# Electrical engineering and applied mathematics

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### SIGNAL PROCESSING

Signal processing is an area of electrical engineering and applied mathematics that deals with operations or analysis of signals. The signals may be either in discrete or continuous time to perform useful operations on those signals. We can perform a useful operation depending upon the application.

The various applications include data compression, data transmission, prediction, filtering, denoising, smoothing, tomographic reconstruction, identification, deblurring, or a variety of other applications.

Mathematics Topics Embraced By Signal Processing

1. Linear signals and systems and transform theory
2. Probability and stochastic processes
3. Programming
4. Calculus and analysis
5. Vector spaces and linear algebra
6. Numerical methods
7. Functional analysis
8. Optimization
9. Statistical decision theory
10. Iterative methods

Let us define some of the functions:

### Transform theory

It is a mathematical term and transforms theory deals with the study of transforms.

The base of the theory is that by selecting a suitable basis for a vector space, a problem may be simplified.

### Spectral Theory

According to the spectral theorem, if b is an n*n self ad joint matrix, there is an orthonormal basis of eigenvectors of b. It specifies that b is diagonalizable. And each eigenvalue is real.

### Linear Algebra

It is also a sub-part of mathematics. It also deals with specific fields of mathematics. These fields include vectors, linear spaces, or linear transformations.

### Vector Space

As the name indicates, it deals with the vector spaces.

### Estimation theory

It is also a subpart of signal processing. In this there is a term named parameters. So its values are imagines or calculated with the help of calculated data. We can clarify it with this example- suppose in a horse race, we have to calculate the people who bet on some specific horse; we will calculate that or have a rough idea by examining a random sample of people.

### Calculus

It is a branch of mathematics that deals with the limits, functions, derivatives, infinite series, and integrals. The major advantage of this subject is that it deals with the modernized mathematics. In this actually we go through the changes. It is just like as we understand the theory of shape with the help of geometry. We can use this topic in various fields of mathematics, etc. It is having two major branches: differential calculus and integral calculus. Its major principles are limits and infinitesimals, differential calculus.

### 1) Analog Signal Processing

This technique of signal processing is used for those signals that have not been digitized, as in classical radio, radar, telephone, and television systems.

This involves linear as well as non-linear circuits. The linear electronic circuits include passive filters, active filters, delay lines, integrators, and additive mixers.

The non-linear circuits include circuits include circuits such as compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage controlled filters, voltage controlled oscillators and phase locked loops.

### 2) DISCRETE TIME SIGNAL PROCESSING

It includes the sampled signals that are considered as defined only at discrete points in time, But not in magnitude. Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers analog delay lines.

### 3) DIGITAL SIGNAL PROCESSING

This technique of signal processing is used for digitized signals. This processing is done by general purpose computers or by digital circuits such as ASICs, field or specialized digital signal processing. The typical arithmetic operations include fixed-point and floating-point real valued and complex valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and look up tables. In this form we deal with binary numbers. The digitals circuits are used for this purpose. They may be computers and microprocessors. One disadvantage is that there is loss. But still mostly this type of processing is preferred because it is much better than analog signal processing. Before converting an analog signal to digital form, there must be sampling and quantization. Sampling means the signal is divided into specific intervals at which we have to take the readings of analog voltage. In quantization the analog voltage is converted into the binary form. The maximum frequency that may be encoded is determined by the size of sampling intervals.

There are many application areas and processing methods. They include enhancement, compression, level compression, storage, etc.

### FIELDS OF SIGNAL PROCESSING

1. Statistical Signal Processing
2. Audio Signal Processing
3. Speech Signal Processing
4. Image Processing
5. Video Processing
6. Array Processing
7. Filtering
8. Seismic Signal Processing

### STATISTICAL SIGNAL PROCESSING

Includes analyzing and extracting information from signals based on their statistical properties.

Statistical signal processing is an area of applied mathematics and signal processing that treats signals as stochastic process, dealing with their statistical properties.

It has a very broad range of application, so statistical signal processing is taught at graduate level in either electrical engineering, applied mathematics or even physics departments. In some areas, signal is represented as deterministic and stochastic.

### AUDIO SIGNAL PROCESSING

It has implementation in electrical signals representing.

It is also referred to as audio processing. It is the international alteration of auditory signals and sound. As audio signal may be electronically represented in either digital or analog format. Digital processors operate mathematically on binary representation of the signal but the analog processors operate directly on the electrical signals.

Human hearing extends from approximately 20 Hz to 20 kHz.

There were many problems in early radio broadcasting, so audio processing was necessary.

In analog representation, it is usually electrical; so the air pressure waveform of the sound is represented by the voltage level.

The pressure waveform is represented as a sequence of symbols, which are usually binary by the digital representation.

Processing methods and application areas include storage, level compression, data compression, transmission, enhancement (e.g. equalization, filtering, noise cancellation, echo or reverb removal or addition, etc).

It is globally the biggest market segment for audio processing. The audio processing takes place before the transmitter.

In audio broadcasting, audio processor must

• Prevent over modulation, and minimize it when it occurs
• Maximize overall loudness
• Compensate for non-linear transmitters, more common with medium wave and shortwave broadcasting.

### SPEECH SIGNAL PROCESSING

Used for processing and interpreting spoken words.

Speech signal processing refers to the acquisition, manipulation, storage, transfer and output of vocal utterances by a computer. The main applications include recognition, synthesis and compression of human speech:

• Speech Recognition: it focuses on capturing the human voice as a digital sound wave and converting it into a computer-readable format.
• Speech Synthesis: it is the reverse process of speech recognition. Advances in this area improve the computer's usability for visually impaired.
• Speech Compression: it is important in telecommunication area for increasing the amount of information which can be transferred, stored, or heard, for a given set of time and space constraints.

### 4) IMAGE PROCESSING

Used in digital cameras, computers, and various imaging systems.

Image processing is any form of signal processing for which the input is an image, such as photographs or frames of video; the output of image processing can be either image or a set of characteristics or parameters related to the image. Mostly in these techniques the image is treated as a 2-dimensional signal. When we talk about image processing, we refer to digital image processing. Still there are two other options also. They are optical and analog image processing. The main applications are: computer vision, face detection, feature detection, lane departure warning system, non-photorealistic rendering, medical image processing, and microscope, morphological image processing.

### 5) VIDEO PROCESSING

Used for interpreting moving pictures.

Video processing is a particular case of signal processing, where input and output signals are video files. Video processing is used in television sets, VCRs, DVDs, video codecs, video players and other devices. For example- commonly only design and video processing is different in TV sets of different manufacturers. Further video filters are of three types. These are prefilters, intrafilters, and postfilters. Prefilters are used before encoding; intrafilters are used inside of codec and the postfilters are used after encoding.

### 6) ARRAY PROCESSING

Used for processing signals from arrays of sensors.

Array processing is signal processing of outputs of an array of sensors to:

• Enhance signal-to-interference-plus-noise ratio(SINR)
• Determining no. of emitting sources
• Track multiple moving sources

### 7) FILTER (Signal Processing)

Used in many fields to process signals.

As the name indicates, the purpose of filter signal processing is to filter or remove a part of signal that is not suitable or that is not in need. It is a class of signal processing that tells feature of filters being complete or partial suppression of some aspect of signal. So in this the frequencies are recognized or found out that are not needed. Then these signals are removed with help of filters. By doing so, we remove the noise or unwanted signals that interrupt in our main signal Filters may be classified on many bases.

Filters may be analog or digital, discrete-time (sampled) or continuous-time, linear or non-linear, passive or active.

Other operations and implementations

Operations and algorithms that take place during processing signals along with examples are:

Filtering: it is used in image enhancing, in equalizers, etc

Spectrum analysis: in modulation type OFDM, magnetic resonance imaging

Digitalization, compression and reconstruction: it is used in image compression as well as sound coding.

Adaptive filtering: it is used while we conference telephone for cancellation of echo, and by radar to detect aircraft by separating information from noise.

Wavetable synthesis: it finds services in modems and in music synthesizers.

Feature extraction: it is used for converting speech to text.

Storage: it is used for reverb and in digital delay lines.

### Conclusion

After studying briefly signal processing, we can say that this technique is of great importance. It has contributed a lot in field of communication.