Digital Signal Processing Tutorial

[Otilia Mojarro]

DigitalSignal Processing is an important branch of Electronics and Telecommunication engineering that deals with the improvisation of reliability and accuracy of the digital communication by employing multiple techniques. This tutorial explains the basic concepts of digital signal processing in a simple and easy-to-understand manner.

This tutorial is meant for the students of E&TC, Electrical and Computer Science engineering. In addition, it should be useful for any enthusiastic reader who would like to understand more about various signals, systems, and the methods to process a digital signal.

Digital signal processing deals with the signal phenomenon. Along with it, in this tutorial, we have shown the filter design using the concept of DSP. This tutorial has a good balance between theory and mathematical rigor. Before proceeding with this tutorial, the readers are expected to have a basic understanding of discrete mathematical structures.

Analog Devices has a broad selection of processors for a wide variety of applications. For more specific information about ADI Processors and Precision Analog Microcontrollers we invite you to explore the following:

Digital Signal Processors (DSP) take real-world signals like voice, audio, video, temperature, pressure, or position that have been digitized and then mathematically manipulate them. A DSP is designed for performing mathematical functions like "add", "subtract", "multiply" and "divide" very quickly.

Signals need to be processed so that the information that they contain can be displayed, analyzed, or converted to another type of signal that may be of use. In the real-world, analog products detect signals such as sound, light, temperature or pressure and manipulate them. Converters such as an Analog-to-Digital converter then take the real-world signal and turn it into the digital format of 1's and 0's. From here, the DSP takes over by capturing the digitized information and processing it. It then feeds the digitized information back for use in the real world. It does this in one of two ways, either digitally or in an analog format by going through a Digital-to-Analog converter. All of this occurs at very high speeds.

To illustrate this concept, the diagram below shows how a DSP is used in an MP3 audio player. During the recording phase, analog audio is input through a receiver or other source. This analog signal is then converted to a digital signal by an analog-to-digital converter and passed to the DSP. The DSP performs the MP3 encoding and saves the file to memory. During the playback phase, the file is taken from memory, decoded by the DSP and then converted back to an analog signal through the digital-to-analog converter so it can be output through the speaker system. In a more complex example, the DSP would perform other functions such as volume control, equalization and user interface.

A DSP's information can be used by a computer to control such things as security, telephone, home theater systems, and video compression. Signals may be compressed so that they can be transmitted quickly and more efficiently from one place to another (e.g. teleconferencing can transmit speech and video via telephone lines). Signals may also be enhanced or manipulated to improve their quality or provide information that is not sensed by humans (e.g. echo cancellation for cell phones or computer-enhanced medical images). Although real-world signals can be processed in their analog form, processing signals digitally provides the advantages of high speed and accuracy.

Because it's programmable, a DSP can be used in a wide variety of applications. You can create your own software or use software provided by ADI and its third parties to design a DSP solution for an application. For more detailed information about the advantages of using DSP to process real-world signals, please read Part 1 of the article from Analog Dialogue titled: Why Use DSP? Digital Signal Processing 101- An Introductory Course in DSP System Design.

Digital Signal Processing is a complex subject that can overwhelm even the most experienced DSP professionals. Although we have provided a general overview, Analog Devices offers the following resources that contain more extensive information about Digital Signal Processing:

DSP workshops are a very fast and efficient way to learn how to use Analog Devices DSP chips. The workshops are designed to develop a strong working knowledge of Analog Devices' DSP through lecture and hands-on exercises.

Today's embedded systems and SoCs contain more and more physical interface IPs (e.g., USB, PCIe, DDR, SATA and HDMI) and mixed-signal IP (e.g., Sigma-delta-ADCs, DACs and PLLs) which directly interact with the digital HW/SW subsystems. For example, many of these mixed-signal IP's are registered-controlled and can be configured and calibrated via the on-chip processor.

Furthermore, while data rates continue to increase, design of these high-speed peripherals requires inclusion of the analog/mixed-signal behavior in the overall signal processing chain to guarantee error-free transmission and reception over the physical channels. This requires new means to model and simulate the algorithms and signal processing capabilities of these peripherals, in combination with the HW/SW subsystems at functional and architecture level. Especially for this purpose, the SystemC language standard has been extended with powerful mixed-signal and signal processing modeling features to tackle the challenges in heterogeneous electronic system-level design and verification.

This highly technical tutorial targets system engineers, integrators, architects and verification engineers active in industrial projects where analog and digital signal processing functionality comes together and where interoperability between mixed-signal and HW/SW subsystems becomes apparent. Note that the tutorial does not target analog/mixed-signal circuit-level and mixed transistor/RTL modeling; instead, it will focus on abstract mixed-signal modeling for system-level design and verification.

This tutorial contains several "labs," so viewers are encouraged to actually create models, run simulations and look at waveforms. The tutorial sections are intended to be completed in order. The labs require a SystemC and SystemC AMS simulation environment.

Discover the realm of digital signal processing and audio buffer manipulation. Learn the basics of the JUCE DSP module and how you can incorporate its classes in your own audio application and plugins.

Before reading this tutorial, make sure you understand the basics of synthesis and have been introduced to MPE. If you would like to find more about MPE, check out this tutorial Tutorial: Build a multi-polyphonic synthesiser.

The project is conceived as a plugin but you can run it as a standalone application by selecting the proper deployment target in your IDE. In Xcode, you can change the target in the top left corner of the main window as shown in the following screenshot:

The demo project provides us with an on-screen MIDI keyboard in the top half of the plugin and a visual representation of the signal through an oscilloscope in the bottom half. Presently if a key is pressed, the plugin does not output any sound unless we provide an implementation of an oscillator.

A time or space domain signal can be converted to the frequency domain by using a transformation formula called the Fourier transform. A common efficient implementation of this transformation function is the Fast Fourier Transform or FFT, which you may encounter in the JUCE DSP module.

The FFT allows us to decompose an audio signal into its frequencies and represent the magnitude and phase information for each of these frequencies. Using its inverse function, we can revert the signal into its original domain thus making it really useful to process individual frequency components such as for filtering.

Within these filter designs, there are a number of different transfer functions that dictate the sharpness of the filter and the amount of ripples that occur at the transition frequency. Many of these designs are inspired by analog filters and different transfer functions try to emulate different analog counterparts.

If you are interested in these filter designs, you can find plenty of resources online that go more in depth about this topic but for the purpose of this tutorial, we have covered more than the basics to get us started.

Similarly to the audio application lifecycle of the AudioProcessor with its prepareToPlay() and getNextAudioBlock() functions, we have to implement the prepare() and renderNextBlock() functions of our AudioEngine class derived from MPESynthesiser.

A convenient template class of the DSP module is the juce::dsp::ProcessorChain which allows us to apply different processes in series by calling the prepare(), process() and reset() methods automatically one after the other.

In the CustomOscillator class, define a juce::dsp::ProcessorChain with juce::dsp::Oscillator and juce::dsp::Gain processors in this top-down order [1]. We want the gain processing to affect the output of the oscillator to be able to trim the level coming out. Also define an enum with processor indices [2] to be able to clearly refer to the corresponding process via its index later on.

In the constructor, get a reference to the Oscillator by supplying the index of the process and use the processorChain.get() method [5]. Let's initialise the oscillator using a lambda function and the std::sin function to provide the sine wave to the oscillator [6].

Since we do not have access to a std version of a sawtooth function, we need to implement a manual mapping of values using the jmap function. To do this, map the range between -Pi .. Pi to -1 .. 1 providing a linear ramp from -1 to 1. Since a sawtooth only has 2 breakpoints, we need only supply 2 discrete points to the lookup table.

Most analog synthesisers will have multiple oscillators and a common trick to get a thicker sound is to add a second oscillator with a slightly detuned frequency. So let's try that by modifying the Voice class.

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