What is Digital Signal Processing (DSP)?

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Digital Signal Processing (DSP) is a branch of engineering and applied mathematics that deals with the processing and analysis of digital signals. A digital signal is a discrete-time signal, that is represented by a sequence of numbers sampled at regular intervals. DSP involves various algorithms, techniques, and methodologies to process these digital signals to retrieve essential information or improve specific features.

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What is a DSP?

Digital Signal Processing (DSP) is used to process the analysis of digital signals to retrieve essential information or improve specific features through algorithms and techniques, that are essential for applications starting from telecommunications and audio processing to medical imaging and control systems.

Digital Signal Processing (DSP) is a specialized branch of engineering and mathematics that involves the processing, analysis, and transformation of digital signals to retrieve information or to change their features by using algorithms and computational techniques. It deals with discrete-time signals, which are represented by sequences of numbers sampled at regular intervals.

What is Digital Signal Processing Used For?

Digital signal processing, officially, is quite complex. It can standardize or solve digital signals, but it can also carry out a variety of other functions, including filtering, compression, and modulation. DSP algorithms are capable of distinguishing between orderly signals and noise, although they may not always achieve perfect results.

Communication systems involves noise levels, irrespective of whether the signals carry both analog and digital in spite of the type of information is transmitted.

Noise exhibits a continuous challenge in digital signal processing to improve the signal-to-noise (S/N) ratio in digital signal processing. To improve an efficiency of the S/N ratio that involves the improvement of transmitted signal power and increases receiver sensitivity.

By using analog-to-digital converter, the analog input signal is converted into digital signal. The final digital signal has two or more levels. The values of voltages or currents are exact and we can predict these levels. So, the noise exists in the input signal and levels which are not at the typical values. To configure the levels by DSP circuit so they can adjust at the correct values. This techniques removes the noise. In the final process, with the help of digital-to-analog converter, the digital signal is converted back into analog signal. To remove noise and reduce errors in the signal, it can be done by DSP as it does signal processing for digital signals

What are the uses of digital signal processing for audio applications?

Different kinds of methods are employed to enhance the quality of the audio and extract significant information. DSP can be used in music production to improve audio recording quality, generate new sounds, and fix audio signal issues.

The following are some more instances of DSP's usage in audio applications:

• Noise reduction involves utilizing a noise gate to eliminate any audio below a predetermined threshold in order to reduce unwanted noise from audio transmissions. Adaptive filtering and spectral subtraction are further methods of reducing noise.
• Equalization is the process of modifying an audio signal's frequency response to enhance recording quality or produce a particular sound impression.
• Compression is used to reduce the size of an audio file that can be decreased to facilitate transmission and storage ,or the dynamic range to enhance the quality of audio signals.
• Pitch correction can be used to produce a particular sound effect, adjust vocal pitch deviations, or adjust the audio signal's pitch.

What's Inside a DSP?

The basic component of DSP are

• Program Memory: This is where the instructions or programs that the DSP will execute are stored.
• Data Memory: Data memory is where the information to be processed is stored.
• Compute Engine: The compute engine is the heart of the DSP. It's used for executing the instructions from the program memory on the data stored in the data memory.
• Input/Output: This component facilitates the interaction between the DSP and the outside world. It handles the input of data to be processed and the output of processed data.

What is a Digital Signal Processing System?

The digital signal processor comprises of different signals that are used such as audio, voice, temperature, and video processing in a digital signal and after that mathematically process the digital signal processor. A DSP performs different mathematical functions very rapidly such as addition, subtraction, multiplication & division.

DSP works with key components such as program memory, data memory, computer engine, and Input/Output.

• Program memory is used to process data by storing the programs.
• Data Memory is used to store the data that can be processed.
• Compute engine performs the mathematical operations, process the information from the data and program memory.
• Input or Output provides as different functions so that it can integrate external data sources

Block Diagram of Digital Signal Processor

Given Below is the Block Diagram of Digital Signal Processor

The block diagram of digital signal processing include the following steps below are:

Step 1: In DSP block diagram, it starts from the receiving of electrical signal. It uses transducer at the input side such as microphone that transforms sound into an electrical signal.

Step 2: After getting an electrical signal, it gives to the input of operational amplifier to sense the analog signal so that it amplifies the signal.

Step 3: For transformation of analog to digital signal, we use anti-aliasing filter. It refers to anti-aliasing filter. It passes frequencies for a limited threshold value. Those frequencies which are higher than the limited threshold, so those frequencies are attenuated. To examine an analog signal, these unwanted frequencies make it complex.

Step 4: The anti-aliasing filter is an essential step in the conversion of analog to a digital signal. It is a low-pass filter that allowing frequencies up to a certain threshold. It attenuates all frequencies above this threshold. These unwanted frequencies create difficulties to sample an analog signal.

Step 5: Now it uses analog to digital converter (ADC) that it senses an analog signal and provides a sequence of binary digits.

Step 6: Now, the main component is digital signal processor. It utilizes CMOS chips to manufacture digital signal processors.

Step 7: Now it uses digital signal processor which is important to compare the acquisition rate of the ADC by slew rate of the DAC.

Step 8: Here, we uses a low pass filter i.e. smoothing filter which removes high frequency components that are not necessary and refines the output.

Step 9: At the last stage, we use op-amp as an amplifier that has output transducer i.e. a speaker.

Features of Digital Signal Processor

Digital signal processing includes following features given below are:

• Digital signal processors are configured to design for managing repeat tasks and computationally complete tasks.
• Digital signal processors manages a data path and has tendency to transfer huge amounts of data to memory rapidly.
• To grow the efficiency of hardware, these processors manages to provide various unique instruction sets to grow the hardware efficiency.
• Digital signal processors has two features which are unique such as the data path that involves multiple-access memory architectures and fast multiply-accumulate units.
• Pipelining is also often utilized to grow the performance of processor. Various processors utilize pipelining that create programming difficult but used in the better growth to increase performance.

Architecture of Digital Signal Processor

Digital signal processors has various architectures components given below are:

Von Neumann Architecture

Given Below is the Von Neumann’s architecture

Von Neumann’s architecture comprises of single memory and a single bus that are used to transfer data in and out of the CPU (central processing unit) of a digital signal processor. It comprises of 3 basic units that is referred to as ISA (Instruction set architecture).

• Central Processing Unit (CPU): CPU consists of 3 basic units such as control unit, main memory unit (registers) and arithmetic logic unit. The CPU is the main part of the system, which consists each component that is needed to analyze input, data storage and produce output. The CPU process instructions of computer program that guides it on which data is analyze in the system.
• Main Memory Unit (Registers): Registers is used to process by the CPU unit of computer memory that is required to accept, store and send data and instructions. To determine the registers in the main memory unit, CPU is required to define the processor registers. In architecture of main memory unit, registers are required to process effectively program execution and its operations and registers are defined to be highly fast memory.
• Input/Output Device: The data is read from the input device into main memory through the CPU instructions of input. By using output components, the data is generated from a computer. If few results are assessed by a computer and archived in it, by using output components we can present them to a user.

Harvard Architecture

Given Below is the Harvard Architecture

Harvard Architecture consists different storage and different buses to process both data and instructions. It is type of computer architecture that has been designed to resolved the limitations of Von Neumann’s Architecture. The main benefit of Harvard Architecture possesses separate buses for both data and instructions so that the CPU could retrieve read or write data and instructions at the same time.

It consists of following components in the architecture mentioned below are:

Buses

• Data Bus: It conveys information enclosed with the processor, main memory and input or output devices.
• Data Address Bus: It conveys the data address from the processor to the main memory.
• Instruction Bus: It conveys instructions enclosed with the processor, main memory and input or output devices.
• Instruction Address Bus: It conveys the instructions address from the processor to the main memory.

Operational Registers

• Program Counter: It contains the address of the next instruction to be carried out.
• Arithmetic and Logic Unit: It is a component of the CPU that performs important computations of the ALU that executes addition, subtraction, comparison, and some other operations.
• Control Unit: The component of the CPU that manages the processor control signals.
• Input/Output System: Using input devices and with the required input instructions of CPU, data is read into main memory.

Types of Digital Signal Processor

Digital signal processors includes two types such as fixed-point processors and floating-point processors.

• Fixed Point : Each number is justified through a 16 bits which are minimum, although length can be used which is different. Each number is designated with unique patterns. Fixed point implies that we have to assume the fractional point location to be fixed and same for the operands as well as the output operations.
• Floating Point : These processors specifically utilizes a 32 bits which are minimum to store each value. This processor has unique feature that is the signified numbers are not equally spaced. This leads to the implementation of counters and signals which are required and is received from the analog to digital converter and send to the digital to analog converter by leading to process the fixed-point numbers.
  

Digital Signal Processor Instruction Sets

Assembly language instructions - TMS320F/C24x DSP are explained below. These instruction sets manages computationally completes signal-processing operations and general-purpose applications like multi-processing. The instruction set ’C24x matches with the ’C2x instruction set is again collect to perform run on the ’C24x as code is written for the ’C2x . The instruction set of TMS320F/C24x DSP is given below.

• Accumulator, arithmetic and logic instructions.
• Auxiliary register and data page pointer instructions.
• TREG, PREG and multiply instructions.
• Branch instructions.
• Control instructions.
• I/O and memory operations.
  

Difference Between Digital Signal Processor and Microprocessor

The difference between digital signal processors and microprocessors involves following points mentioned below are:

Digital Signal Processor

Microprocessor

It is a specific microprocessor chipIt is a processor used in computerDSPs are mainly utilized in telecommunications, audio signal processing, etcMicroprocessors are used in computers for text editing, computation, multimedia display and communication over the Internet.Set of Instructions can be easily executed in one CLK cycleTo execute one instruction, microprocessor utilizes various clock cycles.It requires parallel execution It requires sequential executionTo process an array, DSP is required for its operationIt is required for general-purpose processing.Two Addressing modes i.e. direct and indirect both are used in this processorSome addressing modes are direct, immediate, register indirect, indirect register, etc, are utilized in microprocessor.To generate an address, it leads to combine program sequencers and Directed Acyclic Graph (DAGs).It provides a sequential address and increments a program counterIt comprises of three different computational units: MAC, ALU and Shifter.It uses ALU as the main unitInstruction register and program counter both manages to control the program flowExecution flow can be controlled by the Program counter It comprises different data & program memories.It doesn’t have different memories.It can fetch various operands at once.It can fetch the operand serially.Address and data bus are multiplexed in digital signal processorAddress and data bus are not multiplexed in microprocessor

What are the Fundamentals Of Digital Signal Processing?

Digital Signal Processing fundamentals includes important terms so it help to understand the manipulation of signals:

• Sampling: It is the process that samples the continuous analog signal into a digital signal.
• Quantization: It is the process that assigns digital numbers to the calculated analog signal. It makes a group of the measured values into a set of finite.
• Discrete Fourier Transform (DFT): This method transforms a discrete time signal into its frequency domain. It helps to understand the various frequencies which are present in a signal.
• Fast Fourier Transform (FFT): This algorithm is quite efficient hat performs the DFT quickly. Furthermore, it is the advanced technique of the DFT that assists to explore signals quickly and more productively.

Applications of a Digital Signal Processing System

Digital Signal Processing (DSP) systems find applications across various domains due to their versatility and effectiveness in manipulating digital signals. Some common applications of DSP systems include:

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• Telecommunications: DSP system is utilized in encoding, decoding, and compressing speech and video signals in telecommunications like mobile phones, VoIP, and video conferencing. These are used for error detection and correction, modulation/demodulation.
• Audio Processing: DSP system involved in numerous audio techniques such as filtering, equalization and noise reduction such as speech recognition, better audio quality and in various other fields.
• Image Processing: DSP systems are utilized for performing various tasks in applications like image filtering, compression, and recognition including digital cameras, medical imaging (MRI, CT scans), satellite imaging, and in various other fields.
• Radar and Sonar Systems: DSP systems are very important to process radar and sonar signals for target detection, tracking, range estimation, and interference mitigation in defense, aviation, and in various other fields.
• Control Systems: DSP systems manages digital systems algorithms for feedback control, filtering, manages applications such as robotics, automotive systems, and in various other fields.
• Wireless Communications: DSP systems are involved in wireless communication systems (Wi-Fi, cellular networks) to perform tasks such as signal modulation, demodulation, channel estimation and in various other fields.
• Signal Processing: DSP systems are utilized in different sensors such as accelerometers, gyroscopes that needs in signal processing for condition monitoring, and IOT devices, smart homes, etc.

Advantages of Digital Signal Processing

Digital signal processor has some advantages given below are:

• Noise : It includes digital signal which has a less probability of getting mixed with unwanted signals so that overall noise will be less.
• Detection and correction: It allows usage of numerous error detection and correction characteristics that exists to digital signals such as as a detection and correction tool and utilizes a parity generation and correction .
• Data storage: It is used to store digital data in a simple way. It is required to select from a different varieties of digital memories.
• Encryption : Digital signals are involved in simple encryption.
• Data transmission : It uses a tool which is needed for digital signals to send huge data over unit time by using Time-division multiplexing technique and over one communication path so that more data can be transmitted.

Disadvantages of Digital Signal Processing

Digital signal processor has some disadvantages mentioned below are:

• Complexity : DSP system has some complexities that leads to increase due to the use of additional components.
• Power : Digital signal processor utilizes various transistors which needs huge power compared to the analog signal processors.
• Cost : Digital signal processors are very expensive.
• Bandwidth : Digital communications uses wide range of bandwidth to send the data compared to analog method.
• Sampling and Quantization Errors: It samples analog signals and quantizing them into digital signal can give errors, gives attenuation with respect to information in the signal.

Conclusion

Digital Signal Processing (DSP) is a fundamental technology that has revolutionized the way, manipulate, and analyze digital signals across various domains. Using some computational algorithms and techniques, DSP gives flexibility and precision that matches to basic analog signal processing methods.

It is the process that manages complex algorithms, manages some different tasks, and gives output that has big demand in applications starting from telecommunications to biomedical signal analysis and radar systems. A linear growth in computing technology that has applications to process DSP systems to manages an increasing demand to give structure in applications like communication, healthcare, multimedia, and various other areas, implementing innovation techniques and progress of DSP systems.

Digital Signal Processing

The signals that we are trying to use may contain noises ( unwanted signals) and hence they need to be processed such as filtering the noises using the filters. Also, the information they contain can be displayed, analyzed, or converted to another type of signal. Digital Signal Processing (DSP) incorporates all these methods of processing the signals so as to retrieve the desired information from the signal. 

Signal and Systems

Signal such as sound, heartbeat, heat, earthquake, current, and more are information that get transmitted from one place to another. Systems process those signals to modify or transform them. Signal is fed into the system as time dependent input stream (x(t)) which results in output y(t) which is the response of the system. The mathematical modeling of signals and systems help in the design and development of electronic devices.

Example - Sinusoidal wave:

Consider a simple signal i.e sine wave which is the signal of Alternating Current (AC). It can be represented in mathematical term as:

x(t) = ASin(wt + Ψ),

where A is the amplitude and w is the angular frequency, Ψ is the phase angle (at time, t = 0).

Angular frequency is the rotational rate. Let’s suppose it takes time period T to complete one revolution i.e 360 degree or 2π radian, then

w = 2π/T

The ordinary frequency is the number of oscillations (cycle) in each second of time. If f is the number of oscillations in T then

f = 1/T Hz & w = 2πf

At time t, the the wave profile has angle θ degree and  θ becomes

θ = wt

Generate the Sine and Cosine signal using MATLAB script "sincos.m" as described in the section "Using HPC Cluster".

System is a device or combination of devices such as filters, amplifiers, which can operate on signals and produces corresponding response. Input to a system is called as excitation and output from it is called as response. System can be linear or nonlinear, time variant or invariant, static or dynamic, causal (depends on previous or past inputs or non-causal, invertible or non-invertible, and stable or unstable.

For more info on LTI signal, visit Appendix section.

A filter is a device or a process that removes some unwanted components or features from a signal that helps to retrieve the desired information from the signal.

Analog Filters

In an electric system, a filter (http://www.swarthmore.edu/NatSci/echeeve1/Ref/DataSheet/IntroToFilters.pdf) is a network or a system that alters the amplitude and/or phase characteristics of a signal with respect to frequency. Ideally, a filter will not add new frequencies to the input signal, nor will it change the component frequencies of that signal, but it will change the relative amplitudes of the various frequency components and/or their phase relationships. Filters are often used in electronic systems to emphasize signals in certain frequency ranges and reject signals in other frequency ranges. Such a filter has a gain which is dependent on signal frequency.

Application - FM Tuning:

When you want to listen to your FM at 89.9MHz, you tune your FM radio near it. By doing this, it allows to pass that (89.9MHz) frequency and attenuates the other frequencies so as to listen to that channel clearly without interference.

First Order RC Filter - Low Pass

Let’s build the simple filter via electric circuit using resistor and a capacitor. Having only one reactive component (capacitor), it becomes the first order or one pole (see Appendix: Poles and zeros for details) passive filter. It is a passive filter because it consumes the energy of the signal. The active filters on the other hand can amplify the signal and therefore they require external power.

If the frequency is very low such as almost zero (i.e. dc current is passed), Z becomes infinite i.e capacitor acts as an open circuit and all the voltage drop occurs across the capacitor. So, output voltage is almost same as the input voltage i.e. Gain = Vout/Vin = 1 (approx). However, at higher frequency, Z gets very small and the voltage drops at resistor R. So, the output voltage is almost zero. Hence the name low pass filter i.e. passing only the lower frequency signals.

The capacitors impedance equals the resistors at cut off frequency fc, and the voltage is split between them. Each component can have 70.7% of the voltage drop instead of 50% because the maximum voltages drops are out of phase with each other by π/4 at that point. So, at cut-off frequency, the gain will be -3db (20 log (Vout/Vin)). After this cut-off frequency point, the response of the circuit decreases to zero at a slope of -20dB/ Decade (10 times increase in frequency).

In a Low Pass Filter circuit, all the frequencies below cut-off, ƒc point are unaltered with little or no attenuation and are said to be in the filters Pass bandzone. This pass band zone also represents the Bandwidth of the filter. Any signal frequencies above this point cut-off point are generally said to be in the filters Stop bandzone and they will be greatly attenuated.

As the filter contains a capacitor, the Phase Angle ( Φ ) of the output signal lags behind that of the input, and at the -3dB cut-off frequency ( ƒc ) is - 45 degree out of phase. This is due to the time taken to charge the plates of the capacitor as the input voltage changes, resulting in the output voltage (the voltage across the capacitor) “lagging” behind that of the input signal. The higher the input frequency applied to the filter, the more the capacitor lags and the circuit becomes more and more “out of phase” (see Fig. 2).

The output voltage is given by (http://www.kves.uniza.sk/kvesnew/dokumenty/DREP/Filters/352__EC434__4__3_1_Chapter_03.pdf):

Thus, a high-Q tuned circuit in a radio receiver would be more difficult to tune, but would have more selectivity as it filters out signals from other stations that lie nearby on the spectrum.

Digital Filters

A digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal in contrast to analog electronic filter operating on a continuous-time analog signals.

There are two categories of digital filter: the recursive filter and the non-recursive filter. These are often referred to as Infinite Impulse Response (IIR) filters and Finite Impulse Response (FIR) filters respectively. Many digital filters are based on the fast Fourier transform, a mathematical algorithm that quickly extracts the frequency spectrum of a signal, allowing the spectrum to be manipulated before converting the modified spectrum back into a time-series signal with an inverse FFT operation. These filters give O(n log n) computational costs whereas conventional digital filters tend to be O(n2).

A recursive filter re-uses one or more of its outputs as an input. This feedback typically results in an unending impulse response characterized by either exponentially growing, decaying, or sinusoidal signal output components. . A non-recursive filter only uses input values like x[n − i], unlike recursive filter where it uses previous output values like y[n-i]. It has a finite number of coefficients in the impulse response h[n] (see Appendix: Convolution for details). Although almost all analog electronic filters are IIR, digital filters may be either IIR (e.g. Kalman Filter) or FIR. The impulse response (or response to any finite length input) of FIR is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying response). Digital IIR filters can be based on well-known solutions for analog filters such as the Chebyshev filter, Butterworth filter, and elliptic filter, inheriting the characteristics of those solutions.

The transfer function allows one to judge whether or not a system is bounded-input, bounded-output (BIBO) stable. To be specific, the BIBO stability criterion requires that the ROC (Region of Convergence) of the system includes the unit circle. For example, for a causal system, all poles of the transfer function have to have an absolute value smaller than one. In other words, all poles must be located within a unit circle in the z-plane (see Appendix: Z-Transform & Appendix: Poles and Zeros for details).

Nonrecursive Filter - FIR

Consider a 3-term moving average filter with filter coefficients given by

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