Linear Systems

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.

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