# SPTK

Here are links to all the Signal Processing ToolKit posts. They are in reverse chronological order–I cannot choose the temporal order, so if you want to get the most out of these posts, start at the bottom and work your way up: Start with “Signals.”

There are also “Next SPTK Post” and “Previous SPTK Post” links in each SPTK post.

## SPTK: The Z Transform

I think of the Z transform as the Laplace transform for discrete-time signals and systems.

## SPTK: Practical Filters

We know that ideal filters are not physically possible. Here we take our first steps toward practical–buildable–linear time-invariant systems.

## SPTK: The Laplace Transform

The Laplace transform easily handles signals that are not Fourier transformable by introducing an exponential damping function inside the transform integral.

## SPTK Addendum: Problems with resampling using MATLAB’s resample.m

Sometimes MATLAB’s resample.m gives results that can be trouble for subsequent CSP.

## SPTK: Echo Detection and the Prisoner’s Dilemma

Let’s apply some of our Signal Processing ToolKit tools to a problem in forensic signal processing!

## SPTK: Sampling and The Sampling Theorem

The basics of how to convert a continuous-time signal into a discrete-time signal without losing information in the process. Plus, how the choice of sampling rate influences CSP.

## SPTK (and CSP): Random Processes

The merging of conventional probability theory with signal theory leads to random processes, also known as stochastic processes. The ideas involved with random processes are central to cyclostationary signal processing.

## SPTK: Examples of Random Variables in Communication-Signal Contexts

Some examples of random variables encountered in communication systems, channels, and mathematical models.

## SPTK: Random Variables

Our toolkit expands to include basic probability theory.

## SPTK: The Analytic Signal and Complex Envelope

In signal processing, and in CSP, we often have to convert real-valued data into complex-valued data and vice versa. Real-valued data is in the real world, but complex-valued data is easier to process due to the use of a substantially lower sampling rate.

## SPTK: The Moving-Average Filter

A simple and useful example of a linear time-invariant system. Good for smoothing and discovering trends by averaging away noise.

## SPTK: Ideal Filters

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.

## 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.

## 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.

## SPTK: Frequency Response of LTI Systems

The frequency response of a filter tells you how it scales each and every input sine-wave or spectral component.

## SPTK: Linear Time-Invariant Systems

LTI systems, or filters, are everywhere in signal processing. They allow us to adjust the amplitudes and phases of spectral components of the input.

## SPTK: The Fourier Transform

An indispensable tool in CSP and all of signal processing!

## SPTK: The Fourier Series

A crucial tool for developing the temporal parameters of CSP.