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.

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## 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 […]

## 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 […]

## Introduction to Sampling and Reconstruction

Sampling and reconstruction are two of the most essential and widely used operations in signal-processing systems. In this lesson you will be introduced to the roles of sampling and reconstruction in signal processing and the questions that will be addressed in subsequent lessons. All signals in the physical world, e.g., sound or light intensity, have […]

## Square Wave Fourier Series and the Sinc Function

The square wave Fourier series provides fundamental insight into the nature of Fourier series expansions. You will learn the relationship between the width or duty cycle of a square wave and the concentration of the Fourier series coefficients. You will also be introduced to the sinc function, a function that has widespread significance in all […]