Convolution

Convolution is a mathematical way of combining two signals to form a third signal. It is the
single most important technique in Digital Signal Processing. Using the strategy of impulse
decomposition, systems are described by a signal called the impulse response. Convolution is
important because it relates the three signals of interest: the input signal, the output signal, and
the impulse response. This chapter presents convolution from two different viewpoints, called
the input side algorithm and the output side algorithm. Convolution provides the mathematical
framework for DSP; there is nothing more important in this book.
CHAPTER
Convolution
6

Convolution is a mathematical way of combining two signals to form a third signal. It is the
single most important technique in Digital Signal Processing. Using the strategy of impulse
decomposition, systems are described by a signal called the impulse response. Convolution is
important because it relates the three signals of interest: the input signal, the output signal, and
the impulse response. This chapter presents convolution from two different viewpoints, called
the input side algorithm and the output side algorithm. Convolution provides the mathematical
framework for DSP; there is nothing more important in this book.




The Delta Function and Impulse Response
The previous chapter describes h