FIR filters are a widely-used and powerful signal-processing tool. In this lesson you will learn why FIR filters are so powerful and be introduced to the FIR filter design criteria. You will also learn why optimization techniques are used for designing FIR filters. This information prepares you to learn about specific design procedures.

## Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform

The discrete Fourier transform is one of the most important computational tools in signal processing. This lesson briefly introduces you to some of the applications for the discrete Fourier transform, its definition, and develops the relationship between the discrete Fourier transform and the discrete-time Fourier transform. An understanding of this relationship is essential to proper use […]

## Frequency Sampling FIR Filter Design

The frequency-sampling method takes advantage of the linear relationship between the FIR filter coefficients and the frequency response to write the design problem as the solution to a system of linear equations. In this lesson you will learn how to use the frequency-sampling design method to produce filters with arbitrary magnitude and phase response. You […]

## Important Discrete Fourier Transform Properties

In this lesson you will learn several of the most important properties of the discrete Fourier transform (DFT) for signal processing applications. Not surprisingly, these properties are similar to those of the Fourier transform and the discrete-time Fourier transform. The convolution-multiplication property is deferred to a separate lesson due to its importance in using the […]

## Signals Everywhere

This lesson introduces you to the concepts of “signals” and “signal processing” with computers. You will develop an appreciation for the incredible breadth of signal processing applications. You will also gain valuable perspective of key historical factors that have shaped the field. This information lays the foundation for you to be able to apply signal-processing […]

## The Fourier Series: Continuous-Time Periodic Signals

The Fourier series represents periodic, continuous-time signals as a weighted sum of continuous-time sinusoids. It is widely used to analyze and synthesize periodic signals. This lesson shows you how to compute the Fourier series coefficients, or weights, from the signal. It also introduces you to the conditions that must be met for a signal to […]