# Tutorial

## Convolution: A Visual Digital Signal Processing Tutorial

Understanding convolution is central to understanding filtering, the Discrete Fourier Transform, and other important DSP operations.  In this tutorial, R. C. Kim explains convolution using a visual, intuitive, step-by-step method, and relates it to filtering and the DFT.

## Reducing FFT Scalloping Loss Errors Without Multiplication

In this tutorial, Richard G. Lyons, author of the best-selling DSP book Understanding Digital Signal Processing, discusses the estimation of time-domain sinewave peak amplitudes based on fast Fourier transform (FFT) data.

## Multipath Channel Model Using DSP

Multipath distortion is a common problem in many DSP-based data transmission systems.  Here, Neil Robertson shows how to model multipath channels using complex-coefficient FIR filters.

## Sum of Two Sinusoidal Functions

Many DSP systems use composite signals consisting of a sum of sinusoids of the same frequency, often a sine and cosine. In this tutorial, Richard G. Lyons, author of the best-selling DSP book Understanding Digital Signal Processing, thoroughly covers this important DSP topic by explaining and deriving formulas for the sum of two sinusoids of the same frequency.

## by Robert Bristow-Johnson

A Maximum-Length Sequence (MLS) has two different (but related) definitions:

One is the driving function applied to the input of a linear time invariant (LTI) system:

```   x[n] = X*(-1)^a[n]
```

The other definition is simply the binary sequence, a[n] = 0 or 1, used in the exponent.

## Cascaded Integrator-Comb (CIC) Filter Introduction

In the classic paper, "An Economical Class of Digital Filters for Decimation and Interpolation", Hogenauer introduced an important class of digital filters called "Cascaded Integrator-Comb", or "CIC" for short (also sometimes called "Hogenauer filters").

Here, Matthew Donadio provides a more gentle introduction to the subject of CIC filters, geared specifically to the needs of practicing DSP designers:

CIC Filter Introduction (130K, pdf)

## Quadrature Signals: Complex, But Not Complicated

Understanding complex numbers and quadrature signals is essential for understanding DSP at both a theoretical and a practical level. Yet this strange, complex subject (based on the admittedly imaginary construct of the square root of negative one!) is among the hardest for DSP beginners to grasp - and is confusing at times even for advanced DSPers.

## Digital Signal Processing Tutorials

Digital Signal Processing is a difficult and complex subject. Here, we offer tutorials to clear up some of the mysteries of DSP.