The Simplest Lowpass Filter

This chapter introduces analysis of digital filters applied to a very simple example filter. The initial treatment uses only high-school level math (trigonometry), followed by an easier but more advanced approach using complex variables. Several important topics in digital signal processing are introduced in an extremely simple setting, and motivation is given for the study of further topics such as complex variables and Fourier analysis [83].

- Introduction

- The Simplest Lowpass Filter

- Finding the Frequency Response

- An Easier Way
- Complex Sinusoids
- Complex Amplitude
- Phasor Notation
- Complex Sinusoids as Circular Motion
- Rederiving the Frequency Response

- Summary
- Elementary Filter Theory Problems

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