This course focuses on the fundamentals of digital signal processing that covers the fundamentals of signals, systems and transforms.

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We live in a world filled with signals which can be represented by sequences of numbers in a digital machine. These sequences of numbers can be manipulated by algorithms and have numerous applications in audio, images, video, wireless transmission and countless other domains. 

In this course, you’ll understand the field of digital signal processing with a focus on the design and analysis of signals, and algorithms. You’ll cover the DSP fundamentals of signals, systems and transforms. You’lll learn about the basic signal types and perform different operations. You’ll develop an understanding about the frequency domain and how to represent signals in time, and the transformation from one domain to the other using the Fourier transform. You’ll also learn about digital systems. Finally, you’ll develop a practical OFDM system focusing on modulation and demodulation.

By the end of this course, you’ll be able to model, analyze and design signals and systems in greater depth, in the time and frequency domains.

Fundamentals of Digital Signal Processing

Most signals of practical interest can be considered as a sum of complex sinusoids with different amplitudes and phases. Filters in DSP can then be designed to alter these magnitudes and phases for specific purposes, as follows.

## Lowpass filter

A lowpass filter passes the spectrum around zero while attenuating the remaining high-frequency components. This is achieved by choosing the system frequency response in a manner so that the filter magnitude is $1$ at low frequencies (up to the cutoff frequency) and ideally $0$ for higher frequencies. The frequency response of an ideal lowpass filter is shown in the figure below in which $\omega_{Cut}$ and $\omega_S$ denote the cutoff frequency and sample rate, respectively.

Most signals of practical interest can be considered as a sum of complex sinusoids with different amplitudes and phases. Filters in DSP can then be designed to alter these magnitudes and phases for specific purposes, as follows.

# Lowpass filter

A lowpass filter passes the spectrum around zero while attenuating the remaining high-frequency components. This is achieved by choosing the system frequency response in a manner so that the filter magnitude is $1$ at low frequencies (up to the cutoff frequency) and ideally $0$ for higher frequencies. The frequency response of an ideal lowpass filter is shown in the figure below in which $\omega_{Cut}$ and $\omega_S$ denote the cutoff frequency and sample rate, respectively.

Learn about the classification of filters in the frequency domain according to their passbands and stopbands.

Introduction to Signals

Basic Signals and Operations

Complex Signals and the Frequency Domain

Sampling a Signal

The Discrete Fourier Transform

Fourier Transform Properties

Digital Systems

Putting It All Together: An OFDM Modem

Demodulating an OFDM Signal Stream

The Last Words

Bibliography

Filter Classifications in the Frequency Domain

Lowpass filter