# Digital Signal Processing

The DSP book is written for an audience that does digital signal processing (e.g., people who do neuroscience) but that do not have a strong math or engineering background. The goal of the course is that after you have completed the book you’ll have a fairly sophisticated understanding of how to apply several digital signal processing techniques, including better understanding what is really happening when you push certain buttons in packaged software (e.g., filter settings). After completing the book you’ll also better understand how to collect data (e.g., data sampling rate).

You may purchase a copy of our courseware without any instructional services such as mentor feedback or grading if you are simply seeking reference materials rather than enrolling for a class.

## Syllabus

**Frequency, Amplitude, and Phase
**

Introduction to sine/cosine functions, discussion of time series and spatial data, discussion of amplitude, frequency, and phase, and a section on adding sine waves. There’s also a brief introduction to complex numbers and the Euler Identities. Students also read in time and spatial data (grayscale images).

**Sampling Rate and Aliasing
**

Detailed discussion of the Nyquist Theorem and aliasing (time and spatial domain), a section on multiplying sine waves, and a brief discussion of plotting complex numbers and determining the magnitude and phase of complex numbers.

**Convolution and Filtering – Time Domain**

This chapter focuses on convolution, and via convolution, filtering. Ideas are explored in the time domain. In this process, students are introduced to high- and low-pass filters and gain functions. Students use convolution to filter several time domain datasets.

**Convolution and Filtering – Spatial Domain
**

Generally the same as Chapter 3, but now examining spatial data. Students use convolution methods to filter grayscale and color images. Normal distributions and random noise are also discussed.

**Computing Magnitude and Phase
**

This chapter focuses on using sine and cosine to compute the magnitude and phase of activity at different frequencies: time and spatial data. Students also see that magnitude and phase information can be obtained more easily using complex exponentials.

**The Fourier Transform**

The Fourier transform is finally introduced and some of the limitations (and ways to overcome some of these limitations) of time-frequency transforms examined. Students are also introduced to the idea of filtering using forward and inverse Fourier transforms.