The impulse response of a system is the output of the system in response to a unit impulse input signal. This lesson introduces you convolution, which expresses the output of an LTI system as a function of its input and impulse response. You will learn how the impulse response reveals whether the system is causal […]

# Foundations

## Frequency Response Descriptions for LTI Systems

This lesson will introduce you to the most intuitive description for LTI systems used in signal processing. The frequency response of a system defined as the amplitude and phase of the system output in response to a unit complex sinusoid input signal. You will learn how the frequency response is related to the impulse response […]

## Introduction to the System Function and System Poles and Zeros

This lesson will introduce you to another very useful description for LTI systems: the system function and poles and zeros. You will learn that the system function is a generalization of the frequency response description when the input is an exponentially damped complex sinusoid. Also, the system function for systems described by difference equations is […]

## The Four Fourier Representations

Blog post: Fourier Methods: Why So Prominent? Fourier analysis is a cornerstone concept in signal processing. In this lesson you will learn about the four variations on Fourier representations for signals. All of the Fourier representations express an arbitrary signal as a weighted combination (sum or integral) of sinusoids having different frequencies. Four variations on […]

## Summary Problems for Foundations

The quiz below contains a selection of problems in a pdf file that draws from the material in Foundations. The benefit you derive from these exercises is proportional to the effort you put into them. Here are my suggestions: Try to work the problems without looking at the solution. Don't give up easily. Feel free […]