Understanding Digital Signal Processing: The Fundamentals Explained

Digital signal processing (DSP) is a fundamental building block of modern communications. It is used in various applications, from cell phone baseband processors to audio and video compression, and has revolutionized the field of digital communications. In this article, we’ll break down the fundamentals of digital signal processing and how it works. From the basics of sampling and quantization to filter design, get ready to dive into the world of DSP!

Introduction to Digital Signal Processing

Digital signal processing (DSP) is an engineering branch that analyzes and manipulates digital signals. DSP processes signals from various sources, such as microphones, radio receivers, and sensors. It is also used to improve the quality of digital images and videos.

The first step in understanding DSP is understanding how digital signals are represented. The next step is understanding how these samples are manipulated to achieve the desired result. For example, if we want to remove noise from a digital image, we need to identify it and then apply an algorithm to filter it out.

Digital signal processing algorithms typically involve mathematical operations such as addition, subtraction, multiplication, and division. They also often involve Fourier transforms and convolutions. These operations are performed on the samples to achieve the desired result.

If you're interested in learning more about digital signal processing, there are many resources available online, like the courses offered by Skill-Lync.

What is a signal?

A signal is a representation of a physical quantity that varies over time, space, or some other independent variable. In electronics and telecommunications, signals are typically electric voltages or current waves, whose amplitude (voltage) and/or frequency vary according to the information being transmitted.

In digital signal processing, a signal is often a sequence of digital values representing a waveform. The term can also refer to the process of converting an analog signal into a digital signal (analog-to-digital conversion, or ADC).

Types of Signals

Three main types of signals are commonly used in digital signal processing:

• Analog Signals
• Digital Signals
• Composite Signals

1) Analog Signals

Analog signals are continuous and can take on any value that falls within a specific range. They are typically used to represent things like sound, light, or temperature, which vary continuously over time.

2) Digital Signals

Digital signals are discrete and can only take on a limited number of values. They are typically used to represent things like numbers or text, which can be represented as a finite set of values.

3) Composite Signals

Composite signals are a combination of both analog and digital signals. They often represent video or audio data containing both continuous and discrete components.

Sampling and Quantization

Digital signal processing involves the manipulation of digital signals. To do this, the digital signal must first be converted from an analog signal. This conversion is done through a process called sampling. Sampling is the process of taking an analog signal and converting it into a digital signal. The sample rate is the number of samples taken per second. The higher the sample rate, the more accurate the conversion will be.

Once the analog signal has been sampled, it can then be quantized. Quantization is the process of assigning a numeric value to each sample. The resolution of the quantization is determined by the number of bits used to represent each sample. The higher the resolution, the more accurate the quantization will be.

Discrete-Time Domain Analysis

The most common type of DSP is the discrete-time Fourier transform (DTFT), a tool for analyzing signals in the frequency domain. DTFT allows engineers to see how a signal's amplitude and phase change over time, which can help design filters or other digital systems.

Other popular types of DSP include linear prediction, filter design, and multi-rate processing. These techniques are often used in conjunction with each other to achieve the desired results.

Frequency Domain Representations

In this section, we will look at one of the most important concepts in DSP: the frequency domain representation of signals. The Fourier transform is a mathematical tool that allows us to represent a signal in the form of a sum of sinusoids. This is useful because many signals can be expressed as the sum of sinusoids, and the Fourier transform allows us to work with these signals in the frequency domain.

The Fourier transform of a signal x(t) is given by:

X(f) = ∫x(t)e-j2πftdt

where f is the frequency (in Hz). 

The inverse Fourier transform is given by:

x(t) = (1/2π) ∫X(f)ej2πftdf

The Fourier transform allows us to represent a signal as a function of frequency. This representation is useful because it allows us to analyze and process signals in the frequency domain.

Real-Time Signal Processing Algorithms

Real-time signal processing algorithms process signals as they are received without delay.

DSP algorithms typically fall into one of two categories:

1. Time-invariant - These are the algorithms that do not change over time.
2. Time-varying - These algorithms adapt to changing conditions with respect to time.

Common types of real-time signal processing algorithms include:

• Filtering
• Amplitude modulation
• Frequency modulation
• Phase modulation

Filtering:

Filtering is used to remove unwanted components from a signal. For example, a low-pass filter can be used to remove high-frequency noise from an audio signal.

Amplitude modulation:

Amplitude modulation encodes information in a signal by varying the voltage of the signal. For example, amplitude modulation can be used to transmit digital data over an analog carrier wave.

Frequency modulation:

Frequency modulation encodes information in a signal by varying the frequency of the signal. Frequency modulation can be used to transmit digital data over an analog carrier wave. Example: RF transmitter.

Phase modulation:

In phase modulation, the phase of a carrier wave varies in response to the vibrations of the sound source (PM). This type of modulation is frequently regarded as a variant of FM. 

You can better optimize your audio or video for a higher-quality output by better understanding how signals are altered and manipulated with DSP. For more information about DSP, be sure to check out our other articles on the topic and reach out to us if you have any questions. Skill-Lync offers a variety of exciting courses on biomedical technologies, telecommunications, and wireless communications using MATLAB. We also offer courses on Embedded systems and AUTOSAR to upskill your engineering knowledge.