# 2.1 Dsp00104-sampled time series

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Baldwin explains the meaning of sampling, and identifies some of the problems that arise when sampling and processing analog signals. He explains the concept of the Nyquist folding frequency and illustrates the folding phenomena by plotting time series data as well as spectral data.

Revised: Fri Oct 16 23:11:24 CDT 2015

## Preface

This is one in a series of modules designed to teach you about Digital Signal Processing (DSP) using Java. The purpose of the miniseries is topresent the concepts of DSP in a way that can be understood by personshaving no prior DSP experience. However, some experience in Java programming would be useful. Whenever it is necessary for me to write a program toillustrate a point, I will write it in Java.

## Viewing tip

I recommend that you open another copy of this module in a separate browser window and use the following links to easily find and view the Figureswhile you are reading about them.

## Figures

• Figure 1 . Samples from five different sinusoids.
• Figure 2 . Rectangular representations of samples from five sinusoids.
• Figure 3 . Trapezoidal representations of samples from five sinusoids.
• Figure 4 . Most common representations of samples from five sinusoids.
• Figure 5 . Five sampled sinusoids
• Figure 6 . Result of re-sampling the five sinusoids.
• Figure 7 . Spectral analyses of five sinusoids with no sampling problems.
• Figure 8 . Spectral analyses of five sinusoids with sampling problem.
• Figure 9 . Spectral analyses of five sinusoids with no sampling problems.
• Figure 10 . Spectral analyses of five sinusoids with sampling problem

## Preview

I will explain the meaning of sampling, and will explain some of the problems that arise when sampling and processing analog signals. Those problems generallyrelate to the relationship between the sampling frequency and the high-frequency components contained in the analog signal.

I will explain the concept of the Nyquist folding frequency , which is half the sampling frequency (more commonly called the sampling rate) .

I will illustrate the frequency folding phenomena by plotting sampled time series data as well as spectral data.

## Sinusoids, time series, composition, and decomposition

I introduced you to sinusoids and sampled time series in an earlier module . I taught you about sine and cosine functions, and the Java methods used to calculate their values. I also introduced the concepts of period and frequency for sinusoids.

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