Linear time-invariant (LTI) systems are the most widely used systems in signal processing. In this lesson you will develop a deeper understanding for the role of the impulse response of LTI systems. You will learn how linearity and time invariance result in the convolution sum for expressing the output of an LTI system in terms […]

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## Fourier Series Properties

Fourier series properties provide insight and simplify working with Fourier series expansions. This lesson introduces you to the most important and commonly used Fourier series properties and gives you examples of their use. These properties are direct consequence of the nature of sinusoids. Similar properties exist for the other Fourier representations, so understanding the properties of […]

## Graphical Evaluation of Discrete-Time Convolution

Convolution expresses the output of a linear time-invariant system in terms of the system's impulse response and the input. In this lesson you will learn a graphical approach to evaluating convolution for continuous-time systems. Learning how to interpret convolution graphically will develop your intuition for understanding how the impulse response characteristics impact the system output. […]

## The Window Method of FIR Filter Design

The window method of FIR design is simple to understand and perform. It can be done with pen and paper for many filters and simple windows. In this lesson you will learn the steps to perform window-based design and the factors governing window selection. You will also learn how to use MATLAB to perform window-based […]

## Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform

The convolution-multiplication property is one of the most insightful and useful properties of the Fourier transform and discrete-time Fourier transform. This lesson introduces the convolution-multiplication property for the DFT. Multiplication of DFT coefficients corresponds to circular convolution of time signals. You will gain an understanding of the difference between linear and circular convolution that is […]

## Graphical Evaluation of Continuous-Time Convolution

Convolution expresses the output of a linear time-invariant system in terms of the system's impulse response and the input. In this lesson you will learn a graphical approach to evaluating convolution for continuous-time systems. Learning how to interpret convolution graphically will develop your intuition for understanding how the impulse response characteristics impact the system output. […]