Digital Signal Processing – Complete Guide With Examples

Understand the key concepts of Digital Signal Processing (DSP) including Digital Processing tools and various applications through this tutorial:

The primary key to success for any business in today’s well-connected world is quick, easy, reliable, and secure communication and information exchange. The biggest contributor to this progress is the digital storage of data and easy and reliable transmission of data from place to place.

Digital Signal Processing is the key and its knowledge is becoming very important in comprehending the quality and reliability that it delivers.

While all-natural signals like roaring, singing, dancing, clapping, etc. are analog; digital signals are used in computers, electronic devices, etc. So it is important to understand digital signals, their advantage and the need for digitizing analog signals, and the basics and challenges of analog-to-digital conversion.

Understanding Digital Signal

A digital signal represents information as a sequence of discrete finite values. At any instance of time, it can have one of the finite values only.

In most digital circuits, the signals can have two valid values represented as zero and one. This is the reason they are called logical signals or binary signals. Digital signals with over two values are also used and are called multivalued logic.

A simple way to explain the digital signal is a hard disk, which stores data. The hard disk stores data in binary form and the information stored in it can be shared and processed by all who have access to it.

Recommended Reading=> Analog Vs Digital Signals

What Is Signal Processing

• Any information-carrying mechanism can be called a Signal. Any physical quantity that changes with time or pressure or temperature etc. is a Signal.
• The characteristics of the signal are amplitude, shape, frequency, phase, etc.
• Any process that alters the characteristics of a signal is called signal processing.
• Noise is also a signal, but interfering with the main signal and impacting its quality and distorting the main signal. So noise is an unwanted signal.
• All-natural activity is considered as data in signal processing. Images, audio to seismic vibrations, and everything in between is data.
• Signal processing plays a significant role in converting these analog data to digital and conversely, converting digital data to a human understood analog format.
• It is a high-end technology where both mathematical theory and physical implementation work in conjunction.
• Digital Signal processing is used for storing digital data and streaming or transmitting data.
• DSP involves information interchange so that the data can be analyzed, observed, and transformed into a separate form of signal.

Fundamentals Of Digital Signal Processing

Analog signals like temperature, voice, audio, video, pressure, etc. are digitized and then manipulated for storage and better quality. During digital signal processing, the signals are processed for the information that they need to carry to be easily stored, used, displayed, propagated, and converted for human usage.

Some of the key focus while processing signals are the below parameters:

• Speed of conversion
• Ease of access
• Security
• Reliability

The most common core steps of digital signal processing are:

• Data digitizing – Convert continuous signals to finite discrete digital signals as explained in the next topic, below.
• Eliminate unwanted noise
• Improve quality by increasing/decreasing certain signal amplitudes
• Ensure security during transmission by encoding the data
• Minimize errors by detecting and correcting them
• Store data
• Easy and secure access to the stored data

Signal Processing:

Data Digitization And Quantization: Explained

Data digitizing is the primary step for digital processing if the signal is analog.

ADC, converting Analog data to Digital is explained below for a basic understanding of the primary step taken for digital processing of data. The steps explain digitizing the analog signals captured while taking the actual temperature reading taken at different time intervals.

• Divide the x-axis, representing time interval, and the y-axis representing the magnitude of temperature measured at the specified time.
• This example is for measuring the temperature at specified intervals t0 t1 t2 …..tn
• Let’s set 4 level discreet temperature values captured at set time intervals after 10 minutes after the start time as t0=0,t1=10, t2=20,t3=30,t4=40
• So, the signals can take the temperature at these times only starting from 0 (any starting time) and after intervals of 10 min till 40 min.
• Say, the temperature captured at time t0 = 6 degree Celsius, t1=14°C, t2= 22°C, t3=15°C, t4=33°C as shown in the below table.

The below image represents the Analog Signal Sine Wave:

• The next step is to convert the Analog signal captured to a Digital signal.
• The magnitude in Y-axis can have only the selected value measured at the discrete-time interval.
• Now we need to set the actual temperature to the allowed discrete values.
• At time t1, the temperature is 6°C, and the allowed values closer to this value are either 0 or 10. 6°C is closer to discreet value 10°C but in order to minimize the error the lower discrete value is taken i.e. lower level 0°C is considered.
• Here, there is an error of 6 units as we are taking 0 as the reading instead of 6. In order to reduce these rounding-off errors, we can re-scale the y-axis and make the intervals small.
• In the same manner we will arrive at temperature T at t1= 0°C, T(t2) = 10°C, T(t3) = 20°C, T(t4) = 10°C, T(t5)=30°C
• These discrete data values are stored in bit forms, enabling the data to be reproduced easily. This process is called data quantization.
• The actual graph is the curved wave, and the digitized signal will be shown in the graph as a square wave.
• The rounding off errors at each data point is the difference between the blue circle and red cross (x) in the diagram shown below.
• The rounding off error is also referred to as quantization error.

Digital Signal Square Wave:

To put it simply, the two pictures below depict a smiling face, but one is a continuous line, and the other is not. The picture below is depicted on an enlarged scale. In real life, the scale is generally very minute, and the brain perceives the digital image almost the same as the continuous image.

Analog and digital signal view:

Key Concepts of Digital Signal Processing

1. Sampling
2. Quantization
3. Errors
4. Filters

#1) Sampling

• Sampling is an approach used to convert analog signal s(t) to a time-discrete form x(n) by sampling its value in periodical intervals of duration t_s, the sampling period.
• The amplitude value of the signal is measured at certain intervals in time.
• The sampling rate is the number of samples or data points within a second. It is also referred to as “samples per second”.
• Higher sample rates enable it for higher frequency handling.

#2) Quantization

• It is the step where the continuous analog values are rounded off to the nearest discrete value in binary/digital form.
• Many times during conversion of a continuous signal value to the nearest available discrete digital value, the difference between the actual and the discrete value occurs.
• This difference in the value is called Quantization error. To minimize this error, the resolution of the converter is increased, and the difference is minimized.
• Refer to image “Digital Signal Square Wave”. The actual data captured is the blue dot in the blue Analog curve and the digitized discrete data point on the red square wave is denoted as red ‘x’. There is a slight shift in the data points and these shifts are the quantization error.

Refer to Sampling and Quantization to learn more!

#3) Errors

The most common errors resulting during digitizing and transmission are:

• Noise: It is unwanted disturbance or modification in useful data information that occurred from the interference of natural environment signals or signals from man-made sources. The disturbance can occur during conversion, transmission, or storage i.e. during any step. Noise impacts the amplitude of the signal.
• Aliasing: During reconversion of digital-to-analog signal, sometimes few unwanted components are detected in the reconstructed signal. This phenomenon is called Aliasing. This occurs mainly because of the overlapping of signal frequencies, especially at very low frequencies.
• Jitter: It is the delay in signal transmission and receipt. Impact on signal’s phase, width, period, or cycle is called Jitter. Jitter may result in transmission delay of few data packets and then multiple packets sent together. Many times this causes loss of data, slowness of data transmission, and drop in quality of the signal, especially in a gaming application, audio, and video conference calls.

#4) Filters

• Filters are used to improve the quality of signals by filtering frequencies impacting the quality adversely.
• Primary digital Filters are 1) Finite Impulse Response – FIR filters and 2) Infinite Impulse Response – IIR Filters
• Low-pass FIR filters (LPF) are used to circumvent the Aliasing error. The filter holds all frequencies below the cutoff frequency and weakens frequencies above the cutoff frequency.
• High-pass FIR filters (HPF) are used to circumvent Noise error. High-pass filters hold all frequencies above the cutoff frequency and weaken frequencies below the cutoff frequency.

Digital Processing Tool – Fourier Transform

The tool which has contributed immensely to digital signal processing is the Discrete Fourier Transform. Fourier transform maps a signal in the time and frequency domain. The time and frequency domains are just alternative ways of representing signals, and the Fourier transform is the mathematical relationship between the two representations.

Discrete Fourier Transform (DFT) is a computational algorithm that transforms the time domain signals to the frequency domain components. Fast Fourier Transform (FFT) is more efficient and fast compared to DFT.

Purpose

Some of the reasons for converting Time-domain signals to Frequency domain signals are as follows:

• We generally need to analyze the continuous-time signal captured and transform it into a digital signal.
• Effects of aliasing can be analyzed in frequency domain graphs. By making choices of the sampling frequency, this impact can be observed better.
• Similarly, by filtering frequency, the quality of the signal can be improved.
• Frequency domain supports signal manipulation operations like amplification, mixing of signal, filtering.
• Fourier analysis gives many mathematical tools for arriving at the frequency domain signal for a given value of a time-domain signal.
• DFT is equivalent to solving a set of linear equations.

Reference => DFT 

The below image shows the Continuous Signal Sample for Analysis:

The below image is Digital Signal Processing – Time Domain to Frequency Domain conversion:

[ image source]

Applications Using Digital Signal Processor (DSP)

DSP is used in many modern applications. In today’s world, digital devices have become indispensable as almost all our daily life gadgets are run and monitored by digital processors. The ease of storage, speed, security, and quality are the main value add.

Enlisted below are a few applications:

MP3 Audio Player

Music or audio is recorded and the Analog signals are captured. ADC converts the signal to a digital signal. The digital processor receives the digitized signal as input, processes it, and stores it.

During playback, the digital processor decodes the stored data. DAC converter converts the signal to analog for human hearing. The digital processor also improves quality by improving volume, reducing noise, equalization, etc.

MP3 Audio player working model:

[image source]

Computers and Laptop

The latest computers and laptops with digital processors are more flexible, faster, of better quality, and better portability. The digital signals from a computer are sent to the graphics card and are transmitted through a cable to a digital display. The graphics card converts the digital signals to analog signals and transfers them to an analog display for human viewing.

There are several video ports and connector types: 

• Digital Visual Interface Integrated (DVI-I): Supports Analog and Digital signals
• Digital Visual Interface Digital (DVI-D): Supports only Digital signals
• Digital Visual Interface Analog (DVI-A): Supports only Analog signals
• High-Definition Multimedia Interface (HDMI): Supports Digital audio and video data transmission
• Video Graphics Array (VGA): Supports Analog video signals
• Coaxial, Ethernet cards: Support Analog and Digital audio and video signal

Reference => Ports and connectors 

Smart Phones

The smartphones, IPAD, iPods, etc. are all digital appliances that have a processor that takes inputs from users and converts them to digital form, processes them, and displays the output in a human-understandable form.

Consumer Electronic gadgets

Gadgets like washing machines, microwave ovens, refrigerators, etc are all digital appliances that we use in our daily lives.

Automobile Electronic gadgets

The GPS, music player, dashboard, etc. are all digital processor dependant gadgets that are found in automobiles.

Frequently Asked Questions

Q #1) What is a digital signal?

Answer: A digital signal represents data as a set of finite discrete values. The signal at any given time can hold only one value from a defined set of possible values. The physical quantity captured to represent the information can be an electric current, voltage, temperature, etc.

Q #2) What does digital signal wave look like?

Answer: A digital signal is generally a square wave. Analog signals are sine waves and are continuous and smooth. Digital signals are discrete and are stepping values represented as square waves.

Q #3) What does Digital Signal Processing mean?

Answer: Techniques used to improve the accuracy and quality of digital communication are called Digital Signal Processing (DSP). It mitigates the impact of quality reduction due to noise and aliasing impact on the signal.

Q #4) Where is Digital Signal processing used?

Answer: Digital Signal Processing is used in multiple areas, namely audio signal, speech and voice processing, RADAR, seismology, etc. It is used in mobile phones for speech compression and transmission. Other appliances where it is used are Mp3, CAT scans, computer graphics, MRI, etc.

Q #5) What are the main steps in converting Analog signal to Digital Signal?

Answer: Sampling is the first step towards converting Analog-to-Digital signal. Each signal value is quantified at a specific time interval to the nearest possible discrete digital value. Finally, the discrete values captured are converted to binary values and sent to the system to be processed/stored as a digital signal.

Q #6) Which type of video port provides a digital-only signal?

Answer: Digital Visual Interface (DVI-D) supports only digital signals.

Conclusion

The signal is a function that carries information in the form of data from one point to another by the varying quantities of current or voltage or electromagnetic waves.

A digital signal represents information as a sequence of discrete finite values. Digital signals are preferred as digital processing helps in analyzing analog data, digitizing and processing them for better quality, storage, flexibility, and reproducibility.

The rate of transmission is better, cheaper, and flexible when compared to analog signals. The Filters, Fourier Transform tools DFT, FFT, etc. are some of the tools, which help in digital processing.

Most of the modern appliances used in daily life use digital processors like computers, electronic gadgets, digital phones, etc. ADC converters, digital processing, and DAC converters play a significant role in these appliances to facilitate data storage, transmission, and reproducibility for human usage.

Sharing is good, and with digital technology, sharing is easy – Richard Stallman.